Zeitschriftenartikel: „Switching point control“

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Branco, P. Daniel, Gregory Yablonsky, Guy B. Marin und Denis Constales. „The switching point between kinetic and thermodynamic control“. Computers & Chemical Engineering 125 (Juni 2019): 606–11. http://dx.doi.org/10.1016/j.compchemeng.2016.06.022.

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Jun, Eun-Su, und Sangshin Kwak. „A Highly Efficient Single-Phase Three-Level Neutral Point Clamped (NPC) Converter Based on Predictive Control with Reduced Number of Commutations“. Energies 11, Nr. 12 (18.12.2018): 3524. http://dx.doi.org/10.3390/en11123524.

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This paper proposes a highly efficient single-phase three-level neutral point clamped (NPC) converter operated by a model predictive control (MPC) method with reduced commutations of switches. The proposed method only allows switching states with none or a single commutation at the next step as candidates for future switching states for the MPC method. Because the proposed method preselects switching states with reduced commutations when selecting an optimal state at a future step, the proposed method can reduce the number of switchings and the corresponding switching losses. Although the proposed method slightly increases the peak-to-peak variations of the two dc capacitor voltages, the developed method does not deteriorate the input current quality and input power factor despite the reduced number of switching numbers and losses. Thus, the proposed method can reduce the number of switching losses and lead to high efficiency, in comparison with the conventional MPC method.

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Rustamov, G. A., M. B. Namazov, A. Y. Gasimov und R. G. Rustamov. „Control of Dynamic Objects in the Conditions of Uncertainty in the Point Sliding Mode“. Mekhatronika, Avtomatizatsiya, Upravlenie 20, Nr. 12 (06.12.2019): 714–22. http://dx.doi.org/10.17587/mau.20.714-722.

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There is development of the well-known sliding mode, which in the classical formulation didn’t find the development to be applied to control systems discussed. Alternatively, there is method of organizing one of the uniformity of the sliding mode called the "point sliding mode" proposed. The distinctive feature of this mode is that here the control gaps occur at time-equal points of the switching line (hyperplane) which allows the origin of coordinates for a finite number of switches. The possibility of changing the time interval between these points makes it possible to obtain various modes: a finite mode, in which a given point is reached from any initial state in one switch, and in this mode the switch line is "isochronous"; point sliding mode in which a given point is reached in a finite number of switchings; limit mode, when the length of time intervals tend to zero, and the switching frequency to infinity. Considering this feature the concept of "degree of slip" is introduced. It is shown that in the case of forced movement in the SPS, a sliding motion is observed, which does not allow for ensuring invariance with respect to external disturbances. There are two ways to eliminate the forced component of the movement offered. One of the advantages of using a point sliding mode is that, in order to improve performance, it is not necessary to use a boundary layer, which is realized by entering various logical conditions into the control algorithm. The practical significance of a point sliding mode lies in the fact that, with a small switching frequency, it is possible to maintain the quality indices of an undefined object within an acceptable interval. The studies were conducted for onedimensional second-order linear systems (SISO). Results can be generalized for higher order multidimensional systems. Solution of model problems on MATLAB / Simulink allows us to make a number of positive conclusions that are of great practical importance in terms of expanding the area of use of skipping modes, especially in relation to the management of undefined objects.

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Fang, Ji Wen, Zhi Li Long, Lu Fan Zhang, Jian Dong Cai und Long Sheng Nian. „Control Analysis of Point-to-Point Positioning Based on Macro-Micro Stage“. Applied Mechanics and Materials 278-280 (Januar 2013): 1563–69. http://dx.doi.org/10.4028/www.scientific.net/amm.278-280.1563.

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Macro-micro stage can achieve large travel range and high precision positioning. The macro stage is driven by voice coil motor (VCM). The micro stage is actuated by the piezoelectric (PZT). The positioning theory of macro-micro stage is described. In this paper, the compensating method of point-to-point (PTP) positioning is divided into two types: compensation before steady state (CBS) and compensation after steady state (CAS). The different control strategies are applied to meet CAS and CBS. Because of the structure of macro-micro stage and the saturation of micro stage, switching control plays an important role in realizing high precision PTP motion. When the error of the macro stage is less than the threshold and also the system meets the switching conditions, the compensation signal is sent to the PZT control loop for high resolution compensation. Finally, the numerical simulation results show that the positioning accuracy of dual stage is higher than single macro stage and can reach nanometer scale.

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Karamanakos, Petros, Peter Stolze, Ralph M. Kennel, Stefanos Manias und Hendrik du Toit Mouton. „Variable Switching Point Predictive Torque Control of Induction Machines“. IEEE Journal of Emerging and Selected Topics in Power Electronics 2, Nr. 2 (Juni 2014): 285–95. http://dx.doi.org/10.1109/jestpe.2013.2296794.

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Wang, Lu Jun, Tao Gong und Jun Zhu. „Robust Predictive Control for NPC Grid-Connected Inverters“. Applied Mechanics and Materials 668-669 (Oktober 2014): 522–25. http://dx.doi.org/10.4028/www.scientific.net/amm.668-669.522.

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In this paper, the state space model of neutral point clamped three-level grid-connected inverter is detailed derived and an Robust Predictive Control (RPC) method is proposed. In the proposed method, the total 27 switching vectors composed of a finite set from which the optimal switching vector is selected according to a cost function. The robust performance is improved just by increasing switching frequency. Experimental results show that the proposed method has a flexible control purposes and we can optimize the synthesize performance just by adjusting weighting coefficients of cost function. In addition, RPC controller has a robust performance in tracking output reference current and balancing neutral point voltage.

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Ahmed, Mostafa, Ibrahim Harbi, Ralph Kennel, José Rodríguez und Mohamed Abdelrahem. „Maximum Power Point Tracking-Based Model Predictive Control for Photovoltaic Systems: Investigation and New Perspective“. Sensors 22, Nr. 8 (16.04.2022): 3069. http://dx.doi.org/10.3390/s22083069.

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In this paper, a comparative review for maximum power point tracking (MPPT) techniques based on model predictive control (MPC) is presented in the first part. Generally, the implementation methods of MPPT-based MPC can be categorized into the fixed switching technique and the variable switching one. On one side, the fixed switching method uses a digital observer for the photovoltaic (PV) model to predict the optimal control parameter (voltage or current). Later, this parameter is compared with the measured value, and a proportional–integral (PI) controller is employed to get the duty cycle command. On the other side, the variable switching algorithm relies on the discrete-time model of the utilized converter to generate the switching signal without the need for modulators. In this regard, new perspectives are inspired by the MPC technique to implement both methods (fixed and variable switching), where a simple procedure is used to eliminate the PI controller in the fixed switching method. Furthermore, a direct realization technique for the variable switching method is suggested, in which the discretization of the converter’s model is not required. This, in turn, simplifies the application of MPPT-based MPC to other converters. Furthermore, a reduced sensor count is accomplished. All conventional and proposed methods are compared using experimental results under different static and dynamic operating conditions.

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Sone, Satoru, und Hitomi Irinatsu. „Precise control of switching time point of power semiconductor devices.“ IEEJ Transactions on Power and Energy 106, Nr. 3 (1986): 249–54. http://dx.doi.org/10.1541/ieejpes1972.106.249.

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Matoglu, Melda Ormeci, John H. Vande Vate und Haiyue Yu. „The economic average cost Brownian control problem“. Advances in Applied Probability 51, Nr. 01 (März 2019): 300–337. http://dx.doi.org/10.1017/apr.2019.12.

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AbstractIn this paper we introduce and solve a generalization of the classic average cost Brownian control problem in which a system manager dynamically controls the drift rate of a diffusion process X. At each instant, the system manager chooses the drift rate from a pair {u, v} of available rates and can invoke instantaneous controls either to keep X from falling or to keep it from rising. The objective is to minimize the long-run average cost consisting of holding or delay costs, processing costs, costs for invoking instantaneous controls, and fixed costs for changing the drift rate. We provide necessary and sufficient conditions on the cost parameters to ensure the problem admits a finite optimal solution. When it does, a simple control band policy specifying economic buffer sizes (α, Ω) and up to two switching points is optimal. The controller should invoke instantaneous controls to keep X in the interval (α, Ω). A policy with no switching points relies on a single drift rate exclusively. When there is no cost to change the drift rate, a policy with a single switching point s indicates that the controller should change to the slower drift rate when X exceeds s and use the faster drift rate otherwise. When there is a cost to change the drift rate, a policy with two switching points s < S indicates that the controller should maintain the faster drift rate until X exceeds S and maintain the slower drift rate until X falls below s.

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Szular, Zbigniew, Bartosz Rozegnal und Witold Mazgaj. „A New Soft-Switching Solution in Three-Level Neutral-Point-Clamped Voltage Source Inverters“. Energies 14, Nr. 8 (16.04.2021): 2247. http://dx.doi.org/10.3390/en14082247.

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This paper presents a new soft-switching solution recommended for three-level neutral-point-clamped inverters. The operation principles of the proposed solution, working stages, selection of elements, and the control algorithm are comprehensively discussed herein. The control method of the inverter main switches is the same as that of the switches of an inverter operating according to the hard-switching technique. The correctness of the proposed solution was confirmed by the results of different tests using a laboratory neutral-point-clamped inverter with rated parameters of 3 kW, 2 × 150 V, 12 A, and 3 kHz. Numerical analyses were performed for the inverter of rated power 1.2 MW. The switching losses of the inverter operating with the proposed solution were compared with those of an inverter with hard-switching method. The proposed soft-switching solution increased the inverter efficiency and its competitiveness in relation to other proposals because there were no connections between switches and capacitors or inductors, which pose a risk of damaging the inverter when disturbances in the control system appear.

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Afkar, Mohammad, Roghayeh Gavagsaz-Ghoachani, Matheepot Phattanasak, Serge Pierfederici und Wiset Saksiri. „Local-Stability Analysis of Cascaded Control for a Switching Power Converter“. Journal of Robotics and Control (JRC) 5, Nr. 1 (24.01.2024): 160–72. http://dx.doi.org/10.18196/jrc.v5i1.20302.

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Switching power converters are integral in various applications like transportation and renewable energy. After their design, ensuring stable closed-loop poles is critical to maintain safe operating conditions. This study focuses on a switching DC-DC boost converter with a cascade control approach using an energy controller for the outer loop and indirect-sliding mode control for the inner loop. The research objective involves investigating stability through eigenvalue evaluation at different operating points. A large-signal average model is applied to make controlled performance independent of the operating point by fixing system poles. Nonlinear controllers, specifically indirect-sliding mode control, are chosen for their robustness, constant switching frequency, and implementation ease. Results indicate that insufficient decoupling leads to eigenvalue displacement, impacting control parameter choices. The research contribution is investigating the local stability of cascaded control, considering its advantageous implications for both performance and design. This study contributes to the understanding of switching power converters' stability, emphasizing the proposed methodology's broader applicability to diverse converter structures. The proposed approach, applicable to various switching power converters, sheds light on the importance of proper decoupling between outer and inner loop dynamics.

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Ying, Zi. „Three-level ANPC rectifier loss calculation and balance control method“. Journal of Physics: Conference Series 2561, Nr. 1 (01.08.2023): 012020. http://dx.doi.org/10.1088/1742-6596/2561/1/012020.

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Abstract Traditional three-level neutral-point clamped converter has the problem of the uneven loss distribution, which restricts the increase of converter capacity. Three-level active neutral-point clamped (3L-ANPC) converter can reduce the imbalance of power device loss distribution. At present, three traditional SPWM modulation strategies are used in single-phase three-level ANPC modulation. Considering the loss distribution, it is generally required to input the current and voltage sampling values in real-time and calculate the temperature of the switching device online for control or collect the temperature of the switching device in real-time for feedback control, which is more complicated to realize. This paper proposes a modulation scheme based on two carrier cycles, combined with traditional SPWM1 and 2, to analyze the switching conditions and loss characteristics of each switching device in this scheme. The simulation of a single-phase three-level ANPC rectifier was built, and the experiment was carried out on the Yuankuan HIL semi-physical platform. The results show that this scheme is simple, easy to implement, and can effectively reduce the loss distribution imbalance.

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Mesquita da Silva, Julio Alves, Grace Silva Deaecto und Tarcio Andre dos Santos Barros. „Analysis and Design Aspects of Min-Type Switching Control Strategies for Synchronous Buck–Boost Converter“. Energies 15, Nr. 7 (22.03.2022): 2302. http://dx.doi.org/10.3390/en15072302.

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This paper presents a comparative study among switching control strategies for Buck–Boost converters, taking into account essential aspects in practical implementations, as the switching frequency variation concerning different output voltages and the responses in the transient and steady-states. More specifically, we have considered three switching strategies of min-type, where two of them permit high switching frequencies, while the other considers a limited frequency control strategy. Moreover, we have generalized the control techniques available in the literature to make them able to operate under changes in the equilibrium points without the need for a redesign. A conventional PI controller based on pulse-width modulation (PWM) is adopted for comparison purposes. In contrast to PWM-based control, which operates in the maximum switching frequency, the min-type strategies present variation in the switching frequency that depends on the operation point and may lead to a power loss reduction when compared to conventional techniques. To assure zero-error operation in the steady-state, a correction method is proposed. Experimental tests were made to compare the transient and steady-state responses of these control methodologies, verify the variation of the switching frequency according to the output voltages and the robustness concerning load variations.

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Shishkov, Alexander N., Maxim M. Dudkin und Van Kan Le. „Influence of switching sequences on the neutral point voltage balance in a three-level voltage source invertor“. Izvestiya MGTU MAMI 17, Nr. 2 (27.09.2023): 195–206. http://dx.doi.org/10.17816/2074-0530-125204.

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BACKGROUND:Ensuring the voltage balance of the neutral point of the DC link within acceptable limits is one of the mandatory requirements during the operation of a three-level autonomous neutral point clamped voltage source inverter. It is known that neutral point voltage imbalance can adversely affect the operation of the inverter and the load at all, lead to the failure of both power switches and capacitors in the DC link. Neutral point voltage imbalance mostly often occurs due to the asymmetry of the nominal values of DC capacitors, inconsistent properties of switching devices, asymmetric three-phase load, and also due to the imperfection of the converter control algorithm. AIMS:Selection of the optimal switching sequence that ensures the smallest deviation of the neutral point voltage and the number of switching of power switches in a three-level voltage source inverter. METHODS:For an objective comparison of the considered switching sequences and their influence on the neutral point voltage balance, a simulation model of a three-level neutral point clamped voltage source inverter was developed in theMATLAB/Simulinksoftware. To control this inverter, a space vector modulation method was used with three different switching sequences: five-segment, seven-segment and standard. RESULTS:The topology of a three-level neutral point clamped voltage source inverter is presented. The experimental dependencies of the neutral point voltage deviation error was taken with a change in the modulation coefficient, the frequency of the fundamental harmonic at the inverter output, and load characteristics for three different switching sequences. CONCLUSIONS:In this paper, the influence of the basic vectors and the influence of switching sequences on the neutral point voltage balance are studied. Combinations of states of large and zero basic vectors do not affect the neutral point voltage. For the medium basic vectors, the neutral point voltage can increase or decrease depending on the operating conditions of the inverter. The small basic vectors significantly affect the neutral point voltage. Considering the abovementioned, the seven-segment sequence that ensures both the optimal balance of the neutral point voltage and the level of switching losses should be considered as the best switching sequence for a three-level inverter.

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Rao, Sura Srinivasa, und Choppavarapu Sai Babu. „Voltage Compensation Using Dvr with Modified Switching Band Control“. International Journal of Engineering & Technology 7, Nr. 4.24 (27.11.2018): 53. http://dx.doi.org/10.14419/ijet.v7i4.24.21855.

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This paper presents mitigation of voltage related Power Quality (PQ) issues by using Dynamic Voltage Restorer (DVR). Three phase four wire DVR with modified switching band controller is proposed. A modified filter circuit band controller is proposed for reducing the switching losses, constant switching frequency maintenance and corresponding simulation studies are carried out. Variable hysteresis band (modified band) controller generates accurate injected voltages by using system parameters and low error value between reference injected voltages, actual injected voltages can be achieved, which helps in smoothening and minimizing ripples in PCC (Point of common coupling) voltages. The obtained simulation results are presented.

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Takahata, Akihiko, Kenko Uchida und Utaro Taira. „Minimum Energy type of Air Conditioning Control by Switching Equilibrium Point of Control Variables“. IEEJ Transactions on Electronics, Information and Systems 123, Nr. 9 (2003): 1597–604. http://dx.doi.org/10.1541/ieejeiss.123.1597.

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Sahu, M. K., A. K. Panda und B. P. Panigrahi. „Direct Torque Control for Three-Level Neutral Point Clamped Inverter-Fed Induction Motor Drive“. Engineering, Technology & Applied Science Research 2, Nr. 2 (11.04.2012): 201–8. http://dx.doi.org/10.48084/etasr.117.

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Direct torque control (DTC) is a control technique in AC drive systems to obtain high performance torque control. The classical DTC drive contains a pair of hysteresis comparators and suffers from variable switching frequency and high torque ripple. These problems can be solved by using space vector depending on the reference torque and flux. In this paper the space vector modulation technique is applied to the three-level Neutral Point Clamped (NPC) inverter control in the proposed DTC-based induction motor drive system, resulting to a significant reduce of torque ripple. Three-level neutral point clamped inverters have been widely used in medium voltage applications. This type of inverters have several advantages over standard two-level VSI, such as greater number of levels in the output voltage waveforms, less harmonic distortion in voltage and current waveforms and lower switching frequencies. This paper emphasizes the derivation of switching states using the Space Vector Pulse Width Modulation (SVPWM) technique. The control scheme is implemented using Matlab/Simulink. Experimental results using dSPACE validate the steady-state and the dynamic performance of the proposed control strategy.

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Kashiri, Navvab, Mohammad Ghasemi und Morteza Dardel. „An iterative method for time optimal control of dynamic systems“. Archives of Control Sciences 21, Nr. 1 (01.01.2011): 5–23. http://dx.doi.org/10.2478/v10170-010-0029-0.

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An iterative method for time optimal control of dynamic systemsAn iterative method for time optimal control of a general type of dynamic systems is proposed, subject to limited control inputs. This method uses the indirect solution of open-loop optimal control problem. The necessary conditions for optimality are derived from Pontryagin's minimum principle and the obtained equations lead to a nonlinear two point boundary value problem (TPBVP). Since there are many difficulties in finding the switching points and in solving the resulted TPBVP, a simple iterative method based on solving the minimum energy solution is proposed. The method does not need finding the switching point so that the resulted TPBVP can be solved by usual algorithms such as shooting and collocation. Also, since the solution of TPBVPs is sensitive to initial guess, a short procedure for making the proper initial guess is introduced. To this end, the accuracy and efficiency of the proposed method is demonstrated using time optimal solution of some systems: harmonic oscillator, robotic arm, double spring-mass problem with coulomb friction and F-8 aircraft.

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Yang, Dong, Guangdeng Zong und Jun Zhao. „H∞ fault-tolerant control for switched linear parameter-varying systems: A parameter and state-dependent switching method with dwell time“. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 233, Nr. 1 (04.04.2018): 18–30. http://dx.doi.org/10.1177/0959651818766220.

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This article discusses the issue of H∞ fault-tolerant control for switched linear parameter-varying systems with actuator failures using the multiple discretized parameter-dependent Lyapunov functions method. A key point of this work is to construct the multiple discretized parameter-dependent Lyapunov functions, which provide an effective tool for avoiding the Zeno behavior generated by the parameter and state-dependent switching approach. This is not a simple extension of traditional multiple Lyapunov functions because of the introduction of external parameter and dwell time. First, a switching strategy depending on the parameter, state and dwell time is proposed, which gets rid of the assumption of finite number of switchings on any finite time. Then, the parameter-dependent controller is designed which, together with the parameter and state-dependent switching law with dwell time, can guarantee the [Formula: see text] performance of the closed-loop switched linear parameter-varying system for all admissible actuator failures. Finally, a turbofan engine example is given to demonstrate the applicability of the main results.

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Zulfin, Muhammad, S. Suherman, Rahmad Fauzi, M. Razali und Maksum Pinem. „Cross-Point Comparison of Multistage Non-Blocking Technologies“. International Journal of Engineering & Technology 7, Nr. 3.2 (20.06.2018): 703. http://dx.doi.org/10.14419/ijet.v7i3.2.15348.

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Multistage switching networks play important role in communication and computer network. They make communication nodes connect to each other. In computer hardware switches connect processors and memories. Initially, switches are arranged as one stage interconnection. As clients are growing, multistage is a must. The finding Clos multistage switching initiated multistage technologies. Benes improves Clos by reducing number of cross-points by using a 2 x 2 switch element and call re-routing. Batcher improves the technology by other way which is sorting destination address. Banyan is then joined to Batcher to simplify routing control. This paper analyses the number of cross-point required in Clos, Benes and Batcher Banyan to accomplish multistage switching architecture of 16, 64, 256, 1024 and 2048 input/output ports. As results, Clos cross-point is in averages 495.24% higher than Benes and 160.30% higher than Batcher Banyan. Clos blocking probabilities are closed to zero. Benes blocking probabilities are conditionally zero. Batcher Banyan blocking probabilities are zero.

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Kadhem, Basim Talib, Sumer Sahib Harden, Osama Yaseen Khudair Alatbee und Khalid M. Abdulhassan. „Improve the energy efficiency of PV systems by installing a soft switching boost converter with MPPT control“. International Journal of Power Electronics and Drive Systems (IJPEDS) 14, Nr. 2 (01.06.2023): 1055. http://dx.doi.org/10.11591/ijpeds.v14.i2.pp1055-1069.

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To improve the energy consumption rate of solar cells and reduce switching loss, a maximum power point tracking (MPPT) control approach is presented to manage the boost converter and achieve soft switching. A method for determining the optimal values of the soft switching boost converter design parameters has been proposed, by determining the ideal values for the inductor, capacitor, and duty cycle of the boost converter with soft switching, this method enables the key matching of the PV system with the DC/DC converter configuration. In addition to presenting an analysis of several MPPT methodologies, the entire design of the PV converter system is also included. This study compares the perturb-and-observe (P&O) method and the incremental conductance (IC) method for maximum power point tracking (MPPT) in the MATLAB/Simulink application. The PV systems with both MPPT algorithms have been simulated beginning with an implemented model of the photovoltaic (PV) array together with the soft switching boost converter and its MPPT control. The simulation results based on irradiance and temperature are then shown. In the end, soft-switching is more efficient than hard-switching, especially when operating at full load.

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Motoi, Naoki, Kenta Sasahara und Atsuo Kawamura. „Switching Control Method for Stable Landing by Legged Robot Based on Zero Moment Point“. Journal of Robotics and Mechatronics 25, Nr. 5 (20.10.2013): 831–39. http://dx.doi.org/10.20965/jrm.2013.p0831.

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This paper proposes a switching control method to achieve a smooth transition from an edge landing to a sole landing for a legged robot. When a biped robot walks, an undesirable condition at the moment of landing, such as hunting between the ground and the foot, may occur for several reasons. To avoid this condition, this paper focuses on a method that uses simple controllers to ensure a smooth transition from an edge landing to a sole landing. In the event of an edge landing, a force controller should be implemented for a smooth transition to a sole landing. This is because the force controller enables the foot to contact the ground softly. After the landing state is shifted to the sole landing, the control method should be changed to the position controller. Therefore, it is necessary to switch the control method according to the contact condition between the foot and the ground. To avoid the chattering of the controller switching, several hysteresis values are used for the zeromoment point (ZMP) position and ZMP velocity in the switching function. Simulations and experimental results confirmed the validity of the proposed method.

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Domlan, Elom Ayih, José Ragot und Didier Maquin. „Switching Systems: Active Mode Recognition, Identification of the Switching Law“. Journal of Control Science and Engineering 2007 (2007): 1–11. http://dx.doi.org/10.1155/2007/50796.

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The problem of the estimation of the discrete state of a switching system is studied. The knowledge of the switching law is essential for this kind of system as it simplifies their manipulation for control purposes. This paper investigates the use of a model-based diagnosis method for the determination of the active mode at each time point based on the system input/output data. The issue of the parametric identification of the switching law is also addressed.

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Beye, Mamadou Lamine, Thilini Wickramasinghe, Jean François Mogniotte, Luong Viêt Phung, Nadir Idir, Hassan Maher und Bruno Allard. „Active Gate Driver and Management of the Switching Speed of GaN Transistors during Turn-On and Turn-Off“. Electronics 10, Nr. 2 (07.01.2021): 106. http://dx.doi.org/10.3390/electronics10020106.

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The paper investigates the management of drain voltage and current slew rates (i.e., dv/dt and di/dt) of high-speed GaN-based power switches during the transitions. An active gate voltage control (AGVC) is considered for improving the safe operation of a switching cell. In an application of open-loop AGVC, the switching speeds vary significantly with the operating point of the GaN HEMT on either or both current and temperature. A closed-loop AGVC is proposed to operate the switches at a constant speed over different operating points. In order to evaluate the reduction in the electromagnetic disturbances, the common mode currents in the system were compared using the active and a standard gate voltage control (SGVC). The closed-loop analysis carried out in this paper has shown that discrete component-based design can introduce limitations to fully resolve the problem of high switching speeds. To ensure effective control of the switching operations, a response time fewer than 10 ns is required for this uncomplex closed-loop technique despite an increase in switching losses.

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Beye, Mamadou Lamine, Thilini Wickramasinghe, Jean François Mogniotte, Luong Viêt Phung, Nadir Idir, Hassan Maher und Bruno Allard. „Active Gate Driver and Management of the Switching Speed of GaN Transistors during Turn-On and Turn-Off“. Electronics 10, Nr. 2 (07.01.2021): 106. http://dx.doi.org/10.3390/electronics10020106.

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The paper investigates the management of drain voltage and current slew rates (i.e., dv/dt and di/dt) of high-speed GaN-based power switches during the transitions. An active gate voltage control (AGVC) is considered for improving the safe operation of a switching cell. In an application of open-loop AGVC, the switching speeds vary significantly with the operating point of the GaN HEMT on either or both current and temperature. A closed-loop AGVC is proposed to operate the switches at a constant speed over different operating points. In order to evaluate the reduction in the electromagnetic disturbances, the common mode currents in the system were compared using the active and a standard gate voltage control (SGVC). The closed-loop analysis carried out in this paper has shown that discrete component-based design can introduce limitations to fully resolve the problem of high switching speeds. To ensure effective control of the switching operations, a response time fewer than 10 ns is required for this uncomplex closed-loop technique despite an increase in switching losses.

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Tahir, Zuraidi Md, Auzani Jidin und Mohd Luqman Mohd Jamil. „Multi-carrier switching strategy for high-bandwidth potential balancing control of multilevel inverters“. International Journal of Power Electronics and Drive Systems (IJPEDS) 12, Nr. 4 (01.12.2021): 2384. http://dx.doi.org/10.11591/ijpeds.v12.i4.pp2384-2392.

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This paper confers on investigation of a direct torque control (DTC) of induction motor drive by 3 level neutral point clamp (NPC) multilevel inverter. The imbalance problem may deteriorate the electric drive performances which might cause a short circuit condition. Various balancing control strategies were proposed, however, most of them employed complex space vector modulation (SVM) and hysteresis-based controller that generates variable switching frequencies. The proposed method will offer a reliable balancing control strategy with a constant switching frequency, and moreover, it will provide excellent electric drive performances. This research proposed a new multi carrier switching modulation strategy that establish a high-band-width control for neutral point potential in the NPC inverter. Potency of the proposed high-bandwidth potential balancing strategy is validated through the MATLAB/SIMULINK environment.

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Xin-xin, HU, und Chen Chun-lan. „MSHE-PWM Control of Modular Multilevel Direct Current Transmission System“. Open Electrical & Electronic Engineering Journal 9, Nr. 1 (04.11.2015): 553–59. http://dx.doi.org/10.2174/1874129001509010553.

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In order to optimize the electric energy quality of HVDC access point, a modular multilevel selective harmonic elimination pulse-width modulation (MSHE-PWM) method is proposed. On the basis of keeping the minimum action frequency of the power device, MSHE-PWM method can meet the requirement for accurately eliminating low-order harmonics in the output PWM waveform. Firstly, establish the basic mathematical model of MMC topology and point out the voltage balance control principle of single modules; then, analyze offline gaining principle and realization way of MSHEPWM switching angle; finally, verify MSHE-PWM control performance on the basis of MMC reactive power compensation experimental prototype. The experimental result shows that the proposed MSHE-PWM method can meet such performance indexes as low switching frequency and no lower-order harmonics, and has verified the feasibility and effectiveness thereof for optimizing the electric energy quality of HVDC access point.

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Et. al., M. Sri Lakshmi. „An Adaptive Buffer tradeoff, energy-aware Congestion Control protocol in WSN“. Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, Nr. 3 (11.04.2021): 4880–91. http://dx.doi.org/10.17762/turcomat.v12i3.1993.

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In a Wireless sensor network, network lifetime plays a vital role, wherein regular communication and sensor nodes are positioned at different points. Nodes energy depletion may lead to communication interruption due to unlimited data flow from one point to another; for adequate communication, Nodes energy should be maximized by arranging cutting-edge techniques such as adaptive buffer switching and congestion control significant role. When the incoming data is more wide-ranging than available resources, a congestion situation arises. It results in energy consumption, loss of packets, buffer overflow, and raises end-to-end delay. In this paper, adaptive buffer switching and Congestion Control management are done effectively. Simultaneously, congestion detects based on residual energy, residual buffer space, and sensor nodes conviction level. This methodology shows based on the evaluation of cost, which selects main and spare buffers adaptively. Dynamic buffer switching and swapping are used to enhance the outcome of congestion. Result of the ABETCC approach is compared with the protocol like TCEER and TFCC compared to the data loss ratio and energy consumption

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Campos-Cantón, E. „Chaotic attractors based on unstable dissipative systems via third-order differential equation“. International Journal of Modern Physics C 27, Nr. 01 (Januar 2016): 1650008. http://dx.doi.org/10.1142/s012918311650008x.

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In this paper, we present an approach how to yield 1D, 2D and 3D-grid multi-scroll chaotic systems in [Formula: see text] based on unstable dissipative systems via third-order differential equation. This class of systems is constructed by a switching control law(SCL) changing the equilibrium point of an unstable dissipative system. The switching control law that governs the position of the equilibrium point varies according to the number of scrolls displayed in the attractor.

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Deryusheva, Valentina N., Petr Y. Krauinsch, Aleksandr V. Ioppa, Andrei S. Bazarov und Artem V. Zhukov. „Model of Hydraulic Rotary Control Valve for Control of Pneumohydraulic Impact Unit“. Key Engineering Materials 685 (Februar 2016): 365–69. http://dx.doi.org/10.4028/www.scientific.net/kem.685.365.

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The paper presents constructive scheme, the mathematical model and schematic diagram of the hydraulic rotary control valve of the pneumohydraulic impact unit. Detailed analysis of the mathematical model was made for the purpose to create modes of the movement conducive to improving the work of pneumohydraulic impact unit at the point of switching. The results of mathematical modeling (schematic diagram of matlab) are given.

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Zhang, Guozheng, Yingjie Su, Zhanqing Zhou und Qiang Geng. „A Carrier-Based Discontinuous PWM Strategy of NPC Three-Level Inverter for Common-Mode Voltage and Switching Loss Reduction“. Electronics 10, Nr. 23 (05.12.2021): 3041. http://dx.doi.org/10.3390/electronics10233041.

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For the conventional carrier-based pulse width modulation (CBPWM) strategies of neutral point clamped (NPC) three-level inverters, the higher common-mode voltage (CMV) is a major drawback. However, with CMV suppression strategies, the switching loss is relatively high. In order to solve the above issue, a carrier-based discontinuous PWM (DPWM) strategy for NPC three-level inverter is proposed in this paper. Firstly, the reference voltage is modified by the twice injection of zero-sequence voltage. Switching states of the three-phase are clamped alternatively to reduce both the CMV and the switching loss. Secondly, the carriers are also modified by the phase opposite disposition of the upper and lower carriers. The extra switching at the border of two adjacent regions in the space vector diagram is reduced. Meanwhile, a neutral-point voltage (NPV) control method is also presented. The duty cycle of the switching state that affects the NPV is adjusted to obtain the balance control of the NPV. Still, the switching sequence in each carrier period remains the same. Finally, the feasibility and effectiveness of the proposed DPWM strategy are tested on a rapid control prototype platform based on RT-Lab.

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Sun, Changchun, und Qicheng Xu. „Generating Chaos from Two Three-Dimensional Rigorous Linear Systems via a Novel Switching Control Approach“. International Journal of Bifurcation and Chaos 26, Nr. 13 (15.12.2016): 1650212. http://dx.doi.org/10.1142/s0218127416502126.

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By constructing two three-dimensional (3D) rigorous linear systems, a novel switching control approach for generating chaos from two linear systems is presented. Two 3D linear systems without any constant term have only one common equilibrium point that is the origin. By employing an absolute-value switching law, chaos can be generated by switching between two linear systems. Basic dynamical behaviors of the systems are investigated in detail. Numerical examples illustrate the effectiveness of the presented approach.

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Qu, Ying, Bin Zhang, Hairong Chu, Xiaoxia Yang, Honghai Shen und Jingzhong Zhang. „Linear-Nonlinear Switching Active Disturbance Rejection Speed Controller for Permanent Magnet Synchronous Motors“. Sensors 22, Nr. 24 (08.12.2022): 9611. http://dx.doi.org/10.3390/s22249611.

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To combine the advantages of linear active disturbance rejection control (LADRC) and nonlinear active disturbance rejection control (NLADRC) and improve the contradiction between the response speed and control precision caused by the limitation of parameter α in NLADRC, a linear-nonlinear switching active disturbance rejection control (SADRC) strategy based on linear-nonlinear switching extended state observer (SESO) and linear-nonlinear switching state error feedback control law (SSEF) is proposed in this paper. First, the reasons for the performance differences between LADRC and NLADRC are analysed from a theoretical point of view, then a linear-nonlinear switching function (SF) that can change the switching point by adjusting its parameters is constructed and then propose SESO and SSEF based on this function. Subsequently, the convergence range of the observation error of the SESO is derived, and the stability of the closed-loop system with the application of SSEF is also demonstrated. Finally, the proposed SADRC control strategy is applied to a 707 W permanent magnet synchronous motor (PMSM) experimental platform, and both the dynamic and static characteristics of SADRC are verified. The experimental results show that the proposed SADRC control strategy can well combine the performance advantages of LADRC and NLADRC and can better balance the response speed and control precision and has a better capacity for disturbance rejection, which has potential application in engineering practise.

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Sha, MaiChao, RuiJin Zhu und XueJiao Gong. „Fixed frequency Finite Control Set Model Predictive Control For Three-level APF“. E3S Web of Conferences 233 (2021): 04028. http://dx.doi.org/10.1051/e3sconf/202123304028.

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Active power filter can compensate harmonic and reactive power, Three level neutral point clamp (ANPC) has the characteristics of low output harmonic and low device loss. The control of three-level active power filter needs to consider multiple objectives. Finite control set model predictive control (FCS-MPC) is a new method which can add constraints and multi-objective control. According to the limit of the switch state, it can track the reference current, which has the characteristics of fast dynamic response and good compensation effect. This method not only keeps the neutral point voltage balance, but also solves the problem of unstable switching frequency.

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Shishkina, Irina. „Proportion calculation of the defect parts in track switching equipment“. E3S Web of Conferences 402 (2023): 06012. http://dx.doi.org/10.1051/e3sconf/202340206012.

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This paper presents a direct calculation of the average value of defective elements of point products. Production process control is considered using the example of the control of point products. The calculation of the first four moments in a binomial distribution of the number of defective elements of point products is made. The standard error of the fraction of defective elements is considered in detail.

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Zavalishchin, D. S. „Multi-agent transport system control problem“. Herald of the Ural State University of Railway Transport, Nr. 2 (2024): 23–28. http://dx.doi.org/10.20291/2079-0392-2024-2-23-28.

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A new class of control problems for a certain transport system is considered. The peculiarity of the system is the variable number of participants in the control process. The regrouping of participants, along with their unification and dispersal, is determined by the specified target points of visit, the initial point of departure and the final point of completion of the system’s movement, and the constructed trajectories. The structure of a multi-agent transport system implies the presence of primary and secondary carriers, with the former being able to transport the latter at some stages. It is at such moments that the number of participants in the control process changes. In the constructed mathematical model of the movements of the system under consideration and its control, a hybrid system of differential equations with switching is obtained, containing continuous and discrete components. The problem of finding optimal routes under certain constraints is solved.

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Tatekura, Yosuke, und Takeshi Watanabe. „Sound reproduction system with switching control band range on every listening point“. Journal of the Acoustical Society of America 120, Nr. 5 (November 2006): 3212. http://dx.doi.org/10.1121/1.4788134.

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Stolze, Peter, Petros Karamanakos, Ralph Kennel, Stefanos Manias und Christian Endisch. „Effective variable switching point predictive current control for ac low-voltage drives“. International Journal of Control 88, Nr. 7 (08.08.2014): 1366–78. http://dx.doi.org/10.1080/00207179.2014.942699.

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39

Han, Yetong, Rui Wang, Yi Zhang, Dazhong Ma, Shaoxv Jiang und Liangwu Wen. „An Adaptive Switching Control Strategy under Heavy–Light Load for the Bidirectional LLC Considering Parasitic Capacitance“. Sustainability 14, Nr. 19 (20.09.2022): 11832. http://dx.doi.org/10.3390/su141911832.

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The LLC topology is widely used to link renewable energy and inverters to provide constant voltage in the smart grid. Due to its characteristics, the voltage regulation range under light load conditions is limited, so that the output voltage cannot be maintained constant. The adaptive switching control strategy is proposed in this paper to keep the output constant. Under heavy load conditions, the voltage is kept constant by adjusting the frequency to ensure the accuracy of the control. The phase shift is adjusted to achieve constant voltage, considering the influence of parasitic capacitance on the modeling process for the changing trend of output voltage in light load conditions. The switching point is calculated from the characteristic curve to ensure that the output voltage is stable during mode switching. In addition, there is a new hysteresis control which is robust near the switching point to cope with the instability of the new energy itself and frequent disturbance under light load. Finally, a 400V–36V–1KW prototype is used to verify this control strategy.

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Koronkiewicz, Bryan. „Control Stimuli in Experimental Code-Switching Research“. Languages 4, Nr. 3 (29.08.2019): 67. http://dx.doi.org/10.3390/languages4030067.

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The current study investigates whether there is variation among different types of control stimuli in code-switching (CS) research, how such stimuli can be used to accommodate heterogeneity, and how they can also be used as a baseline comparison of acceptability. A group of native Spanish–English bilinguals (n = 20) completed a written acceptability judgment task with a 7-point Likert scale. Five different types of control stimuli were included, with three types considered to be completely acceptable (complex-sentence switches, direct-object switches, and subject–predicate switches) and two types considered to be completely unacceptable (pronoun switches and present–perfect switches). Additionally, a set of present–progressive switches were included as a comparison, as their acceptability status is still actively debated. The participants as a whole exhibited the expected grammatical distinctions among the control stimuli, but with a high degree of individual variability. Pronoun switches and auxiliary verb switches were rated significantly lower than the complex-sentence switches, direct-object switches, and subject–predicate switches. These results show that control stimuli can also establish a baseline comparison of acceptability, and recommendations for inclusion in experimental CS research are provided.

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Oh, Soo Kwang, Seoyeon Hong und Hee Sun Park. „The Tipping Point“. International Journal of Social Media and Online Communities 12, Nr. 1 (Januar 2020): 23–39. http://dx.doi.org/10.4018/ijsmoc.2020010103.

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While previous researchers have addressed motivations to join and continue using social media, this paper focuses on why users quit certain social media and change their favorite platforms, such as the current shift from Facebook to Twitter to Instagram and Snapchat. Furthermore, this exploratory study seeks to build an understanding of social media usage and motivations for switching from a cross-cultural perspective by comparing findings from Korean and U.S. users. Findings from 19 focus group sessions (n = 118) highlight influences regarding modes of usage, user control, commitment, addiction, privacy, perceived relationships, self-construals, and social/cultural trends. Findings are further analyzed and compared in light of relevant theoretical frameworks and cultural differences.

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Lin, Nan, Changfu Zong und Shuming Shi. „Method for Switching between Traction and Brake Control for Speed Profile Optimization in Mountainous Situations“. Energies 11, Nr. 11 (06.11.2018): 3042. http://dx.doi.org/10.3390/en11113042.

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Making full use of front road grade information to achieve the best fuel efficiency is important for intelligent vehicles. Normal theoretical studies pay too much attention to engine continuous feedback control. The theoretical foundation of switching between traction and brake control has been ignored. In mountainous terrain, both the engine and road slopes are energy sources. Switching between traction and brake control is the key point. This research focuses on broadening the normal control range. The comprehensive objective function that contains traction and brake control is built, and then the analytical switching control law is derived based on Pontryagin’s maximum principle (PMP). Analytical switching control laws express the mechanism of switching between traction and brake control for economic cruise control (ECC). Simulation results show that the model can solve the switch time and the entire speed profile precisely. Brake control is very important in downhill situations. The parameters in the objective function influence not only the switch time but also the switch process. This research offers a theoretical foundation for ECC with road slopes and can make onboard control more precise and efficient.

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Hoyos, Fredy E., John E. Candelo-Becerra und Carlos I. Hoyos Velasco. „Application of Zero Average Dynamics and Fixed Point Induction Control Techniques to Control the Speed of a DC Motor with a Buck Converter“. Applied Sciences 10, Nr. 5 (06.03.2020): 1807. http://dx.doi.org/10.3390/app10051807.

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Several technological applications require well-designed control systems to induce a desired speed in direct current (DC) motors. Some controllers present saturation in the duty cycle, which generates variable switching frequency and subharmonics. The zero average dynamics and fixed point induction control (ZAD-FPIC) techniques have been shown to reduce these problems; however, little research has been done for DC motors, considering fixed switching frequency, quantization effects, and delays. Therefore, this paper presents the speed control of a DC motor by using a buck converter controlled with the ZAD-FPIC techniques. A fourth-order, non-linear mathematical model is used to describe the system dynamics, which combines electrical and electromechanical physical models. The dynamic response and non-linear system dynamics are studied for different scenarios where the control parameters are changed. Results show that the speed of the motor is successfully controlled when using ZAD-FPIC, with a non-saturated duty cycle presenting fixed switching frequency. Simulation and experimental tests show that the controlled system presents a good performance for different quantization levels, which makes it robust to the resolution for the measurement and type of sensor.

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Alepuz, Salvador, Joan Nicolás-Apruzzese, Roya Rafiezadeh, Sergio Busquets-Monge, Mariana Raya und Àlber Filbà-Martínez. „Active Thermal Control in Neutral-Point-Clamped Multilevel Converters Based on Switching-Cell Arrays“. Electronics 12, Nr. 19 (27.09.2023): 4055. http://dx.doi.org/10.3390/electronics12194055.

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Neutral-point-clamped multilevel converters are a suitable solution to the implementation of low–medium voltage and power applications at present, thanks to their intrinsic superior voltage and current quality. The conventional configurations of these converters present uneven power loss distribution, causing thermal stress in some power semiconductors, which weakens the power converter reliability. To overcome this, an implementation of the neutral-point-clamped multilevel converter based on a switching-cell array is introduced, adding redundant conduction paths on one side and more options to distribute the switching losses on the other side. An active thermal control is proposed to balance the temperature distribution in the converter. A four-level converter has been implemented to evaluate the proposed solution. The experimental results show that the proposed implementation and active thermal control presents an enhanced temperature distribution in the converter and, therefore, reduced thermal stress and better reliability.

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TREFFERS-DALLER, JEANINE. „The IC model and code-switching“. Bilingualism: Language and Cognition 1, Nr. 2 (August 1998): 98–99. http://dx.doi.org/10.1017/s1366728998000212.

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In his contribution Green proposes a very interesting model of bilingual speech processing, the inhibitory control (IC) model. The model's aim is to account for the way in which bilinguals control their two language systems. Although the model was not developed to account for code-switching, the author explicitly goes into implications of his model for code-switching and this makes it very relevant for linguists working in that field. Until now, psycholinguistic aspects of code-switching have received far less attention in the literature than the syntactic aspects of code-switching. The model therefore offers an excellent starting point for incorporating insights from psycholinguistics into code-switching research and vice versa.

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Yue, Yun Tao, und Zhi Yong Xu. „Research on Neutral-Point Balancing for Three-Level Space Voltage Vector Converter“. Advanced Materials Research 748 (August 2013): 473–76. http://dx.doi.org/10.4028/www.scientific.net/amr.748.473.

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A novel hybrid clamped dual-PWM three-level converter topology is proposed for induction motor drives in this paper. The switching states of hybrid clamp three-level converters increase to sixty-four from twenty-seven switching states of diode clamp three-level converters. In order to realize optimization of its redundant voltage space vectors by detecting voltage of clamp capacitor and difference of capacitor voltage in DC side, Generating an optimized switching pattern, The hybrid clamped three-level converter increases the voltage levels number, reducing the harmonics associated to the commutation frequency and limiting the dv/dt by all the switches . It can quickly balance the DC voltage, Realized system of 4-Quardant Running. the control circuit and main circuit was designed with DSP and CPLD, experimentation results proved it is very effective and practicability.

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Ningappa, Sridhara Somaguddu, Siddesh Kondapur Basavarajan, Sudharashan Mungasavalli Katappa, Sandeep Velur Ramareddy, Lavakumar Tavane Basavarajappa und Tole Sutikno. „Sliding mode control technique of step down converter using reaching law“. International Journal of Applied Power Engineering (IJAPE) 12, Nr. 1 (01.03.2023): 102. http://dx.doi.org/10.11591/ijape.v12.i1.pp102-108.

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The robust reaching law based sliding mode control is used for chattering suppression, minimization of steady state error and reaching speed kept minimized. With fine tuning of parameters of robust reaching law, the sliding mode reaches the equilibrium point at the earliest. The stability of the proposed reaching law is analyzed. In one hand, they guarantee the system reach the sliding face rapidly and stay on it, in another way they decline the chattering effectively, even unmatched certainties and disturbances. Such that the system response can better realize the unification of rapidity. A proposed reaching law ia analyzed mathematically and applied to SMC DC-DC buck converter to lessen the chattering, because switching devices are existing in the model, it reduces effectively in the switching losses in the switching devices of the dc-dc converter. In turn effectiveness of the efficiency increases. MATLAB/Simulink results give significant decline of chattering and switching losses in the buck converter.

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Ramasamy, Palanisamy, Ramkumar Ravindran, Neetu Gupta, Gunjan Sardana, Indumathi Sekar, Venugopala Aparna Marthanda und Selvakumar Kuppusamy. „Simulation of 3D-space vector modulation for neutral point clamped inverters“. Bulletin of Electrical Engineering and Informatics 12, Nr. 2 (01.04.2023): 719–26. http://dx.doi.org/10.11591/eei.v12i2.4502.

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This paper gives an idea to simulation of three-dimensional space vector modulation for neutral point clamped multilevel inverter. Three dimensional-space vector modulation (3D-SVM) algorithm is progressed method of two dimensional-space vector modulation (2D-SVM) algorithm; it leads to reduce the complexity in reference vector identification and switching time calculation, also it includes the various advantages of 2D-SVM like minimized total harmonic distortion, reduced EMI issues. A simple system for the assortment of switching state vectors to track the reference voltage vectors without using any redundant switching vectors. This proposed method tracks the reference vector by identifyinglsubcubes and prisms by using mathematicallconditions. Here the cost of the proposedltechnique is independentlof voltagellevels oflinverter. This paper realizes the accomplishment of 3D-SVM using a neutral point clamped inverter. The simulation results of the proposed method are verified using MATLAB/Simulink.

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Wang, Yangjing, Jinquan Huang, Muxuan Pan und Wenxiang Zhou. „Game-Theory-Based Mode Switch Control Schedule Design for Variable Cycle Engine“. Aerospace 10, Nr. 2 (24.01.2023): 112. http://dx.doi.org/10.3390/aerospace10020112.

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The variable cycle engine selects the appropriate working mode through mode switch to meet the requirements of low specific fuel consumption and high unit thrust. When the variable cycle engine switches between different modes, it should ensure the smooth transition of working modes and obtain the expected performance at the same time. Consequently, a general control schedule design method for mode switch is investigated in this paper. The feasible switching domains of single-bypass working mode and double-bypass working modes are obtained based on multifurcating tree traversal, and the switching point in the feasible switching domain is determined by solving the collaboration-game optimization problem based on sequential quadratic programming (SQP). Finally, the schedule of control variables is designed to realize smooth and fast switching between different working modes of variable cycle engine. The simulations show that based on the general control schedule of mode switch proposed in this paper, smooth transition of thrust and rotor speed can be achieved under the premise of safe engine operation, with small fluctuations and a short switching time, which is about 2.5 s.

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Zhu, Chenglong, Li He, Kanjian Zhang, Wei Sun und Zengxiang He. „Optimal Timing Fault Tolerant Control for Switched Stochastic Systems with Switched Drift Fault“. Mathematics 10, Nr. 11 (30.05.2022): 1880. http://dx.doi.org/10.3390/math10111880.

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In this article, an optimal timing fault tolerant control strategy is addressed for switched stochastic systems with unknown drift fault for each switching point. The proposed controllers in existing optimal timing control schemes are not directly aimed at the switched drift fault system, which affects the optimal control performance. A cost functional with system state information and fault variable is constructed. By solving the optimal switching time criterion, the switched stochastic system can accommodate switching drift fault. The variational technique is presented for the proposed cost function in deriving the gradient formula. Then, the optimal fault tolerant switching time is calculated by combining the Armijo step-size gradient descent algorithm. Finally, the effectiveness of the proposed controller design scheme is proved by the safe trajectory planning for a four wheel drive mobile robot and numerical example.

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