Journal articles: 'Singular Perturbation based guidance design'

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Manickavasagam, M., A. K. Sarkar, and V. Vaithiyanathan. "A Singular Perturbation Based Midcourse Guidance Law for Realistic Air-to-Air Engagement." Defence Science Journal 67, no. 1 (December 23, 2016): 108. http://dx.doi.org/10.14429/dsj.1.9236.

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In this study, a singular perturbation based technique is used for synthesis and analysis of a near optimal midcourse guidance law for realistic air-to-air engagement. After designing the proposed midcourse guidance law using three dimensional point mass formulation it has been validated through detailed realistic six degrees of freedom simulation. During terminal phase only proportional navigation guidance have been used. The calculation of optimal altitude in present guidance law has been carried out using Newton’s method, which needs generally one iteration for convergence and suitable for real-time implementation. Extended Kalman filter based estimator has been used for obtaining evader kinetic information from both radar and seeker noisy measurements available during midcourse and terminal guidance. The data link look angle constraint due to hardware limitation which affects the performance of midcourse guidance has also been incorporated in guidance law design. Robustness of complete simulation has been carried out through Monte Carlo studies. Extension of launch boundary due to singular perturbation over proportional navigation guidance at a given altitude for a typical engagement has also been reported.<br />

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Yefei, Yin, Li Xu, and Li Qiaoqi. "Design of Guidance Law for Smart Missile Based on Direct Mode Configuration with Implicit Dynamic-Inverse." Journal of Physics: Conference Series 2478, no. 11 (June 1, 2023): 112036. http://dx.doi.org/10.1088/1742-6596/2478/11/112036.

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Abstract The design of guidance law for smart missile based on implicit dynamic-inverse direct mode configuration is described in this paper. The dynamic-inverse theory and direct mode algorithm are applied to the design of guidance law. The pitching acceleration and yaw acceleration are designed for the pitch channel by using the augmented proportional guidance and for the yaw channel by using the dynamic-inverse theory respectively. The attacking time parameter and the attack time error equation are introduced as the constraint criteria for the design of the dynamic-inverse. According to the singular perturbation theory, the fast and slow subsystems are designed by dynamic-inverse control, and then the required control quantities are obtained by solving the relative motion equations of the missile and the target. The simulation results showed that the guidance law can fully meet the guidance trajectory performance requirements of the smart missile.

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Zhao, Penglei, Wanchun Chen, and Wenbin Yu. "Optimal perturbation guidance with constraints on terminal flight-path angle and angle of attack." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 12 (January 13, 2019): 4436–46. http://dx.doi.org/10.1177/0954410018823472.

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This paper presents the design of a singular-perturbation-based optimal guidance with constraints on terminal flight-path angle and angle of attack. By modeling the flight-control system dynamics as a first-order system, the angle of attack is introduced into the performance index as a state variable. To solve the resulting high-order optimal guidance problem analytically, the posed optimal guidance problem is divided into two sub-problems by utilizing the singular perturbation method according to two time scales: range, altitude, and flight-path angle are the slow time-scale variables while the angle of attack is the fast time-scale variable. The outer solutions are the optimal control of the slow-scale subsystem. Thereafter, by applying the stretching transformation, the fast-scale subsystem establishes the relationships between the outer solutions and acceleration command. Then, the optimal command can be obtained by solving the fast-scale subsystem also using the optimal control theory. The proposed guidance can achieve a near-zero terminal acceleration as well as a small miss distance. The superior performance of the guidance is demonstrated by adequate trajectory simulations.

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Fan, Yunsheng, Bowen Liu, Guofeng Wang, and Dongdong Mu. "Adaptive Fast Non-Singular Terminal Sliding Mode Path Following Control for an Underactuated Unmanned Surface Vehicle with Uncertainties and Unknown Disturbances." Sensors 21, no. 22 (November 10, 2021): 7454. http://dx.doi.org/10.3390/s21227454.

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This paper focuses on an issue involving robust adaptive path following for the uncertain underactuated unmanned surface vehicle with time-varying large sideslips angle and actuator saturation. An improved line-of-sight guidance law based on a reduced-order extended state observer is proposed to address the large sideslip angle that occurs in practical navigation. Next, the finite-time disturbances observer is designed by considering the perturbations parameter of the model and the unknown disturbances of the external environment as the lumped disturbances. Then, an adaptive term is introduced into Fast Non-singular Terminal Sliding Mode Control to design the path following controllers. Finally, considering the saturation of actuator, an auxiliary dynamic system is introduced. By selecting the appropriate design parameters, all the signals of the whole path following a closed-loop system can be ultimately bounded. Real-time control of path following can be achieved by transferring data from shipborne sensors such as GPS, combined inertial guidance and anemoclinograph to the Fast Non-singular Terminal Sliding Mode controller. Two examples as comparisons were carried out to demonstrate the validity of the proposed control approach.

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Ha, Cheol-Keun, and Hyoung-Sik Choi. "Design of Autolanding Guidance and Control Algorithm Using Singular Perturbation." Journal of Control, Automation and Systems Engineering 11, no. 8 (August 1, 2005): 726–32. http://dx.doi.org/10.5302/j.icros.2005.11.8.726.

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Annam, Chandrakanth, Ashwini Ratnoo, and Debasish Ghose. "Singular-Perturbation-Based Guidance of Pulse Motor Interceptors with Look Angle Constraints." Journal of Guidance, Control, and Dynamics 44, no. 7 (July 2021): 1356–70. http://dx.doi.org/10.2514/1.g005508.

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Landolsi, F., and F. H. Ghorbel. "Design and singular perturbation control of a piezotube-based nanomanipulator." Nonlinear Dynamics 83, no. 1-2 (September 8, 2015): 971–81. http://dx.doi.org/10.1007/s11071-015-2381-x.

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Song, Seong Ho, Chang Seop Kim, and Jeom Keun Kim. "Stability Analysis of Internal Model Based Gain Control System for Three-Level EDFA Model." Applied Mechanics and Materials 339 (July 2013): 33–37. http://dx.doi.org/10.4028/www.scientific.net/amm.339.33.

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In this paper, stability analysis of an optical fiber amplifier gain controller is presented. The mathematical model of an EDFA (Eribium-Doped Fiber Amplifier) control system is described by two-time scaled system and thus singular perturbation approach can be applied to the design and analysis of the control system. In order to handle the channel variations such as add/drop, we adopt an internal model. The performance of the control system is theoretically analyzed based on a novel singular-perturbation-like approach.

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Wardi, Mohamed Lazhar, Messaoud Amairi, and Mohamed Naceur Abdelkrim. "Fractional PID controller design for nonlinear systems based on singular perturbation technique." International Journal of Digital Signals and Smart Systems 2, no. 2 (2018): 95. http://dx.doi.org/10.1504/ijdsss.2018.093172.

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Wardi, Mohamed Lazhar, Mohamed Naceur Abdelkrim, and Messaoud Amairi. "Fractional PID controller design for nonlinear systems based on singular perturbation technique." International Journal of Digital Signals and Smart Systems 2, no. 2 (2018): 95. http://dx.doi.org/10.1504/ijdsss.2018.10014373.

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Kuang, Zhiming. "The Norm Dependence of Singular Vectors." Journal of the Atmospheric Sciences 61, no. 23 (December 1, 2004): 2943–49. http://dx.doi.org/10.1175/jas-3308.1.

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Abstract For a linearized system such as ∂ψ/∂t = 𝗠ψ, singular vector analysis can be used to find patterns that give the largest or smallest ratios between the sizes of 𝗠ψ and ψ. Such analyses have applications to a wide range of atmosphere–ocean problems. The resulting singular vectors, however, depend on the norm used to measure the sizes of 𝗠ψ and ψ, as noted in various applications. This causes complications because the choices of norm are generally nonunique. Based on perturbation theory, a derivation of how singular vectors change with norms typically used in the atmosphere–ocean literature is provided, and it is shown that the norm dependences observed in previous studies can be understood as general properties of singular vectors. This will hopefully clarify the interpretation of these observed norm dependencies, and provide guidance to new studies on how singular vectors would vary for different norms. It is further argued, based on these results, that there may not be as much norm-related ambiguity in problems, such as designing targeted observations or ensemble forecasts, as is often assigned to them.

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Tellili, Adel, Aymen Elghoul, and Mohamed Naceur Abdelkrim. "Additive fault tolerant control of nonlinear singularly perturbed systems against actuator fault." Journal of Electrical Engineering 68, no. 1 (January 1, 2017): 68–73. http://dx.doi.org/10.1515/jee-2017-0009.

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AbstractThis paper presents the design of an additive fault tolerant control for nonlinear time-invariant singularly perturbed systems against actuator faults based on Lyapunov redesign principle. The overall system is reduced into subsystems with fast and slow dynamic behavior using singular perturbation method. The time scale reduction is carried out when the singular perturbation parameter is set to zero, thus avoiding the numerical stiffness due to the interaction of two different dynamics. The fault tolerant controller is computed in two steps. First, a nominal composite controller is designed using the reduced subsystems. Secondly, an additive part is combined with the basic controller to overcome the fault effect. The derived ε - independent controller guarantees asymptotic stability despite the presence of actuator faults. The Lyapunov stability theory is used to prove the stability provided the singular perturbation parameter is sufficiently small. The theoretical results are simulated using a numerical application.

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Mohan Rayguru, Madan, Balakrishnan Ramalingam, and Mohan Rajesh Elara. "A singular perturbation based adaptive strategy for bounded controller design in feedback linearizable systems." International Journal of Adaptive Control and Signal Processing 36, no. 2 (November 30, 2021): 264–81. http://dx.doi.org/10.1002/acs.3360.

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Liu, Ye, Zhu Ying Li, Xiang Yu, and Wen Kang Cao. "Design of Cylindrical Metamaterial Invisible Cloak with Non-Singular Electromagnetic Tensors." Advanced Materials Research 1082 (December 2014): 10–13. http://dx.doi.org/10.4028/www.scientific.net/amr.1082.10.

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Based on line transformation, cylindrical metamaterial invisible cloak with non-singular electromagnetic tensors is designed. The results of simulation software based on finite element methods (FEM) show that the singularity in the electromagnetic tensors of the cloak has been eliminated, comparing with the cylindrical cloak with ideal tensors. From the simulation results, although there is electromagnetic perturbation in the free-space of the solution region, this cloak exhibits nice electromagnetic invisible performance. The bending wave front is clearly seen when the incoming wave transmits into the cloak region. Because of the non-singular electromagnetic tensors, the designed cloak may have more engineering application than the cloak with idea tensors.

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Paarya, A. R., and H. Zarabadipour. "Digital Controller Design for Half-Car Active Suspension System with Using Singular Perturbation Theory." Advanced Materials Research 403-408 (November 2011): 4800–4805. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.4800.

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In this paper the digital controller design for vehicle suspension system, based on a half-car model using singular perturbed systems is considered. This strategy is based on the slow and fast subsystems controller design. The simulation results show them favorable performance of the controller and achieve fast and good response.

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Wang, Bing-Long, Yan Cai, Jin-Chun Song, and Qian-Kun Liang. "A Singular Perturbation Theory-Based Composite Control Design for a Pump-Controlled Hydraulic Actuator with Position Tracking Error Constraint." Actuators 12, no. 7 (June 28, 2023): 265. http://dx.doi.org/10.3390/act12070265.

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Pump-controlled hydraulic actuators (PHAs) contain slow mechanical and fast hydraulic dynamics, and thus singular perturbation theory can be adopted in the control strategies of PHAs. In this article, we develop a singular perturbation theory-based composite control approach for a PHA with position tracking error constraint. Disturbance observers (DOBs) are used to estimate the matched and mismatched uncertainties for online compensation. A sliding surface-like error variable is proposed to transform the second-order mechanical subsystem into a first-order error subsystem. Consequently, the position tracking error constraint of the PHA is decomposed into the output constraint of the first-order error subsystem and the stabilizing of the first-order hydraulic subsystem. Slow and fast control laws can be easily designed without using the backstepping technique, thus simplifying the control design and reducing the computational burden to a large extent. Theoretical analysis verifies that desired stability properties can be achieved by an appropriate selection of the control parameters. Simulations and experiments are performed to confirm the efficacy and practicability of the proposed control strategy.

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Ma, Caipeng, Jinjun Jia, Tiedong Zhang, Shaoqun Wu, and Dapeng Jiang. "Horizontal Trajectory Tracking Control for Underactuated Autonomous Underwater Vehicles Based on Contraction Theory." Journal of Marine Science and Engineering 11, no. 4 (April 10, 2023): 805. http://dx.doi.org/10.3390/jmse11040805.

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In this paper, contraction theory is applied to design a control law to address the horizontal trajectory tracking problem of an underactuated autonomous underwater vehicle. Suppose that the vehicle faces challenges such as model uncertainties, external environmental disturbances, and actuator saturation. Firstly, a coordinate transformation is introduced to solve the problem of underactuation. Then, a disturbance observer is designed to estimate the total disturbances, which are composed of model uncertainties and external environmental disturbances. Next, a saturated controller is designed based on singular perturbation theory and contraction theory. Meanwhile, contraction theory is used to analyse the convergence properties of the observer and the full singular perturbation system, and make quantitative analysis of the estimation error and the tracking error. Finally, the results of numerical simulations prove that the method in this paper enables the vehicle to track the desired trajectory with relatively high accuracy, while the control inputs do not exceed the limitations of the actuators.

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Razmjooei, Hamid, and Mohammad Hossein Shafiei. "A novel finite-time disturbance observer-based partial control design: A guidance application." Journal of Vibration and Control 26, no. 11-12 (December 18, 2019): 1001–11. http://dx.doi.org/10.1177/1077546319890951.

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This paper presents a novel technique to design a robust finite-time partial stabilizer, based on the non-singular terminal sliding mode method and a disturbance observer for the missile guidance problem. In the proposed method, the finite-time stability is desired for only a part of the state variables in the guidance system. Accordingly, the guidance system is divided into two subsystems where the finite-time stability is desired only for the first subsystem. Then, a partial diffeomorphism transformation is used to convert the first subsystem into the normal form. Finally, the components of the input vector appearing in the transformed form of the first subsystem are designed to achieve finite-time stability based on a partial disturbance observer. In the proposed finite-time disturbance observer, the disturbances are estimated in a finite time without any knowledge about their upper bounds. Simulation results demonstrate the effectiveness of the designed guidance law to intercept maneuvering and non-maneuvering targets compared to the existing methods.

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Demetriou, Michael A., and Nikolaos Kazantzis. "Natural Observer Design for Singularly Perturbed Vector Second-Order Systems." Journal of Dynamic Systems, Measurement, and Control 127, no. 4 (December 13, 2004): 648–55. http://dx.doi.org/10.1115/1.2101847.

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Our aim in the present research study is to develop a systematic natural observer design framework for vector second-order systems in the presence of time-scale multiplicity. Specifically, vector second-order mechanical systems are considered along with fast sensor dynamics, and the primary objective is to obtain accurate estimates of the unmeasurable slow system state variables that are generated by an appropriately designed model-based observer. Within a singular perturbation framework, the proposed observer is designed on the basis of the system dynamics that evolves on the slow manifold, and the dynamic behavior of the estimation error that induces is analyzed and mathematically characterized in the presence of the unmodeled fast sensor dynamics. It is shown, that the observation error generated by neglecting the (unmodeled) fast sensor dynamics is of order O(ε), where ε is the singular perturbation parameter and a measure of the relative speed/time constant of the fast (sensor) and the slow component (vector second-order system) of the overall instrumented system dynamics. Finally, the performance of the proposed method and the convergence properties of the natural observer designed are evaluated in an illustrative example of a two-degree of freedom mechanical system.

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Reynolds, C. A., M. S. Peng, S. J. Majumdar, S. D. Aberson, C. H. Bishop, and R. Buizza. "Interpretation of Adaptive Observing Guidance for Atlantic Tropical Cyclones." Monthly Weather Review 135, no. 12 (December 1, 2007): 4006–29. http://dx.doi.org/10.1175/2007mwr2027.1.

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Abstract Adaptive observing guidance products for Atlantic tropical cyclones are compared using composite techniques that allow one to quantitatively examine differences in the spatial structures of the guidance maps and relate these differences to the constraints and approximations of the respective techniques. The guidance maps are produced using the ensemble transform Kalman filter (ETKF) based on ensembles from the National Centers for Environmental Prediction and the European Centre for Medium-Range Weather Forecasts (ECMWF), and total-energy singular vectors (TESVs) produced by ECMWF and the Naval Research Laboratory. Systematic structural differences in the guidance products are linked to the fact that TESVs consider the dynamics of perturbation growth only, while the ETKF combines information on perturbation evolution with error statistics from an ensemble-based data assimilation scheme. The impact of constraining the SVs using different estimates of analysis error variance instead of a total-energy norm, in effect bringing the two methods closer together, is also assessed. When the targets are close to the storm, the TESV products are a maximum in an annulus around the storm, whereas the ETKF products are a maximum at the storm location itself. When the targets are remote from the storm, the TESVs almost always indicate targets northwest of the storm, whereas the ETKF targets are more scattered relative to the storm location and often occur over the northern North Atlantic. The ETKF guidance often coincides with locations in which the ensemble-based analysis error variance is large. As the TESV method is not designed to consider spatial differences in the likely analysis errors, it will produce targets over well-observed regions, such as the continental United States. Constraining the SV calculation using analysis error variance values from an operational 3D variational data assimilation system (with stationary, quasi-isotropic background error statistics) results in a modest modulation of the target areas away from the well-observed regions, and a modest reduction of perturbation growth. Constraining the SVs using the ETKF estimate of analysis error variance produces SV targets similar to ETKF targets and results in a significant reduction in perturbation growth, due to the highly localized nature of the analysis error variance estimates. These results illustrate the strong sensitivity of SVs to the norm (and to the analysis error variance estimate used to define it) and confirm that discrepancies between target areas computed using different methods reflect the mathematical and physical differences between the methods themselves.

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Ge, Shuzhi S., and Ian Postlethwaite. "Adaptive Neural Network Controller Design for Flexible Joint Robots using Singular Perturbation Technique." Transactions of the Institute of Measurement and Control 17, no. 3 (August 1995): 120–31. http://dx.doi.org/10.1177/014233129501700304.

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In this paper, an adaptive neural network controller is presented for flexible joint robots using Singular Perturbation techniques by modelling the elastic forces as the fast variables and link variables as slow variables. The neural network controller is to control the slow dynamics in order to eliminate the tedious preliminary computation of the regressor matrix. Unlike many neural network (NN) controllers in the literature, inverse dynamical model evaluation is not required and no time-consuming training process is necessary except for initialising the NNs based on approximate function values at the initial posture at time t = 0. It can be shown that the controller can control the system successfully by intensive computer simulation tests.

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Cong, Zhang, and Wu Yun-jie. "Non-singular terminal dynamic surface control based integrated guidance and control design and simulation." ISA Transactions 63 (July 2016): 112–20. http://dx.doi.org/10.1016/j.isatra.2016.03.013.

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Shahravi, Morteza, and Milad Azimi. "Attitude and Vibration Control of Flexible Spacecraft Using Singular Perturbation Approach." ISRN Aerospace Engineering 2014 (May 29, 2014): 1–13. http://dx.doi.org/10.1155/2014/163870.

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This paper addresses a composite two-time-scale control system for simultaneous three-axis attitude maneuvering and elastic mode stabilization of flexible spacecraft. By choosing an appropriate time coordinates transformation system, the spacecraft dynamics can be divided into double time-scale subsystems using singular perturbation theory (SPT). Attitude and vibration control laws are successively designed by considering a time bandwidths separation between the oscillatory flexible parts motion describing a fast subsystem and rigid body attitude dynamics as a slow subsystem. A nonlinear quaternion feedback control, based on modified sliding mode (MSM), is chosen for attitude control design and a strain rate feedback (SRF) scheme is developed for suppression of vibrational modes. In the attitude control law, the modification to sliding manifold for slow subsystem ensures that the spacecraft follows the shortest possible path to the sliding manifold and highly reduces the switching action. Stability proof of the overall closed-loop system is given via Lyapunov analysis. The proposed design approach is demonstrated to combine excellent performance in the compensation of residual flexible vibrations for the fully nonlinear system under consideration, as well as computational simplicity.

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Yuan, Chengren, Changgeng Shuai, Yuan Fang, and Jianguo Ma. "Decoupled Planes’ Non-Singular Adaptive Integral Terminal Sliding Mode Trajectory Tracking Control for X-Rudder AUVs under Time-Varying Unknown Disturbances." Journal of Marine Science and Engineering 10, no. 10 (October 2, 2022): 1408. http://dx.doi.org/10.3390/jmse10101408.

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This paper analyzes the trajectory tracking problem in decoupled planes for X-rudder AUVs under time-varying, unknown environmental interferences. The proposed scheme consists of the kinematic control law based on the compound line-of-sight guidance law and the dynamic control law based on a non-singular adaptive integral terminal sliding mode control (NAITSMC) to avoid the chattering problems, parameter perturbation, and time-varying disturbances. Meanwhile, we introduce a reduced-order extended state observer (RESO) to compensate for unknown ocean currents by the first-order Gauss–Markov process. We verify the whole system of the proposed scheme through global asymptotic stability, then present a set of numerical simulations revealing robustness and adaptability performances in decoupled planes.

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Liao, Zhiming, Yue Hao, Tao Guo, Bingxin Lv, and Qiang Wang. "Second-Order Sliding Mode Control of Permanent Magnet Synchronous Motor Based on Singular Perturbation." Energies 15, no. 21 (October 28, 2022): 8028. http://dx.doi.org/10.3390/en15218028.

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The second-order sliding mode control has strong robustness. Its application has greatly improved the anti-jamming ability of permanent magnet synchronous motor(PMSM) speed control systems. However, the influence of noise is unavoidable due to the introduction of a differentiator in the second-order sliding mode control, and the steady-state performance of the system is poor due to the absence of a q-axis current loop. This paper proposes a second-order sliding mode control method based on singular perturbation, which decouples the PMSM speed control system into two subsystems, the slow subsystem, including the speed variable, adopts second-order sliding mode control, and the fast subsystem, including the current variable of q-axis, adopts linear control. The design of a sliding surface for the slow subsystem avoids the application of the differentiator, which reduces the chattering better. Besides this, the steady-state performance of the system is improved due to the introduction of the feedback current of the q-axis. Experimental results show that the proposed method has strong robustness and can achieve high-precision control.

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Liu, Shu Qing, Qian Jia, and Hao Zhou. "Composite Controller Design for Rigid-Flexible Coupling Mechanical System." Applied Mechanics and Materials 722 (December 2014): 258–61. http://dx.doi.org/10.4028/www.scientific.net/amm.722.258.

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A dynamic model in singular perturbation form is established for the deformation and vibration of rigid-flexible coupling mechanical system due to the drive force, inertia force and gravity. This model is divided into slow subsystem and fast subsystem. A PD controller is designed for slow subsystem while optimal controller for fast subsystem and a composite controller is developed based on this. The validity of the composite controller is verified through MATLAB simulation with a flexible scissor-like deployable mechanism as an example. The results can be used in control of CNC machine, robot, spatial mechanism etc.

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Bizzo, Bruno Salgado, Guilherme Araujo Pimentel, Rafael da Silveira Castro, and Ricardo Pérez-Ibacache. "Model reduction and feedback design based on singular perturbation method applied to a lumped DER-microgrid model." International Journal of Electrical Power & Energy Systems 132 (November 2021): 107154. http://dx.doi.org/10.1016/j.ijepes.2021.107154.

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Yurkevich, Valery D. "PWM Controller Design based on Singular Perturbation Technique: A Case Study of Buck-Boost DC-DC Converter." IFAC Proceedings Volumes 44, no. 1 (January 2011): 9739–44. http://dx.doi.org/10.3182/20110828-6-it-1002.00963.

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Krishnamurthy, Prashanth, and Farshad Khorrami. "A Singular Perturbation Based Global Dynamic High Gain Scaling Control Design for Systems With Nonlinear Input Uncertainties." IEEE Transactions on Automatic Control 58, no. 10 (October 2013): 2686–92. http://dx.doi.org/10.1109/tac.2013.2257968.

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Guan, Jun, and Wenjun Yi. "Integrated Guidance and Control Design for Guided Projectile Using Sliding Mode Method." Journal of Physics: Conference Series 2478, no. 10 (June 1, 2023): 102012. http://dx.doi.org/10.1088/1742-6596/2478/10/102012.

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Abstract According to the characteristics of special launch and flight environment such as high dynamic and large disturbance of guided projectile, the separate design method of traditional guidance system and control system will bring large errors, even affect the stability of the system, and the accuracy of projectile hitting the target is poor. In this paper, the guidance and control integrated control law of guided projectile is designed based on the sliding mode variable structure theory. The correctness, accuracy and stability of the designed control law are verified by numerical simulation. Numerical simulation shows that the guidance control integrated control law designed by sliding mode control theory can still have high control accuracy in the case of large perturbation. At the same time, Monte Carlo simulation shows that this method can meet the needs of engineering.

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MengXiuyun, SongQiaozhen. "Design and Simulation of Guidance Law with Angular Constraint Based on Non-singular Terminal Sliding Mode." Physics Procedia 25 (2012): 1197–204. http://dx.doi.org/10.1016/j.phpro.2012.03.220.

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Zhao, Hongqian, Honghua Dai, and Zhaohui Dang. "Fast guidance method of lunar landing based on dynamic programming." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 39, no. 1 (February 2021): 159–66. http://dx.doi.org/10.1051/jnwpu/20213910159.

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In this paper, a novel multi-stage trajectory transfer and fixed-point landing time optimal guidance method for the lunar surface emergency rescue mission is proposed. Firstly, the whole process motion and dynamics model for the lunar surface emergency rescue with four stages are established. Then, in the initial orbit transfer phase, the Lambert algorithm based on "prediction + correction" is designed for the non spherical gravitational perturbation of the moon. In the powered descent phase, the Hamiltonian function is used to design a time suboptimal explicit guidance law that can be applied in orbit in real time. Finally, aiming at the multi-stage global time optimal guidance, the whole time process guidance law is obtained by establishing the allowable control set for each stage in the whole process. The simulation results show that compared with the piecewise optimal control method, the present method has better optimization effect and shorter whole process time. It is of great significance to the possible emergency rescue mission of manned lunar exploration in the future.

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Hoover, Brett T., Chris S. Velden, and Sharanya J. Majumdar. "Physical Mechanisms Underlying Selected Adaptive Sampling Techniques for Tropical Cyclones." Monthly Weather Review 141, no. 11 (October 25, 2013): 4008–27. http://dx.doi.org/10.1175/mwr-d-12-00269.1.

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Abstract To efficiently and effectively prioritize resources, adaptive observations can be targeted by using some objective criteria to estimate the potential impact an initial condition perturbation (or analysis increment) in a specific region would have on the future forecast. Several objective targeting guidance techniques have been developed, including total-energy singular vectors (TESV), adjoint-derived sensitivity steering vectors (ADSSV), and the ensemble transform Kalman filter (ETKF), all of which were tested during the 2008 The Observing System Research and Predictability Experiment (THORPEX) Pacific Asian Regional Campaign (T-PARC) and the Office of Naval Research Tropical Cyclone Structure-2008 (TCS-08) field experiments. An intercomparison between these techniques is performed in order to find underlying physical mechanisms in the respective guidance products, based on four tropical cyclone (TC) cases from the T-PARC/TCS-08 field campaigns. It is found that the TESV energy norm and the ADSSV response function are largely indirect measures of the TC track divergence that can be produced by an initial condition perturbation, explaining the strong correlation between these products. The downstream targets routinely chosen by the ETKF guidance system are often not found in the TESV and ADSSV guidance products, and it is found that downstream perturbations can affect the steering of a TC through the development of a Rossby wave in the subtropics that modulates the strength of the nearby subtropical ridge. It is hypothesized that the ubiquitousness of these downstream targets in the ETKF is largely due to the existence of large uncertainties downstream of the TC that are not taken into consideration by either the TESV or ADSSV techniques.

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Wang, Yi, Wei-dong Song, Dan Fang, and Qing-wei Guo. "Guidance and Control Design for a Class of Spin-Stabilized Projectiles with a Two-Dimensional Trajectory Correction Fuze." International Journal of Aerospace Engineering 2015 (2015): 1–15. http://dx.doi.org/10.1155/2015/908304.

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A guidance and control strategy for a class of 2D trajectory correction fuze with fixed canards is developed in this paper. Firstly, correction control mechanism is researched through studying the deviation motion, the key point of which is the dynamic equilibrium angle. Phase lag of swerve response is the dominating factor for correction control, and formula is deduced with the Mach number as argument. Secondly, impact point deviation prediction based on perturbation theory is proposed, and the numerical solution and application method are introduced. Finally, guidance and control strategy is developed, and simulations to validate the strategy are conducted.

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Xu, Bin, and Pengchao Zhang. "Composite Learning Sliding Mode Control of Flexible-Link Manipulator." Complexity 2017 (2017): 1–6. http://dx.doi.org/10.1155/2017/9430259.

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This paper studies the control of a flexible-link manipulator with uncertainty. The fast and slow dynamics are derived based on the singular perturbation (SP) theory. The sliding mode control is proposed while the adaptive design is developed using neural networks (NNs) and disturbance observer (DOB) where the novel update laws for NN and DOB are designed. The closed-loop system stability is guaranteed via Lyapunov analysis. The effectiveness of the proposed method is verified via simulation test.

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Yang, Rongrong, Yongjie Ma, Jiali Zhao, Ling Zhang, and Hua Huang. "Automatic Current-Constrained Double Loop ADRC for Electro-Hydrostatic Actuator Based on Singular Perturbation Theory." Actuators 11, no. 12 (December 17, 2022): 381. http://dx.doi.org/10.3390/act11120381.

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For an electro-hydrostatic actuator (EHA), the position, speed, and current cascade three-loop control architecture are dominant in existing active disturbance rejection control (ADRC). However, this architecture suffers from many problems, such as severe noise sensitivity of the extended state observer (ESO), excessive complexity of control structure, and too many tuned parameters, which makes the controller not easy to implement in practice. Aiming at the above drawbacks, a novel cascade double-loop ADRC strategy that is automatic current-constrained is proposed, which makes the whole ADRC architecture simplified to the position and the integrated speed–current double-loop architecture. Firstly, for the position control loop, the singular perturbation theory is used to reasonably reduce the order of the model for the position subsystem of EHA. A reduced order ADRC controller (ROADRC) is synthesized, which not only effectively reduces the noise sensitivity of ESO, but also circumvents use of the actuation acceleration information in the controller design process. Secondly, the integrated speed–current ADRC controller is designed by taking the speed and current subsystems of EHA into synthesis, which avoids the problem of excessive current loop bandwidth in conventional three-loop control architecture, and the number of tuned parameters is significantly reduced. Additionally, an uncomplicated and effective automatic current-constrained ADRC controller (CACADRC) is designed to solve the problem in the integrated speed–current ADRC that the current cannot be automatically constrained. Finally, by comparing the three-loop PI controller with the traditional three-loop ADRC, a detailed simulation analysis is carried out to verify the effectiveness and merits of the proposed controller. The simulation results show that the proposed controller not only inherits the advantages of high precision and strong disturbance rejection performance of the conventional ADRC, but can also efficiently decrease the noise sensitivity of ESO and effectively achieve the current-constrained control.

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Huisinga, Hauke, and Lutz Hofmann. "Order reduction in electrical power systems using singular perturbation in different coordinate systems." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 37, no. 4 (July 2, 2018): 1525–34. http://dx.doi.org/10.1108/compel-08-2017-0360.

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Purpose Efficient calculations of the transient behaviour after disturbances of large-scale power systems are complex because of, among other things, the non-linearity and the stiffness of the overall state equation system (SES). Because of the rising amount of flexible transmission system elements, there is an increasing need for reduced order models with a negligible loss of accuracy. With the Extended Nodal Approach and the application of the singular perturbation method, it is possible to reduce the order of the SES adapted to the respective setting of the desired tasks and accuracy requirements. Design/methodology/approach Based on a differential-algebraic equation for the electric power system which is formulated with the Extended Nodal Approach, the automatic decomposition into reduced order models is shown in this paper. The paper investigates the effects of different coordinate systems for an automatic order reduction with the singular perturbation method, as well as a comparison of results calculated with the full and reduced order models. Findings The eigenvalues of the full system are approximated sufficiently by the three subsystems. A simulation example demonstrates the good agreement between the reduced order models and the full model independent of the choice of the coordinate system. The decomposed subsystems in rotating coordinates have benefits as compared to those in static coordinates. Originality/value The paper presents a systematic decomposition based only on a differential-algebraic equation system of the electric power system into three subsystems.

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Song, Junhong, and Shenmin Song. "Robust impact angle constraints guidance law with autopilot lag and acceleration saturation consideration." Transactions of the Institute of Measurement and Control 41, no. 1 (March 26, 2018): 182–92. http://dx.doi.org/10.1177/0142331218758885.

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In this paper, for the three-dimensional terminal guidance problem of a missile intercepting a manoeuvring target, a robust continuous guidance law with impact angle constraints in the presence of both an acceleration saturation constraint and a second-order-lag autopilot is developed. First, based on non-singular fast terminal sliding mode and adaptive control, a step-by-step backstepping method is used to design the guidance law. In the process of guidance law design, with the use of a finite-time control technique, virtual control laws are developed, a tracking differentiator is used to eliminate the ‘explosion of complexity’ problem inherent in the traditional backstepping method, and an additional system is constructed to deal with the acceleration saturation problem; its states are used for guidance law design and stability analysis. Moreover, the target acceleration is considered bounded disturbance, but the upper bound is not required to be known in advance, whereas the upper bound is estimated online by a designed adaptive law. Next, finite-time stability of the guidance system is strictly proved by using a Lyapunov method. Finally, numerical simulations are presented to demonstrate the excellent guidance performances of the proposed guidance law in terms of accuracy and efficiency.

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Xiong, Genliang, Jingxin Shi, and Haichu Chen. "Cascaded Control of Flexible-Joint Robots Based on Sliding-Mode Estimator Approach." Journal of Robotics 2020 (October 26, 2020): 1–12. http://dx.doi.org/10.1155/2020/8861847.

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The inherent highly nonlinear coupling and system uncertainties make the controller design for a flexible-joint robot extremely difficult. The goal of the control of any robotic system is to achieve high bandwidth, high accuracy of trajectory tracking, and high robustness, whereby the high bandwidth for flexible-joint robot is the most challenging issue. This paper is dedicated to design such a link position controller with high bandwidth based on sliding-mode technique. Then, two control approaches ((1) extended-regular-form approach and (2) the cascaded control structure based on the sliding-mode estimator approach) are presented for the link position tracking control of flexible-joint robot, considering the dynamics of AC-motors in robot joints, and compared with the singular perturbation approach. These two-link position controllers are tested and verified by the simulation studies with different reference trajectories and under different joint stiffness.

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Zhao, F. J., and H. You. "New three-dimensional second-order sliding mode guidance law with impact-angle constraints." Aeronautical Journal 124, no. 1273 (December 3, 2019): 368–84. http://dx.doi.org/10.1017/aer.2019.130.

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AbstractAiming at the issue of missiles attacking on-ground maneuvering targets in three-dimensional space, a three-dimensional finite-time guidance law with impact-angle constraints is proposed. In order to improve convergence speed and restrain chattering phenomenon, the nonsingular fast terminal three-dimensional second-order sliding mode guidance law with coupling terms is designed based on the theory of nonhomogeneous fast terminal sliding surface and second-order sliding mode control. The system model need not be linearized during the design process, and the singular problem is avoided. A nonhomogeneous disturbance observer is designed to estimate and compensate the total disturbance, which is caused by target maneuvering information and coupling terms of line of sight. And the stability and finite-time convergence of the guidance law are proved strictly and mathematically. Finally, simulation results have verified the effectiveness and superiority of the proposed guidance law.

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Soo, Von-Wun, and Tse-Ching Wang. "Integration of qualitative and quantitative reasoning in iterative parametric mechanical design." Artificial Intelligence for Engineering Design, Analysis and Manufacturing 6, no. 2 (May 1992): 95–109. http://dx.doi.org/10.1017/s0890060400002985.

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A framework IPD (Iterative Parametric Design) is proposed to assist the iterative parametric mechanical design process. To effectively find a set of satisfiable values for the design parameters the key is to find good heuristics to adjust or tune the parametric values resulting from previous design iterations. We propose that heuristics can come from two aspects by both qualitative and quantitative reasoning. Qualitative reasoning, based on confluences, provides global control over the feasible directions of variable adjustments, while quantitative reasoning, based on the dependency network and perturbation analysis, can be used to propose actual quantity of local variable adjustments. We used the design of a helical compression spring as an example to illustrate the performance of IPD system. We show that IPD can often find a solution faster than those without guidance of qualitative and quantitative reasoning.

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Yeh, Chi-An, and Kunihiko Taira. "Resolvent-analysis-based design of airfoil separation control." Journal of Fluid Mechanics 867 (March 26, 2019): 572–610. http://dx.doi.org/10.1017/jfm.2019.163.

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We use resolvent analysis to design active control techniques for separated flows over a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of$23\,000$and a free-stream Mach number of$0.3$are considered at two post-stall angles of attack of$6^{\circ }$and$9^{\circ }$. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. To provide physics-based guidance for the effective choice of these control input parameters, we conduct global resolvent analysis on the baseline turbulent mean flows to identify the actuation frequency and wavenumber that provide large perturbation energy amplification. The present analysis also considers the use of a temporal filter to limit the time horizon for assessing the energy amplification to extend resolvent analysis to unstable base flows. We incorporate the amplification and response mode from resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. This metric is compared to the results from a large number of three-dimensional large-eddy simulations of open-loop controlled flows. With the agreement between the resolvent-based metric and the enhancement of aerodynamic performance found through large-eddy simulations, we demonstrate that resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. We believe that the present resolvent-based approach provides a promising path towards mean flow modification by capitalizing on the dominant modal mixing.

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Liu, Sheng, Changkui Xu, and Lanyong Zhang. "Robust Course Keeping Control of a Fully Submerged Hydrofoil Vessel with Actuator Dynamics: A Singular Perturbation Approach." Mathematical Problems in Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/6402012.

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This paper presents a two-time scale control structure for the course keeping of an advanced marine surface vehicle, namely, the fully submerged hydrofoil vessel. The mathematical model of course keeping control for the fully submerged hydrofoil vessel is firstly analyzed. The dynamics of the hydrofoil servo system is considered during control design. A two-time scale model is established so that the controllers of the fast and slow subsystems can be designed separately. A robust integral of the sign of the error (RISE) feedback control is proposed for the slow varying system and a disturbance observer based state feedback control is established for the fast varying system, which guarantees the disturbance rejection performance for the two-time scale systems. Asymptotic stability is achieved for the overall closed-loop system based on Lyapunov stability theory. Simulation results show the effectiveness and robustness of the proposed methodology.

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Zhu, G., S. S. Ge, and T. H. Lee. "Simulation studies of tip tracking control of a single-link flexible robot based on a lumped model." Robotica 17, no. 1 (January 1999): 71–78. http://dx.doi.org/10.1017/s0263574799000971.

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In this paper, tip tracking control of a single-link flexible robot is studied through computer simulations. The controller investigated is of a two-loop PD type, which is deduced from a control approach originally developed for elastic joint robots. A very simple model, with the flexible link of the robot being lumped to a spring-mass unit, is employed for the controller design. Bounded Input and Bounded Output (BIBO) stable tip tracking performance is guaranteed. The controller is robustly stable under system parameter uncertainties, and is comparatively easy to implement. In the simulations, different payloads are considered, and the system performance is compared with the traditional Singular Perturbation (SP) method. The simulation results show that the PD type controller designed based on the simple lumped model is able to provide quite satisfactory performance.

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Yoo, Heonjong, and Zoran Gajic. "New Designs of Reduced-Order Observer-Based Controllers for Singularly Perturbed Linear Systems." Mathematical Problems in Engineering 2017 (2017): 1–14. http://dx.doi.org/10.1155/2017/2859548.

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The slow and fast reduced-order observers and reduced-order observer-based controllers are designed by using the two-stage feedback design technique for slow and fast subsystems. The new designs produce an arbitrary order of accuracy, while the previously known designs produce the accuracy of O(ϵ) only where ϵ is a small singular perturbation parameter. Several cases of reduced-order observer designs are considered depending on the measured state space variables: only all slow variables are measured, only all fast variables are measured, and some combinations of the slow and fast variables are measured. Since the two-stage methods have been used to overcome the numerical ill-conditioning problem for Cases (III)–(V), they have similar procedures. The numerical ill-conditioning problem is avoided so that independent feedback controllers can be applied to each subsystem. The design allows complete time-scale separation for both the reduced-order observer and controller through the complete and exact decomposition into slow and fast time scales. This method reduces both offline and online computations.

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Dana Karimtaevna, Satybaldina, and Kalmаganbetova Zhuldyzay Asylbekkyzy. "Robust control for a tracking electromechanical system." International Journal of Electrical and Computer Engineering (IJECE) 12, no. 5 (October 1, 2022): 4883. http://dx.doi.org/10.11591/ijece.v12i5.pp4883-4891.

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<p>A strategy for the design of robust control of tracking electromechanical systems based on 𝐻∞ synthesis is proposed. Proposed methods are based on the operations on frequency characteristics of control systems designed and developed using the MATLAB robust control toolbox. Determination of the singular values for a transfer matrix of the control system reduces the disturbances and guarantees its stability margin. For selecting the weighted transfer functions, the basic recommendations are formulated. The efficiency of the proposed approach is verified by robust control of an elastically coupled two-mass system whose parameter values are adjusted by matching them with the parameters of one of the supplied robots. The simulation results confirm that the proposed strategy of design of robust control of two-mass elastic coupling system using the 𝐻∞ synthesis is very efficient and significantly reduces the perturbation of parameters of the controlled plant.</p>

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Ju, Jinyong, Wei Li, Yuqiao Wang, Mengbao Fan, and Xuefeng Yang. "Two-Time Scale Virtual Sensor Design for Vibration Observation of a Translational Flexible-Link Manipulator Based on Singular Perturbation and Differential Games." Sensors 16, no. 11 (October 28, 2016): 1804. http://dx.doi.org/10.3390/s16111804.

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Lai, Chao, Weihong Wang, Zhenghua Liu, and Zheng Ma. "Three-dimensional integrated guidance and control for terminal angle constrained attack against ground maneuvering target." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 7 (May 29, 2018): 2393–412. http://dx.doi.org/10.1177/0954410018778988.

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A neuro-adaptive fast terminal sliding-mode dynamic surface control method based on a finite-time stable nonlinear extended state observer is applied to integrated guidance and control design for skid-to-turn missile attacking a ground maneuvering target with terminal angle constraints. A three-dimensional integrated guidance and control design model against a maneuvering target for skid-to-turn missile is established without the assumption that the missile velocity vector and the line of sight coincide with each other. The non-singular fast terminal sliding surface is applied to construct the first error surface of dynamic surface control and the first virtual control law is designed to guarantee hitting accuracy with desired terminal angles. The finite-time stable nonlinear extended state observer is designed separately to estimate uncertainties in the system. And the neuro-adaptive technique is applied to compensate estimation errors of nonlinear extended state observer by training a three-layer feedforward neural network online. Synthesizing all of above, a neuro-adaptive fast terminal sliding-mode dynamic surface control based on nonlinear extended state observer is derived on Lyapunov stability theory, which guarantees stability of the system. Finally, the numerical simulations are conducted to demonstrate the effectiveness of the proposed three-dimensional integrated guidance and control scheme.

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Chandran, Karthik, Weidong Zhang, Rajalakshmi Murugesan, S. Prasanna, A. Baseera, and Sanjeevi Pandiyan. "Adaptive Decentralized Tracking Control for Nonlinear Large-Scale Systems." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, Supp02 (December 2020): 93–110. http://dx.doi.org/10.1142/s0218488520400176.

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Decentralized Model Reference Adaptive Control problems are investigated for a class of linear time-invariant two time-scale model, having fast and slow dynamics and unmatched interconnections. Design of full state feedback controller is a critical task to the system having interrelated dynamics and nonlinear interconnections of time varying lags, however, can be addressed by singular perturbation procedures and time scale modeling. In this research, full order observer-based state feedback control is designed to two-time scale system to ensure the stability of the closed loop system. Then, decentralized model reference adaptive controller with the novel reference model is designed to individual subsystems. It is found that the proposed design enforces the system states to track the reference state asymptotically. To investigate the proposed design, an example of drying process is considered. Simulation results are analyzed to confirm the efficacy of the proposed control scheme.

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Kim, In Hyuk, and Young Ik Son. "Design of a Low-Order Harmonic Disturbance Observer with Application to a DC Motor Position Control." Energies 13, no. 5 (February 25, 2020): 1020. http://dx.doi.org/10.3390/en13051020.

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Among various tools implemented to counteract undesired effects of time-varying uncertainties, disturbance observer (DOB)-based controller has gained wide popularity as a result of its flexibility and efficacy. In this paper, a low-order DOB that is capable of compensating for the effects of a biased harmonic disturbance, as well as plant uncertainties is presented. The proposed low-order DOB can asymptotically estimate a harmonic disturbance of known frequency but unknown amplitude and phase, by using measurable output variables. An analysis carried out by using the singular perturbation theory shows that the nominal performance of the system can be recovered from a real uncertain system when the observer gain is sufficiently large. The observer gains that result in the performance recovery of the real uncertain system are obtained from the stability condition of the boundary-layer system. To test the performance of the proposed observer, computer simulations with a numerical example and laboratory experiments using a DC motor system have been carried out. The experimental results show that the proposed low-order DOB-based control scheme can provide enhanced performance.

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Journal articles on the topic 'Singular Perturbation based guidance design'

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