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1
Han, Seongik. "Grey Wolf and Weighted Whale Algorithm Optimized IT2 Fuzzy Sliding Mode Backstepping Control with Fractional-Order Command Filter for a Nonlinear Dynamic System." Applied Sciences 11, no. 2 (January 6, 2021): 489. http://dx.doi.org/10.3390/app11020489.
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In this study, a fractional-order sliding mode backstepping control method was proposed, which involved the use of a fractional-order command filter, an interval type-2 fuzzy logic system approximation method, and a grey wolf and weighted whale optimization algorithm for multi-input multi-output nonlinear dynamic systems. For designing the stabilizing controls of the backstepping control, a novel fractional-order sliding mode surface was suggested. Further, the transformed errors that occurred during the recursive design steps were easily compensated by the controllers constructed using a new fractional-order command filter. Thus, the differentiation issue of the virtual control in the conventional backstepping control design could be bypassed with a simpler controller structure. Subsequently, the unknown plant dynamics were approximated by an interval type-2 fuzzy logic system. The uncertainties, such as the approximation error and the external disturbance, were compensated by the fractional-order sliding mode control that was added in the backstepping controller. Furthermore, the controller parameters and the fuzzy logic system were optimized via a grey wolf and weighted whale optimization algorithm to obtain a faster tuning process and an improved control performance. Simulation results demonstrated that the fractional-order sliding mode backstepping control scheme provides enhanced control performance over the conventional backstepping control system. Thus, in this paper, a fractional-order sliding mode surface and fractional-order backstepping control are studied, which provide more rapid convergence and enhanced robustness. Furthermore, a hybrid grey wolf and weighted whale optimization algorithm are proposed to provide an improved learning performance than those of conventional grey wolf optimization and weighted whale optimization methods.
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Liu, Jinglong, Jing Wen, Xiaoxiong Liu, and Qizhi He. "A Modified Backstepping Control and Dynamic Control Allocation Method for Command Tracking." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 1 (February 2018): 117–23. http://dx.doi.org/10.1051/jnwpu/20183610117.
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This paper uses the modified Backstepping (BS) Control method and the Dynamic Control Allocation (DCA) method to solve the problem that when the fighter aircraft under different flight conditions, it will be adaptively tracking different commands. Firstly, we introduce the classical Lyapunov method and classical backstepping control method, and then propose a modified backstepping control method to be applied by general flight control system model. Finally, for the problem that the common control allocation method can't compensate for ignoring the actuator dynamics, a dynamic control allocation method is introduced, and it is successfully applied to the design of the whole closed loop control system. The controller reserves the stable nonlinear term of the system, eliminates the unstable nonlinear term, and minimize the impact of ignoring the actuator dynamic through the dynamic allocation. The simulation results show that the methods in this paper have a good response. It can be implemented in different flight conditions with a good performance of command tracking and lots of robustness.
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Kolsi-Gdoura, E., M. Feki, and N. Derbel. "Observer Based Robust Position Control of a Hydraulic Servo System Using Variable Structure Control." Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/724795.
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This paper deals with the position control of a hydraulic servo system rod. Our approach considers the surface design as a case of virtual controller design using the backstepping method. We first prove that a linear surface does not yield to a robust controller with respect to the unmatched uncertainty and perturbation. Next, to remedy this deficiency, a sliding controller based on the second-order sliding mode is proposed which outperforms the first controller in terms of chattering attenuation and robustness with respect to parameter uncertainty only. Next, based on backstepping a nested variable structure design method is proposed which ensures the robustness with respect to both unmatched uncertainty and perturbation. Finally, a robust sliding mode observer is appended to the closed loop control system to achieve output feedback control. The stability and convergence to reference position with zero steady state error are proven when the controller is constructed using the estimated states. To illustrate the efficiency of the proposed methods, numerical simulation results are shown.
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Barros, João Dionísio Simões, Luis Rocha, and J. Fernando Silva. "Backstepping Control of NPC Multilevel Converter Interfacing AC and DC Microgrids." Energies 16, no. 14 (July 20, 2023): 5515. http://dx.doi.org/10.3390/en16145515.
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This work introduces modified backstepping methods to design controllers for neutral point clamped (NPC) converters interfacing a DC/AC microgrid. The modified backstepping controllers are derived from a proper converter model, represented in dq coordinates, and are designed to regulate the DC voltage and to balance the two NPC converter DC capacitor voltages through a DC offset in the sinusoidal pulse width modulation (SPWM) carriers. The averaged and separated dynamics backstepping controllers also enforce nearly sinusoidal AC currents at a given power factor. The two proposed NPC converter controllers are evaluated through MATLAB/Simulink simulations and experimental implementation using a laboratory prototype. Simulations and experimental results show that the two modified backstepping controllers regulate the microgrid DC voltage in steady state and in transient operation, even with load disturbances or DC voltage reference changes, while enforcing nearly AC sinusoidal currents at a given power factor or injected reactive power. The modified backstepping-controlled NPC converter is bidirectional, converting energy from DC renewable energy sources or storage systems to AC or charging storage systems from AC. The results also highlight the effective balancing of the NPC DC capacitor voltages.
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Ismail, S., A. A. Pashilkar, R. Ayyagari, and N. Sundararajan. "Diagonally dominant backstepping autopilot for aircraft with unknown actuator failures and severe winds." Aeronautical Journal 118, no. 1207 (September 2014): 1009–38. http://dx.doi.org/10.1017/s0001924000009726.
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Abstract A novel formulation of the flight dynamic equations is presented that permits a rapid solution for the design of trajectory following autopilots for nonlinear aircraft dynamic models. A robust autopilot control structure is developed based on the combination of the good features of the nonlinear dynamic inversion (NDI) method, integrator backstepping method, time scale separation and control allocation methods. The aircraft equations of motion are formulated in suitable variables so that the matrices involved in the block backstepping control design method are diagonally dominant. This allows us to use a linear controller structure for a trajectory following autopilot for the nonlinear aircraft model using the well known loop by loop controller design approach. The resulting autopilot for the fixed-wing rigid-body aircraft with a cascaded structure is referred to as the diagonally dominant backstepping (DDBS) controller. The method is illustrated here for an aircraft auto-landing problem under unknown actuator failures and severe winds. The requirement of state and control surface limiting is also addressed in the context of the design of the DDBS controller.
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Nguyen, Vi H., and Thanh T. Tran. "A Novel Hybrid Robust Control Design Method for F-16 Aircraft Longitudinal Dynamics." Mathematical Problems in Engineering 2020 (September 22, 2020): 1–10. http://dx.doi.org/10.1155/2020/5281904.
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This paper presents a hybrid robust control design method for a third-order lower-triangular model of nonlinear dynamic systems in the presence of disturbance. In this paper, a novel control design is presented systematically to synthesize a robust nonlinear feedback controller, called backstepping sliding mode control (BSMC), for the proposed system by a combined approach of backstepping design and sliding mode control. In this approach, a family of the “sliding surface” is introduced in state transformations. Then, a smooth switching function of the sliding surface is introduced and enforced to include in virtual feedbacks and a real control law from the control selection phrases of the backstepping design loop. The achieved control method proves a well-tracking command with asymptotic stability, provides a robustness in the presence of uncertainties, and eliminates completely a chattering phenomenon. The application of flight-path angle control corresponding to the longitudinal dynamics of a high-performance F-16 aircraft simulation model is implemented. Under some assumptions, full nonlinear longitudinal dynamics is reformed into a lower-triangular system for a direct application to formulate a control law. A closed-loop system is achieved for in-flight simulation with different flight profiles for a comparison of the existing methods. Also, an external disturbance on different loading/unloading conditions in flight is applied to verify and validate robustness of the proposed control method.
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Zhang, Chao, Xing Wang, Zhengfeng Ming, and Zhuang Cai. "Enhanced Nonlinear Robust Control for TCSC in Power System." Mathematical Problems in Engineering 2018 (2018): 1–11. http://dx.doi.org/10.1155/2018/1416059.
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This paper proposes an enhanced robust control method, which is for thyristor controlled series compensator (TCSC) in presences of time-delay nonlinearity, uncertain parameter, and external disturbances. Unlike conventional adaptive control methods, the uncertain parameter is estimated by using system immersion and manifold invariant (I&I) adaptive control. Thus, the oscillation of states caused by the coupling between parameter estimator and system states can be avoided. In addition, in order to overcome the influences of time-delay nonlinearity and external disturbances, backstepping sliding mode control is adopted to design control law recursively. Furthermore, robustness of TCSC control subsystem is achievable provided that dissipation inequality is satisfied in each step. Effectiveness and efficiencies of the proposed control method are verified by simulations. Compared with adaptive backstepping sliding mode control and adaptive backstepping control, the time of reaching steady state is shortened by at least 11% and the oscillation amplitudes of transient responses are reduced by at most 50%.
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Rodríguez-Abreo, Omar, Juan Manuel Garcia-Guendulain, Rodrigo Hernández-Alvarado, Alejandro Flores Rangel, and Carlos Fuentes-Silva. "Genetic Algorithm-Based Tuning of Backstepping Controller for a Quadrotor-Type Unmanned Aerial Vehicle." Electronics 9, no. 10 (October 21, 2020): 1735. http://dx.doi.org/10.3390/electronics9101735.
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Backstepping is a control technique based on Lyapunov’s theory that has been successfully implemented in the control of motors and robots by several nonlinear methods. However, there are no standardized methods for tuning control gains (unlike the PIDs). This paper shows the tuning gains of the backstepping controller, using Genetic Algorithms (GA), for an Unmanned Aerial Vehicle (UAV), quadrotor type, designed for autonomous trajectory tracking. First, a dynamic model of the vehicle is obtained through the Newton‒Euler methodology. Then, the control law is obtained, and self-tuning is performed, through which we can obtain suitable values of the gains in order to achieve the design requirements. In this work, the establishment time and maximum impulse are considered as such. The tuning and simulations of the system response were performed using the MATLAB-Simulink environment, obtaining as a result the compliance of the design parameters and the correct tracking of different trajectories. The results show that self-tuning by means of genetic algorithms satisfactorily adjusts for the gains of a backstepping controller applied to a quadrotor and allows for the implementation of a control system that responds appropriately to errors of different magnitude.
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Ali, Sadia, Alvaro Prado, and Mahmood Pervaiz. "Hybrid Backstepping-Super Twisting Algorithm for Robust Speed Control of a Three-Phase Induction Motor." Electronics 12, no. 3 (January 29, 2023): 681. http://dx.doi.org/10.3390/electronics12030681.
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This paper proposes a Hybrid Backstepping Super Twisting Algorithm for robust speed control of a three-phase Induction Motor in the presence of load torque uncertainties. First of all, a three-phase squirrel cage Induction Motor is modeled in MATLAB/Simulink. This is then followed by the design of different non-linear controllers, such as sliding mode control (SMC), super twisting SMC, and backstepping control. Furthermore, a novel controller is designed by the synergy of two methods, such as backstepping and super twisting SMC (Back-STC), to obtain the benefits of both techniques and, thereby, improve robustness. The sigmoid function is used with an exact differentiator to minimize the high-speed discontinuities present in the input channel. The efficacy of this novel design and its performance were evidenced in comparison with other methods, carried out by simulations in MATLAB/Simulink. Regression parameters, such as ISE (Integral Square error), IAE (Integral Absolute error) and ITAE (Integral Time Absolute error), were calculated in three different modes of operation: SSM (Start-Stop Mode), NOM (Normal Operation Mode) and DRM (Disturbance Rejection Mode). In the end, the numerical values of the regression parameters were quantitatively analyzed to draw conclusions regarding the tracking performance and robustness of the implemented non-linear control techniques.
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Zhang, Hua. "Neural Network Command Filtered Control of Fractional-Order Chaotic Systems." Computational Intelligence and Neuroscience 2021 (October 21, 2021): 1–15. http://dx.doi.org/10.1155/2021/8962251.
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An adaptive neural network (NN) backstepping control method based on command filtering is proposed for a class of fractional-order chaotic systems (FOCSs) in this paper. In order to solve the problem of the item explosion in the classical backstepping method, a command filter method is adopted and the error compensation mechanism is introduced to overcome the shortcomings of the dynamic surface method. Moreover, an adaptive neural network method for unknown FOCSs is proposed. Compared with the existing control methods, the advantage of the proposed control method is that the design of the compensation signals eliminates the filtering errors, which makes the control effect of the actual system improve well. Finally, two examples are given to prove the effectiveness and potential of the proposed method.
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Zhao, He-Wei, and Li-bin Yang. "Global adaptive neural backstepping control of a flexible hypersonic vehicle with disturbance estimation." Aircraft Engineering and Aerospace Technology 94, no. 4 (October 5, 2021): 492–504. http://dx.doi.org/10.1108/aeat-08-2020-0178.
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Purpose This paper aims to discuss the precise altitude and velocity tracking control of a hypersonic vehicle, a global adaptive neural backstepping controller was studied based on a disturbance observer (DOB). Design/methodology/approach The DOB combined with a radial basis function (RBF) neural network (NN) was used to estimate the disturbance terms that are generated by the flexible modes of the hypersonic vehicle system. A global adaptive neural method was introduced to approximate the unknown system dynamics, with robust control terms pulling the system transient states back into the neural approximation domain externally. Findings The globally uniformly ultimately bounded for all signals of a closed-loop system can be guaranteed by the proposed control algorithm. Additionally, the command filtered backstepping methods can avoid the explosion of the complexity problem caused by the backstepping design process. In addition, the effectiveness of the proposed controller can be verified by the simulation used in this study. Research limitations/implications Normally lateral dynamics issue should be discussed in the process of control system designed, the lateral dynamics are not included in the nonlinear dynamic model of hypersonic vehicle used in this paper, merely the longitudinal flight dynamics are discussed in this paper. Originality/value The flexible states in rigid modes are considered as the disturbance of the system, which is estimated by structuring DOB with NN approximations. The compensating tracking error and prediction error are used in the update law of RBF NN weight. The differential explosions complexity derived from the backstepping procedure is dealt with by using command filters.
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Zhao, He-Wei, and Li-bin Yang. "Global adaptive neural backstepping control of a flexible hypersonic vehicle with disturbance estimation." Aircraft Engineering and Aerospace Technology 94, no. 4 (October 5, 2021): 492–504. http://dx.doi.org/10.1108/aeat-08-2020-0178.
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Purpose This paper aims to discuss the precise altitude and velocity tracking control of a hypersonic vehicle, a global adaptive neural backstepping controller was studied based on a disturbance observer (DOB). Design/methodology/approach The DOB combined with a radial basis function (RBF) neural network (NN) was used to estimate the disturbance terms that are generated by the flexible modes of the hypersonic vehicle system. A global adaptive neural method was introduced to approximate the unknown system dynamics, with robust control terms pulling the system transient states back into the neural approximation domain externally. Findings The globally uniformly ultimately bounded for all signals of a closed-loop system can be guaranteed by the proposed control algorithm. Additionally, the command filtered backstepping methods can avoid the explosion of the complexity problem caused by the backstepping design process. In addition, the effectiveness of the proposed controller can be verified by the simulation used in this study. Research limitations/implications Normally lateral dynamics issue should be discussed in the process of control system designed, the lateral dynamics are not included in the nonlinear dynamic model of hypersonic vehicle used in this paper, merely the longitudinal flight dynamics are discussed in this paper. Originality/value The flexible states in rigid modes are considered as the disturbance of the system, which is estimated by structuring DOB with NN approximations. The compensating tracking error and prediction error are used in the update law of RBF NN weight. The differential explosions complexity derived from the backstepping procedure is dealt with by using command filters.
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Aghajary, Mohammad Mahdi, and Arash Gharehbaghi. "A novel adaptive control design method for stochastic nonlinear systems using neural network." Neural Computing and Applications 33, no. 15 (February 18, 2021): 9259–87. http://dx.doi.org/10.1007/s00521-021-05689-1.
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AbstractThis paper presents a novel method for designing an adaptive control system using radial basis function neural network. The method is capable of dealing with nonlinear stochastic systems in strict-feedback form with any unknown dynamics. The proposed neural network allows the method not only to approximate any unknown dynamic of stochastic nonlinear systems, but also to compensate actuator nonlinearity. By employing dynamic surface control method, a common problem that intrinsically exists in the back-stepping design, called “explosion of complexity”, is resolved. The proposed method is applied to the control systems comprising various types of the actuator nonlinearities such as Prandtl–Ishlinskii (PI) hysteresis, and dead-zone nonlinearity. The performance of the proposed method is compared to two different baseline methods: a direct form of backstepping method, and an adaptation of the proposed method, named APIC-DSC, in which the neural network is not contributed in compensating the actuator nonlinearity. It is observed that the proposed method improves the failure-free tracking performance in terms of the Integrated Mean Square Error (IMSE) by 25%/11% as compared to the backstepping/APIC-DSC method. This depression in IMSE is further improved by 76%/38% and 32%/49%, when it comes with the actuator nonlinearity of PI hysteresis and dead-zone, respectively. The proposed method also demands shorter adaptation period compared with the baseline methods.
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Tarammim, Absana, and Musammet Tahmina Akter. "A Comparative Study of Synchronization Methods of Rucklidge Chaotic Systems with Design of Active Control and Backstepping Methods." International Journal of Modern Nonlinear Theory and Application 11, no. 02 (2022): 31–51. http://dx.doi.org/10.4236/ijmnta.2022.112003.
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Zhu, Chenqi, and Zhengyu Guo. "Design of Head-Pursuit Guidance Law Based on Backstepping Sliding Mode Control." International Journal of Aerospace Engineering 2019 (December 3, 2019): 1–18. http://dx.doi.org/10.1155/2019/8214042.
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In order to meet the needs of high-precision guidance for intercepting hypersonic targets, a novel head-pursuit guidance law considering the dynamic characteristics of a missile control system and the target mobility is presented via combining a fast power reaching law with backstepping sliding mode control in this paper. Initially, a three-dimensional head-pursuit system model of the missile and target is established. Subsequently, the system model is decomposed into a pitch plane system and lateral plane system, the control system dynamics are equivalent to second-order systems, and finite-time disturbance observers are introduced to estimate the target accelerations. On the basis of the previous work, the head-pursuit guidance laws of the vertical system and the lateral system which can stabilize the closed-loop system are designed separately and strict proofs of the methods are given. Finally, simulations are carried out to verify the effectiveness of this head-pursuit guidance law.
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Gehring, Nicole, Abdurrahman Irscheid, Joachim Deutscher, Frank Woittennek, and Joachim Rudolph. "Control of distributed-parameter systems using normal forms: an introduction." at - Automatisierungstechnik 71, no. 8 (August 1, 2023): 624–46. http://dx.doi.org/10.1515/auto-2023-0051.
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Abstract This paper gives an overview of the control of distributed-parameter systems using normal forms. Considering linear controllable PDE-ODE systems of hyperbolic type, two methods derive tracking controllers by mapping the system into a form that is advantageous for the control design, analogous to the finite-dimensional case. A flatness-based controller makes use of the hyperbolic controller canonical form that follows from a parametrization of the system’s solutions. A backstepping design exploits the strict-feedback form of the system to recursively stabilize and transform the subsystems.
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Zhang, Xiang. "Application of Backstepping Stability Control in the Diffusion Process." Advanced Materials Research 791-793 (September 2013): 704–9. http://dx.doi.org/10.4028/www.scientific.net/amr.791-793.704.
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In this paper, 1-D mathematical model of the coagulation process of the polyacrylonitrile (PAN) carbon fiber is established using Fick diffusion law. Boundary stabilization for a linear parabolic diffusion-reaction partial differential equation (PDE) is considered. We use the method of backstepping to implement the boundary control of the concentration diffusion in the forming process of carbon fiber. By using the coordinate transformation, we transform the original system to a standard static system. The transformation depends on a so called gain kernel function, and we can design the boundary feedback controller using the kernel function. For the model in this paper, the kernel function itself is a hyperbolic PDE, and there is no explicit formation. Therefore, we use numerical methods to obtain the kernel function, and give the simulation results for the closed-loop control response. The simulation results show that the open-loop unstable system is stabilized by a boundary feedback.
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Euldji, Rafik, Noureddine Batel, Redha Rebhi, Noureddine Kaid, Chutarat Tearnbucha, Weerawat Sudsutad, Giulio Lorenzini, Hijaz Ahmad, Houari Ameur, and Younes Menni. "Optimal Backstepping-FOPID Controller Design for Wheeled Mobile Robot." Journal Européen des Systèmes Automatisés 55, no. 1 (February 28, 2022): 97–107. http://dx.doi.org/10.18280/jesa.550110.
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A design of an optimal backstepping fractional order proportional integral derivative (FOPID) controller for handling the trajectory tracking problem of wheeled mobile robots (WMR) is examined in this study. Tuning parameters is a challenging task, to overcome this issue a hybrid meta-heuristic optimization algorithm has been utilized. This evolutionary technique is known as the hybrid whale grey wolf optimizer (HWGO), which benefits from the performances of the two traditional algorithms, the whale optimizer algorithm (WOA) and the grey wolf optimizer (GWO), to obtain the most suitable solution. The efficiency of the HWGO algorithm is compared against those of the original algorithms WOA, GWO, the particle swarm optimizer (PSO), and the hybrid particle swarm grey wolf optimizer (HPSOGWO). The simulation results in MATLAB–Simulink environment revealed the highest efficiency of the suggested HWGO technique compared to the other methods in terms of settling and rise time, overshoot, as well as steady-state error. Finally, a star trajectory is made to illustrate the capability of the mentioned controller.
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Deng, Pan, Liangcai Zeng, and Yang Liu. "RBF Neural Network Backstepping Sliding Mode Adaptive Control for Dynamic Pressure Cylinder Electrohydraulic Servo Pressure System." Complexity 2018 (December 2, 2018): 1–16. http://dx.doi.org/10.1155/2018/4159639.
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According to the hydraulic principle diagram of the subgrade test device, the dynamic pressure cylinder electrohydraulic servo pressure system math model and AMESim simulation model are established. The system is divided into two parts of the dynamic pressure cylinder displacement subsystem and the dynamic pressure cylinder output pressure subsystem. On this basis, a RBF neural network backstepping sliding mode adaptive control algorithm is designed: using the double sliding mode structure, the two RBF neural networks are used to approximate the uncertainties in the two subsystems, provide design methods of RBF sliding mode adaptive controller of the dynamic pressure cylinder displacement subsystem and RBF backstepping sliding mode adaptive controller of the dynamic pressure cylinder output pressure subsystem, and give the two RBF neural network weight vector adaptive laws, and the stability of the algorithm is proved. Finally, the algorithm is applied to the dynamic pressure cylinder electrohydraulic servo pressure system AMESim model; simulation results show that this algorithm can not only effectively estimate the system uncertainties, but also achieve accurate tracking of the target variables and have a simpler structure, better control performance, and better robust performance than the backstepping sliding mode adaptive control (BSAC).
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Boudali, Abdelkader, Karim Negadi, Sarah Bouradi, Abderrahmane Berkani, and Fabrizio Marignetti. "Design of Nonlinear Backstepping Control Strategy of PMSG for Hydropower Plant Power Generation." Journal Européen des Systèmes Automatisés 54, no. 1 (February 28, 2021): 1–8. http://dx.doi.org/10.18280/jesa.540101.
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In this paper, renewable hydropower plant generators with permanent magnet synchronous generator are coupled via a diode bridge rectifier - DC/DC boost converter and three-phase inverter to a power grid. This paper studies a new control structure focused a backstepping control of the energy generation system.The proposed methods for adjusting the active and reactive power by adjusting the currents, the DC bus voltage on the main side converter, as well as the voltage at the output of the DC-DC boost converter. The main objective of this control is to obtain purely sinusoidal and symmetrical grid current signals, to suppress oscillations in reactive power and to cancel active power chattering in the event of grid imbalance. In order to optimize the energy flow in the different parts of the production process, an energy control algorithm is developed in order to attenuate the fluctuations in the water flow, the grid system of the hydropower plant considered has been implemented in Matlab/Simulink, the results show the effectiveness of the proposed method. To analyze our approach, a prototype is modeled, simulated and can be performed in an experimental test setup.
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Huang, Haifeng, Mohammadamin Shirkhani, Jafar Tavoosi, and Omar Mahmoud. "A New Intelligent Dynamic Control Method for a Class of Stochastic Nonlinear Systems." Mathematics 10, no. 9 (April 22, 2022): 1406. http://dx.doi.org/10.3390/math10091406.
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This paper presents a new method for a comprehensive stabilization and backstepping control system design for a class of stochastic nonlinear systems. These types of systems are so abundant in practice that the control system designer must assume that random noise with a definite probability distribution affects the dynamics and observations of state variables. Stochastic control is intended to determine the time course of control variables so that the control target is achievable even with minimal cost. Since the mathematical equations of stochastic nonlinear systems are not always constant, not every model-based controller can be accurate. Therefore, in this paper, a type-3 fuzzy neural network is used to estimate the parameters of the backstepping control method. In the simulation, the proposed method is compared with the Type-1 fuzzy and RBFN methods. Results clearly show that the proposed method has a very good performance and can be used for any system in this class.
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Sun, Hui, Jinming Li, Rui Wang, and Kaixin Yang. "Attitude Control of the Quadrotor UAV with Mismatched Disturbances Based on the Fractional-Order Sliding Mode and Backstepping Control Subject to Actuator Faults." Fractal and Fractional 7, no. 3 (March 3, 2023): 227. http://dx.doi.org/10.3390/fractalfract7030227.
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Considering mismatched disturbances, aerodynamic interference, chattering, and actuator failure in the attitude control of the quadrotor unmanned aerial vehicle (UAV), this paper establishes a new quadrotor UAV model with mismatched disturbances, based on quaternion, and designs a fault tolerant controller. First, in order to reduce the chattering of the traditional reaching law, a new reaching law based on the sigmoid function is introduced into the design. Second, the sliding mode control and backstepping control methods are adopted, based on the new fractional-order sliding mode surface when the faults occur in quadrotor UAV actuators, and parameters in the sliding mode control are adaptively adjusted. The simulation results show that the fault tolerant control method can control the attitude of UAV quickly and achieve good robustness.
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Ahmed, Nigar, and Mou Chen. "Robust model reference adaptive backstepping sliding-mode control for quadrotor attitude with disturbance observer." Aircraft Engineering and Aerospace Technology 93, no. 7 (June 17, 2021): 1156–70. http://dx.doi.org/10.1108/aeat-11-2020-0277.
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Purpose The purpose of this research paper is to design a disturbance observer-based control based on the robust model reference adaptive backstepping sliding-mode control for attitude quadrotor model subject to uncertainties and disturbances. Design/methodology/approach To estimate and reject the disturbance, a disturbance observer is designed for the exogenous disturbances with perturbation while a control criterion is developed for the tracking of desired output. To achieve the control performance, backstepping and sliding-mode control techniques are patched together to obtain robust chattering-free controller. Furthermore, a model reference adaptive control criterion is also combined with the design of robust control for the estimation and rejection of uncertainties and unmodeled dynamics of the attitude quadrotor. Findings The findings of this research work includes the design of a disturbance observer-based control for uncertain attitude quadrotor system with the ability of achieving tracking control objective in the presence of nonlinear exogenous disturbance with and without perturbation. Practical implications In practice, the quadrotor flight is opposed by different kinds of the disturbances. In addition, being an underactuated system, it is difficult to obtain an accurate mathematical model of quadrotor for the control design. Thus, a quadrotor model with uncertainties and disturbances is inevitable. Hence, it is necessary to design a control system with the ability to achieve the control objectives in the presence of uncertainties and disturbances. Originality/value Designing the control methods for quadrotor control without uncertainties and disturbances is a common practice. However, investigating the uncertain quadrotor plant in the presence of nonlinear disturbances is rarely taken into consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the uncertainties and disturbances as well as investigate a control algorithm to achieve tracking performance.
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Li, Yahui, Feng Gao, Franco Bernelli-Zazzera, Zeyou Tong, Fugui Li, Aojia Ma, Lei Zhang, and Jifeng Guo. "A Novel Robust Adaptive Backstepping Method Combined with SMC on Strict-Feedback Nonlinear Systems Using Neural Networks." MATEC Web of Conferences 291 (2019): 01001. http://dx.doi.org/10.1051/matecconf/201929101001.
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Adaptive backstepping methodology is a powerful tool for nonlinear systems, especially for strict-feedback ones, but its robustness still needs improvements. In this paper, combined with sliding mode control (SMC), a new backstepping design method is proposed to guarantee the robustness. In this method, based on the novel combining method, the auxiliary controller is introduced only in the final step of the real controller, unlike traditional methods, which usually all include an auxiliary controller in every de-signing step to guarantee the robustness of the closed-loop systems. The novel combing methods can avoid calculating multiple and high-order derivatives of the auxiliary controllers in the intermediate steps, low-ering the computational burden in evaluating the controller. The effectiveness of the proposed approach is illustrated from simulation results.
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Wang, Huapeng, Nan Jiang, Ting Liu, and Yangyang Cao. "ADAPTIVE STABLE CONTROL OF MANIPULATOR SYSTEM BASED ON IMMERSION AND INVARIANCE." Mathematical Modelling and Analysis 23, no. 3 (June 14, 2018): 379–89. http://dx.doi.org/10.3846/mma.2018.023.
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This work focused on the manipulator system containing uncertainties, and proposes an immersion and invariance (I&I) control strategy, in order to avoid the damage on the mechanical and the operation object caused by parameter uncertainty. A stable target system with lower dimension than the manipulator system was chosen to design the control law and estimation laws of uncertain parameters. Then finding an invariant and attractive manifold in state space with internal dynamics a copy of the desired closed-loop dynamics. Finally, design a control law that can steer the state of the system sufficiently close to the manifold. The immersion and invariance adaptive control does not rely on certainty equivalence. The whole uncertain parameter estimations are the sum of two terms. One is obtained by an iterative law like the traditional adaptive backstepping method. On the other hand, a nonlinear function is introduced. The role of this additional term makes the parameter estimations more exible and effective. Lyapunov function is not necessary for the process of designing adaptive controllers. So immersion and invariance can effectively avoid the 'computing expansion' of backstepping method. Compared with the traditional adaptive methods, simulation results show that the proposed immersion and invariance adaptive controller can improve the system performance, including dynamic response, stability and accuracy of parameter estimations.
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Do, K. D. "Global path-following control of underactuated ships under deterministic and stochastic sea loads." Robotica 34, no. 11 (March 20, 2015): 2566–91. http://dx.doi.org/10.1017/s0263574715000211.
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SUMMARYThis paper presents a new method to design global path-following controllers for underactuated ships under both deterministic and stochastic sea loads. The path-following errors are first interpreted in a moving frame attached to the path. These errors are then to be stabilized at the origin by a design of controllers based on backstepping and Lyapunov's direct methods. Weak and strong nonlinear Lyapunov functions are introduced to overcome difficulties caused by underactuation and Hessian terms induced by stochastic differentiation rule, and to guarantee boundedness of the sway velocity. Potential projection functions are introduced to design update laws that provide bounded estimates of the mean values and covariances of the disturbances. Simulations are included to illustrate the effectiveness of the proposed approach.
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Dong, Minzhou, Xinkai Xu, and Feng Xie. "Constrained Integrated Guidance and Control Scheme for Strap-Down Hypersonic Flight Vehicles with Partial Measurement and Unmatched Uncertainties." Aerospace 9, no. 12 (December 17, 2022): 840. http://dx.doi.org/10.3390/aerospace9120840.
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This paper investigates the issue of integrated guidance and control (IGC) design for strap-down hypersonic flight vehicles with partial measurement information and unmatched uncertainties. A constrained IGC scheme is proposed by combining the barrier Lyapunov function-based backstepping methodology and the specific output-based finite-time disturbance observer. Different from the existing methods, which require the state information and matched disturbances, the main features of the presented approach is capable of addressing the partial measurement knowledge and unmatched uncertainties simultaneously. The IGC model of hypersonic flight vehicles is first formulated, and based on that, the specific output-based finite-time disturbance observer (OFTDO) is proposed to achieve the finite-time estimation of the unmatched uncertainties through the output. Then, the constrained IGC strategy is constructed via the backstepping technique. The stability of the closed-loop system including the estimation and tracking errors dynamics is analyzed in detail. The effectiveness of the proposed method is verified by numerical simulations and Monte-Carlo tests.
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Xu, Bo, Xiaoping Liu, Huanqing Wang, and Yucheng Zhou. "Event-Triggered Adaptive Backstepping Control for Strict-Feedback Nonlinear Systems with Zero Dynamics." Complexity 2019 (October 10, 2019): 1–13. http://dx.doi.org/10.1155/2019/7890968.
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This paper focuses on the problem of event-triggered control for a class of uncertain nonlinear strict-feedback systems with zero dynamics via backstepping technique. In the design procedure, the adaptive controller and the triggering event are designed at the same time to remove the assumption of the input-to-state stability with respect to the measurement errors. Besides, we propose an assumption to deal with the problem of zero dynamics. Three different event-triggered control strategies are designed, which guarantees that all the closed-loop signals are globally bounded. The effectiveness of the proposed methods is illustrated and compared using simulation examples.
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Wang, Yihao, Changzhong Pan, Jinsen Xiao, Zhijing Li, and Chenchen Cui. "LESO-Based Nonlinear Continuous Robust Stabilization Control of Underactuated TORA Systems." Actuators 11, no. 8 (August 4, 2022): 220. http://dx.doi.org/10.3390/act11080220.
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In this paper, we consider the robust stabilization control problem of underactuated translational oscillator with a rotating actuator (TORA) system in the presence of unknown matched disturbances by employing continuous control inputs. A nonlinear continuous robust control approach is proposed by integrating the techniques of backstepping and linear extended state observer (LESO). Specifically, based on the backstepping design methodology, a hyperbolic tangent virtual control law is designed for the first subsystem of the cascaded TORA model, via which an integral chain error subsystem is subsequently constructed and the well-known LESO technique is easy to implement. Then, an LEO is designed to estimate the lumped matched disturbances in real-time, and the influence of the disturbances is compensated by augmenting the feedback controller with the disturbance estimation. The convergence and stability of the entire control system are rigorously proved by utilizing Lyapunov theory and LaSalle’s invariance principle. Unlike some existing methods, the proposed controller is capable of generating robust and continuous control inputs, which guarantee that both the rotation and translation of TORA systems are stabilized at the origin simultaneously and smoothly, attenuating the influence of disturbances. Comparative simulation results are presented to demonstrate the effectiveness and superior control performance of the proposed method.
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Furtat, I. B., and A. N. Nekhoroshikh. "Modified Backstepping Algorithm and its Application to Control of Distillation Column." Mekhatronika, Avtomatizatsiya, Upravlenie 20, no. 2 (February 13, 2019): 90–96. http://dx.doi.org/10.17587/mau.20.90-96.
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A novel robust algorithm is proposed for control of plants under parametric and structural uncertainties, as well as, external bounded disturbances. The algorithm design is based on the modified backstepping approach that allows to compensate mismatched disturbances under presence of nonlinearities. The obtained results are extended to control of network systems with nonlinear agents and with nonlinear links in the presence of mismatched disturbances. Effectiveness of the proposed algorithm is demonstrated on control of a distillation column which is described by parametric and structurally uncertain differential equation in presence of external bounded disturbances. It is assumed that only scalar input and output of the distillation column are available for measurement, but not their derivatives. The developed algorithm provides output tracking of a smooth bounded reference signal with a required accuracy at a finite time. The synthesis of control algorithm is separated into ρ steps, where ρ is an upper bound of the relative degree of the distillation column model. Therefore, the dynamical order of the proposed algorithm is equal to ρ. The sufficient conditions of the closed-loop stability is formulated and proved by using methods of stability of singular perturbed differential equations and Lyapunov functions. The simulations illustrate effectiveness of the proposed algorithm and confirm analytical results.
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Huynh, Thinh, Minh-Thien Tran, Dong-Hun Lee, Soumayya Chakir, and Young-Bok Kim. "A Study on Vision-Based Backstepping Control for a Target Tracking System." Actuators 10, no. 5 (May 19, 2021): 105. http://dx.doi.org/10.3390/act10050105.
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This paper proposes a new method to control the pose of a camera mounted on a two-axis gimbal system for visual servoing applications. In these applications, the camera should be stable while its line-of-sight points at a target located within the camera’s field of view. One of the most challenging aspects of these systems is the coupling in the gimbal kinematics as well as the imaging geometry. Such factors must be considered in the control system design process to achieve better control performances. The novelty of this study is that the couplings in both mechanism’s kinematics and imaging geometry are decoupled simultaneously by a new technique, so popular control methods can be easily implemented, and good tracking performances are obtained. The proposed control configuration includes a calculation of the gimbal’s desired motion taking into account the coupling influence, and a control law derived by the backstepping procedure. Simulation and experimental studies were conducted, and their results validate the efficiency of the proposed control system. Moreover, comparison studies are conducted between the proposed control scheme, the image-based pointing control, and the decoupled control. This proves the superiority of the proposed approach that requires fewer measurements and results in smoother transient responses.
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Ferrei̇ra, Diogo, Paulo Oliveira, and Afzal Suleman. "A Leader-Follower Trajectory Tracking Controller for Multi-Quadrotor Formation Flight." Volume 03 Issue 01 vm03, is01 (June 28, 2022): 13–20. http://dx.doi.org/10.23890/ijast.vm03is01.0102.
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The aim of this work is to design a control system based on modern control methods to control flight formations of quadrotor unmanned aerial vehicles. A leader-follower methodology is implemented where the leader vehicle has some predefined trajectory, and the follower vehicles are controlled in order to track the leader while keeping a constant displacement. The formation control system, responsible for the vehicle formation, considers, at first, only the motion at a constant height, and secondly, the three-dimensional motion. In both cases, the nonlinear control laws are derived based on Lyapunov stability theory and the Backstepping method. The control laws are validated in simulation, resorting to a realistic environment and vehicle models.
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Dong, Jie, Yanzhao Zhang, Xiaotian Liu, and Zhankui Song. "Velocity-Free Adaptation Compensation Control of MEMS with Prescribed Performance." Mathematical Problems in Engineering 2022 (June 16, 2022): 1–11. http://dx.doi.org/10.1155/2022/1499685.
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This study investigates the prescribed performance control problem for microelectro-mechanical system (MEMS) gyroscope subject to system parameters’ uncertainty. A finite-time observer is firstly designed to estimate the unmeasurable velocity state of MEMS gyroscope. Subsequently, a coordinate transformation with the performance function is introduced into an error system which will be kept bounded to ensure expected dynamic and steady-state responses. Based on the proposed finite time-velocity reconstruction system, the adaptive backstepping design procedure is further designed to deal with the lumped uncertainty term. Furthermore, when considering actuator saturation, an improved control strategy is developed with a nonlinear input updating law, and meanwhile, it is proved that the system error converges to a preset compact set around zero in a preassigned time. Simulation results show the effectiveness and reliability of the proposed methods.
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Xu, Chenyang, Humin Lei, Jiong Li, Jikun Ye, and Dongyang Zhang. "Adaptive Neural Control for Nonaffine Pure-Feedback System Based on Extreme Learning Machine." Mathematical Problems in Engineering 2019 (June 16, 2019): 1–13. http://dx.doi.org/10.1155/2019/5613212.
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For nonaffine pure-feedback systems, an adaptive neural control method based on extreme learning machine (ELM) is proposed in this paper. Different from the existing methods, this scheme firstly converts the original system into a nonaffine system containing only one unknown term by equivalent transformation, thus avoiding the cumbersome and complex indirect design process of traditional backstepping methods. Secondly, a high-performance finite-time-convergence-differentiator (FD) is designed, through which the system state variables and their derivatives are accurately estimated to ensure the control effect. Thirdly, based on the implicit function theorem, the ELM neural network is introduced to approximate the uncertain items of the system, which simplifies the repeated adjustment process of the network training parameters. Meanwhile, the minimum learning parameter algorithm (MLP) is adopted to design the adaptive law for the norm of the network weight vector, which significantly reduces calculations. And it is theoretically proved that the closed-loop control system is stable and the tracking error is bounded. Finally, the effectiveness of the designed controller is verified by simulation.
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Rincón, Alejandro, Fabiola Angulo, and Fredy Hoyos. "Controlling a DC Motor through Lypaunov-like Functions and SAB Technique." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 4 (August 1, 2018): 2180. http://dx.doi.org/10.11591/ijece.v8i4.pp2180-2198.
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<p>In this paper, state adaptive backstepping and Lyapunov-like function methods are used to design a robust adaptive controller for a DC motor. The output to be controlled is the motor speed. It is assumed that the load torque and inertia moment exhibit unknown but bounded time-varying behavior, and that the measurement of the motor speed and motor current are corrupted by noise. The controller is implemented in a Rapid Control Prototyping system based on Digital Signal Processing for dSPACE platform and experimental results agree with theory.</p>
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Zhang, Peng, and Yunhua Li. "Research on Control Methods for the Pressure Continuous Regulation Electrohydraulic Proportional Axial Piston Pump of an Aircraft Hydraulic System." Applied Sciences 9, no. 7 (April 1, 2019): 1376. http://dx.doi.org/10.3390/app9071376.
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The objective of this paper is to design a pump that can match its delivery pressure to the aircraft load. Axial piston pumps used in airborne hydraulic systems are required to work in a constant pressure mode setting based on the highest pressure required by the aircraft load. However, the time using the highest pressure working mode is very short, which leads to a lot of overflow lose. This study is motivated by this fact. Pressure continuous regulation electrohydraulic proportional axial piston pump is realized by combining a dual-pressure piston pump with electro-hydraulic proportional technology, realizing the match between the delivery pressure of the pump and the aircraft load. The mathematical model is established and its dynamic characteristics are analyzed. The control methods such as a proportional integral derivative (PID) control method, linear quadratic regulator (LQR) based on a feedback linearization method and a backstepping sliding control method are designed for this nonlinear system. It can be seen from the result of simulation experiments that the requirements of pressure control with a pump are reached and the capacity of resisting disturbance of the system is strong.
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Tran, Hoang T., Dong L. T. Tran, Vinh Q. Nguyen, Hai T. Do, and Minh T. Nguyen. "A Novel Framework of Modelling, Control, and Simulation for Autonomous Quadrotor UAVs Utilizing Arduino Mega." Wireless Communications and Mobile Computing 2022 (August 19, 2022): 1–17. http://dx.doi.org/10.1155/2022/3044520.
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In recent decades, there has been a constant increase in the use of unmanned aerial vehicles (UAVs). There has also been a huge growth in the number of control algorithms to support the many applications embodied by the vehicles, including challenges and open issues to develop. This paper focuses on three major classes of control methods applied to quadrotors in order to create an open-source model based on the Arduino Mega that allows for the derivation and design of quadrotor control strategies. We consider the perspective classes, including linear, nonlinear, and intelligent methods representing in details with applications in developing an open-source controller for the quadrotor using the Arduino Mega and the BNO055 9 DOF sensor. We propose Proportional Integral Derivative (PID), backstepping integrator, and model predictive control (MPC) to track a generated Lissajous curve for surveillance. Simulations in the Matlab–Simulink environment with 3D visualization of a developed quadrotor model using CAD software, with robustness and performance discussion, are provided. Our experimental work is developed with an extensive illustration of the hardware and algorithm design and by demonstrating the effectiveness of the proposed architectures. The results show promise in practical and in intelligent applications.
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Wang, Xingjian, and Shaoping Wang. "Adaptive Fuzzy Robust Control for a Class of Nonlinear Systems via Small Gain Theorem." Mathematical Problems in Engineering 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/201432.
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Practical nonlinear systems can usually be represented by partly linearizable models with unknown nonlinearities and external disturbances. Based on this consideration, we propose a novel adaptive fuzzy robust control (AFRC) algorithm for such systems. The AFRC effectively combines techniques of adaptive control and fuzzy control, and it improves the performance by retaining the advantages of both methods. The linearizable part will be linearly parameterized with unknown but constant parameters, and the discontinuous-projection-based adaptive control law is used to compensate these parts. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown nonlinearities. Robust control law ensures the robustness of closed-loop control system. A systematic design procedure of the AFRC algorithm by combining the backstepping technique and small-gain approach is presented. Then the closed-loop stability is studied by using small gain theorem, and the result indicates that the closed-loop system is semiglobally uniformly ultimately bounded.
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Yan, Zheping, Da Xu, Tao Chen, and Jiajia Zhou. "Formation control of unmanned underwater vehicles using local sensing means in absence of follower position information." International Journal of Advanced Robotic Systems 18, no. 1 (January 1, 2021): 172988142098674. http://dx.doi.org/10.1177/1729881420986745.
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Formation control is one of the essential problems in multi-unmanned underwater vehicle (UUV) coordination. In this article, a practically oriented UUV formation control structure and method are proposed for the problem of large communication in leader–follower approach. To solve the problem of large communication in multi-UUVs, local sensing means of acoustic positioning is used to provide the real relative distance and angle information for the follower UUV. So, only a small amount of state information of the leader UUV needs to be sent to the follower UUV by acoustic communication. Then, the formation control structure in absence of follower position information is proposed. In this control structure, only the relative distance and angle, as well as velocity and heading of the leader UUV, are used for the formation controller design of the follower UUV. Backstepping and Lyapunov methods are used to design the formation controller without position information of the follower UUV. Two formation configurations of rectangle and triangle with five UUVs are simulated to verify the effectiveness of the method proposed. The simulation results show that the follower UUV can successfully constitute and maintain the desired formation by controlling each real relative distance and angle.
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Nie, Yong, Jiajia Liu, Zhenhua Lao, and Zheng Chen. "Modeling and Extended State Observer-Based Backstepping Control of Underwater Electro Hydrostatic Actuator with Pressure Compensator and External Load." Electronics 11, no. 8 (April 18, 2022): 1286. http://dx.doi.org/10.3390/electronics11081286.
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Electro hydrostatic actuator (EHA) has been successfully developed for flight control applications to replace the cumbersome centralized hydraulic system. It also has excellent potential for ocean applications due to its advantages on miniaturization and energy-savings. One of the special technologies for EHA’s underwater application is pressure compensation, which is used to equalize the return pressure of the hydraulic system and the seawater pressure. This paper investigates the modeling and control design of underwater EHA to improve performance, especially considering the effect of additional pressure compensator and uncertain external load. The nonlinear hydraulic model is extended by the dynamic characteristics of the pressure compensator. Two low-order extended state observers were constructed to cope with the external load fore and the effect of the pressure compensator, respectively. The backstepping methods were designed to guarantee the robust stability of the entire high-order nonlinear hydraulic system. Finally, the theoretical proving and simulation on Matlab/Simulink are conducted to demonstrate the high tracking performance of the proposed control strategy.
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Nazir, Muhammad Saqib, Iftikhar Ahmad, Muhammad Jawad Khan, Yasar Ayaz, and Hammad Armghan. "Adaptive Control of Fuel Cell and Supercapacitor Based Hybrid Electric Vehicles." Energies 13, no. 21 (October 26, 2020): 5587. http://dx.doi.org/10.3390/en13215587.
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In this paper, an adaptive nonlinear control strategy for the energy management of a polymer electrolyte membrane fuel cell and supercapacitor-based hybrid electric vehicle is proposed. The purpose of this work was to satisfy: (i) tight DC bus voltage regulation, (ii) good fuel cell reference current tracking, (iii) better supercapacitor reference current tracking (iv) global asymptotic stability of the closed-loop control system, and (v) better vehicle performance by catering to slowly-varying parameters. We have selected the power stage schematic of a hybrid electric vehicle and utilized adaptive backstepping and adaptive Lyapunov redesign-based nonlinear control methods to formally derive adaptive parametric update laws for all slowly-varying parameters. The performance of the proposed system has been tested under varying load conditions using experimental data from the “Extra Urban Driving Cycle.” Mathematical analysis and Matlab/Simulink results show that proposed controllers are globally asymptotically stable and satisfy all the design requirements. The physical effectiveness of proposed system has been verified by comparing simulation results with the real-time controller hardware in the loop experimental results. Results show that proposed system shows satisfactory performance and caters for the time-varying parametric variations and the load requirements.
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Jiang, Xiyun, and Yuanhui Wang. "Prescribed Performance Control of Marine Surface Vessel Trajectory Tracking in Finite-Time with Full-State Constraints and Input Saturation." Journal of Marine Science and Engineering 9, no. 8 (August 12, 2021): 866. http://dx.doi.org/10.3390/jmse9080866.
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This manuscript mainly solves a fully actuated marine surface vessel prescribed performance trajectory tracking control problem with full-state constraints and input saturation. The entire control design process is based on a backstepping technique. The prescribed performance control is introduced to embody the analytical relationship between the transient performance and steady-state performance of the system and the parameters. Meanwhile, a new finite time performance function is introduced to ensure that the performance of the system tracking error is constrained within the preset constraints in finite time, and the full-state constraints problem of the system can be solved simultaneously in the entire control design, at the same time without introducing additional theory and parameters. To solve the non-smooth input saturation function matrix is not differentiable, the smooth function matrix is introduced to replace the non-smooth characteristics. Combining the Moore-Penrose generalized inverse matrix to design the virtual control law, the dynamic surface control is introduced to avoid the complicated virtual control derivation process, and finally the actual control law is designed using the properties of Nussbaum function. In addition, in view of the uncertainties in the system, a fractional disturbance observer is designed to estimate it. With the proposed control, the full-state will never be violated constraints, and the system tracking error satisfies transient and steady-state performance. Compared with other methods, the simulation results show the effectiveness and advantages of the proposed method.
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Li, Menghan, Shaobo Li, Junxing Zhang, Fengbin Wu, and Tao Zhang. "Neural Adaptive Funnel Dynamic Surface Control with Disturbance-Observer for the PMSM with Time Delays." Entropy 24, no. 8 (July 26, 2022): 1028. http://dx.doi.org/10.3390/e24081028.
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This paper suggests an adaptive funnel dynamic surface control method with a disturbance observer for the permanent magnet synchronous motor with time delays. An improved prescribed performance function is integrated with a modified funnel variable at the beginning of the controller design to coordinate the permanent magnet synchronous motor with the output constrained into an unconstrained one, which has a faster convergence rate than ordinary barrier Lyapunov functions. Then, the specific controller is devised by the dynamic surface control technique with first-order filters to the unconstrained system. Therein, a disturbance-observer and the radial basis function neural networks are introduced to estimate unmatched disturbances and multiple unknown nonlinearities, respectively. Several Lyapunov-Krasovskii functionals are constructed to make up for time delays, enhancing control performance. The first-order filters are implemented to overcome the “complexity explosion” caused by general backstepping methods. Additionally, the boundedness and binding ranges of all the signals are ensured through the detailed stability analysis. Ultimately, simulation results and comparison experiments confirm the superiority of the controller designed in this paper.
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Yao, Yangang, Jieqing Tan, and Jian Wu. "Finite-Time Tracking Control for Nonstrict-Feedback State-Delayed Nonlinear Systems with Full-State Constraints and Unmodeled Dynamics." Complexity 2020 (November 8, 2020): 1–18. http://dx.doi.org/10.1155/2020/8887925.
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The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by time-varying state delays are compensated for and unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method.
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Psillakis, Haris E., and Antonio T. Alexandridis. "Coordinated Excitation and Static Var Compensator Control with Delayed Feedback Measurements in SGIB Power Systems." Energies 13, no. 9 (May 1, 2020): 2181. http://dx.doi.org/10.3390/en13092181.
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In this paper, we present a nonlinear coordinated excitation and static var compensator (SVC) control for regulating the output voltage and improving the transient stability of a synchronous generator infinite bus (SGIB) power system. In the first stage, advanced nonlinear methods are applied to regulate the SVC susceptance in a manner that can potentially improve the overall transient performance and stability. However, as distant from the generator measurements are needed, time delays are expected in the control loop. This fact substantially complicates the whole design. Therefore, a novel design is proposed that uses backstepping methodologies and feedback linearization techniques suitably modified to take into account the delayed measurement feedback laws in order to implement both the excitation voltage and the SVC compensator input. A detailed and rigorous Lyapunov stability analysis reveals that if the time delays do not exceed some specific limits, then all closed-loop signals remain bounded and the frequency deviations are effectively regulated to approach zero. Applying this control scheme, output voltage changes occur after the large power angle deviations have been eliminated. The scheme is thus completed, in a second stage, by a soft-switching mechanism employed on a classical proportional integral (PI) PI voltage controller acting on the excitation loop when the frequency deviations tend to zero in order to smoothly recover the output voltage level at its nominal value. Detailed simulation studies verify the effectiveness of the proposed design approach.
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Hu, Chaofang, Zelong Zhang, Xianpeng Zhou, and Na Wang. "Command filter-based fuzzy adaptive nonlinear sensor-fault tolerant control for a quadrotor unmanned aerial vehicle." Transactions of the Institute of Measurement and Control 42, no. 2 (August 9, 2019): 198–213. http://dx.doi.org/10.1177/0142331219865377.
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In this paper, a novel asymptotic fuzzy adaptive nonlinear fault tolerant control (FTC) scheme is presented for the under-actuated dynamics of a quadrotor unmanned aerial vehicle (UAV) subject to diverse sensor faults. The proposed FTC approach can deal with both additive sensor faults (bias, drift, loss of accuracy) and multiplicative sensor fault (loss of effectiveness). The overall dynamics is separated into position loop and attitude loop for FTC controllers design. Combining uncertain parameters and external disturbances, the four types of faults occurring in velocity sensors and Euler angle rate sensors are transformed equivalently into the unknown nonlinear function vectors and uncertain control gains. Fuzzy logic systems are used to approximate the lumped nonlinear functions, and adaptive parameters are estimated online. Nussbaum technique is introduced to deal with the unknown control gains. For both control loops, FTC controllers are designed via command filter-based backstepping approach, in which sliding mode control is introduced to establish asymptotic stability. All tracking error signals of the closed-loop control system are proved to converge to zero asymptotically. Finally, simulation comparisons with other methods demonstrate the effectiveness of the proposed FTC approach for quadrotor UAV with sensor faults.
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Kuz’menko, A. A. "Robust Control of Permanent Magnet Synchronous Motor: Synergetic Approach." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 8 (August 5, 2020): 480–88. http://dx.doi.org/10.17587/mau.21.480-488.
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Permanent magnet synchronous motors (PMSM) are widely used in practice due to its high-energy efficiency, compactness, reliability and high regulation performance. When controlling a PMSM rotor speed, the main control principle is the principle of cascade control with PI-regulators, which includes an external control loop for speed and two internal loops for stator currents along the (d, q)-axes. There are attempts to eliminate the disadvantages of this principle using for the control laws synthesis of modern methods of nonlinear control such methods as linearization feedback, backstepping, predictive control, sliding mode control, methods of robust and adaptive control, fuzzy and neural network control, a combination of these methods etc. However, in most cases, the use of these methods are intended to by means of an appropriate method to synthesize a static or dynamic set points for the standard PI-controllers of rotor speed and currents. In this paper we propose to consider two approaches of synergetic control theory (SCT) to construct a robust control law of PMSM: a sliding mode control laws design by the SCT method with subsequent invariant manifolds aggregation and the principle of integral adaptation (PIA). These approaches implement vector control and are not guided by the standard structure of the principle of cascade regulation of PMSM. The proposed approaches simplify the stability analysis of the closed-loop system: stability conditions consist of stability conditions of functional equations of SCT and the stability conditions for finish decomposed system, which the dimension is substantially less than the dimension of the original system. From the results of the comparisons of synthesized the PMSM robust control laws, we can say that more preferable laws synthesized in accordance with the PIA. The theoretical positions of this paper are illustrated by the results of modeling, which are showing the fulfillment of the control tasks: the achievement of targets, robustness to the change of the PMSM load moment.
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Härkegård, Ola, and S. Torkel Glad. "Flight Control Design Using Backstepping." IFAC Proceedings Volumes 34, no. 6 (July 2001): 283–88. http://dx.doi.org/10.1016/s1474-6670(17)35187-x.
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Ilyas, M., N. Abbas, M. UbaidUllah, Waqas A. Imtiaz, M. A. Q. Shah, and K. Mahmood. "Control Law Design for Twin Rotor MIMO System with Nonlinear Control Strategy." Discrete Dynamics in Nature and Society 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/2952738.
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Modeling of complex air vehicles is a challenging task due to high nonlinear behavior and significant coupling effect between rotors. Twin rotor multi-input multioutput system (TRMS) is a laboratory setup designed for control experiments, which resembles a helicopter with unstable, nonlinear, and coupled dynamics. This paper focuses on the design and analysis of sliding mode control (SMC) and backstepping controller for pitch and yaw angle control of main and tail rotor of the TRMS under parametric uncertainty. The proposed control strategy with SMC and backstepping achieves all mentioned limitations of TRMS. Result analysis of SMC and backstepping control schemes elucidates that backstepping provides efficient behavior with the parametric uncertainty for twin rotor system. Chattering and oscillating behaviors of SMC are removed with the backstepping control scheme considering the pitch and yaw angle for TRMS.
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Li, Mei Hong, Jian Yin, Xue Yang Sun, Jin Xiang Xu, and Mei Mei Zhang. "Design of Missile Longitudinal Control System Based on Backstepping Control." Applied Mechanics and Materials 496-500 (January 2014): 1401–6. http://dx.doi.org/10.4028/www.scientific.net/amm.496-500.1401.
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Missile control system is not block strict feedback system which is suitable to use backstepping method. So in this paper, a backstepping control method is proposed to design a missile longitudinal autopilot and is proved to be asymptotically stable by Lyapunov stability theory. The simulation results show that the designed system can still track commands quickly and accurately and is robust with aerodynamic perturbation and control input saturation.