Discrete-time Variable Structure Control Research Articles

Electrical Drives Control via Discrete-Time Variable Structure Systems with Sliding Mode

Modern control techniques of electrical drives (EDs) use robust control algorithms. One of such algorithms is variable structure control (VSC) with sliding mode (SM). SM control needs more information on the controlled plant than the conventional PI(D) control. Valid mathematical model of the controlled plant is necessary for the SM controller design. Generalized mathematical model of two-phase electrical machine and its adaptation to direct current (DC) and induction motor (IM) are given in this paper, employed in the cascade control structure. Also, the basic SM control theory and discrete-time controller design approach, developed by the authors, are given. Finally, experimentally realized examples of speed and position control of DC and IM are given as an illustration of the efficiency of the promoted EDs controller design via discrete-time VSC.

Design scheme of discrete time variable structure controllers applied to multi‐input‐multi‐output linear systems with chattering elimination

Designing discrete time variable structure control with sliding mode (SM) schemes implies finding an asymptotically stable sliding surface with a control policy which assures the existence of a SM. Based on a recently innovative approach, where the authors developed a flexible design of sliding surfaces applied to discrete time linear multi-input multi-output (MIMO) systems, a novelty controller design strategy is proposed, where a switching surface parameter is used for the adjustment of the control signal limitations and for the improvement of the controlled system dynamics against model uncertainties. It is the first time that these drawbacks are solved modifying the switching surface values because it has been always resolved via control law adjustment. Moreover, a new chattering elimination method using adjustable sigmoid functions is also implemented in the controller. The main advantages of the proposed methodology are: firstly, it can be easily applied to high-order linear MIMO systems; secondly, system dynamics coordinates representation transformations are not needed and thirdly, the non-ideal SM dynamics is considered in the design procedure. Both the sliding surface and the control law specification are included in the proposed methodology. An illustrative example is included.

A robust and self-tuning speed control for permanent magnet synchronous motors via meta-heuristic optimization

In a reconfigurable manufacturing scenario, control system design needs innovative approaches to face the rapid changes in hardware and software modules. The control system should be able to automatically tune its parameters to enhance machine performances and dynamically adapt to different control objectives (e.g., minimize control efforts or maximize tracking performances) while preserving at the same time stability and robustness properties. In this paper, a robust control system for permanent magnet synchronous motors (PMSMs), together with an online self-tuning method, is presented. In particular, a robust discrete-time variable structure control (VSC) has been designed. A heuristic bio-inspired approach has been then implemented on a digital signal processor (DSP) to find the VSC parameter set which minimizes a specific objective function each time a novel speed reference is provided. Experimental results on a PMSM motor show the effectiveness of the proposed controller and tuning method, with noticeable improvements with respect to the original manufacturer-designed controller.

Design and Control of a Novel Compliant Constant-Force Gripper Based on Buckled Fixed-Guided Beams

This paper presents the design and control of a novel gripper device with a passive type of compliant constant-force mechanism. The function of constant-force output is achieved by using the combination of a positive-stiffness and a negative-stiffness mechanism. The negative stiffness is generated by a bistable buckled fixed-guided beam. Conventionally, when gripping a target-object using a high-stiffness gripper, both the displacement control and force control are required to prevent the damage of the object. The uniqueness of the developed constant-force gripper is that it can eliminate the dependence on force control while keeping the force constant via its mechanical structure. The gripper performance is evaluated by the established analytical model and nonlinear finite-element analysis, and validated through experimental study on a fabricated prototype. To achieve a precise position output of the gripper jaw, a discrete-time variable structure control strategy based on a nonswitching type of reaching law is realized. The effectiveness of the gripper system is verified by conducting experimental studies on grasp-hold-release operations of a micro copper wire.

Advanced control for fault-tolerant dynamic positioning of an offshore supply vessel

The paper presents a solution to guarantee a fault-tolerant robust control for the dynamic positioning of an over-actuated offshore supply vessel. Fault detection is obtained by a combination of two model-based techniques: the parity space approach and the Luenberger observer. The dynamic positioning system is provided by a bank of reconfigurable Discrete-Time Variable-Structure Controllers (DTVSC), selected by a supervisor, based on a fault isolation logic. The control system is combined with a wave compensation based on a Multi-rate Extended Kalman Filter (MREKF). The proposed solution is compared with a standard Proportional-Integral-Derivative (PID) control system and a passive nonlinear wave filter to assess its robustness to input disturbances and uncertainties in the model parameters. The simulation tests developed for a scale model of an offshore supply vessel show that, in the case of actuators faults, dynamic positioning is guaranteed by the proposed solution.

A Local Controller for Discrete-Time Large-Scale System by Using Integral Variable Structure Control

A new local controller for discrete-time integral variable structure control of a large-scale system with matched and unmatched uncertainty is presented. The local controller is able to bring the large-scale system into stability by using only the states feedback from individual subsystem itself. A new theorem is established and proved that the controller is able to handle the effect of interconnection for the large-scale system with matched and unmatched uncertainty, and the system stability is ensured. The controller is able to control the system to achieve the quasi-sliding surface and remains on it. The results showed a fast convergence to the desired value and the attenuation of disturbance is achieved.

Control of 400 Watt Belt-Drive and 400 Watt Ball-Screw Servo Systems Using Discrete-Time Variable Structure Control

This paper develops a discrete-time variable structure control method for servo drives. The objective is to achieve tungless control in industrial servo systems. The developed control method is experimentally evaluated for load variations and parameter uncertainties. Experiments are performed on typical automation applications: a 400 W servo motor with a belt-drive connection and a 400 W servo motor with a ball-screw connection. The experimental results show that the developed discrete-time variable structure controller provides better performance characteristics than the conventional commercial servo controller.

Output Tracking in Causal Nonminimum Phase Systems Using Discrete-time Stable System Center

Output tracking is considered for discrete-time causal single input single output nth order linear time invariant system with nonminimum phase zeros via discrete-time variable structure control. The stable system center method was developed originally for controlling the output in continuous time nonminimum phase causal system using sliding mode control. The developed discrete-time stable system center technique transforms an output tracking problem to a corresponding state variable tracking problem. The causal disturbances and output tracking profiles are assumed to obey a linear exogenous system with known characteristic polynomial. The theoretical results are confirmed by discrete variable structure control synthesis for the tracking of const signal.

Experimental results of Discrete Time Variable Structure Control for Dynamic Positioning of Marine Surface Vessels

This paper presents a Discrete-Time Variable-Structure Control (DTVSC) for the dynamic positioning system of a marine supply vessel to guarantee robustness with respect to disturbances and parametric variations. The control system is combined with a wave compensation based on a Multirate Extended Kalman Filter (MR-EKF). The dynamic positioning system is provided by a DTVS controller. The proposed solution has been tested on a real vessel and the experimental results are corroborated by simulations.

Application of Variable Structure Control Base on Kalman Filter Rearch Law to Electro-Mechanical Actuator

A control scheme of direct DC electro-mechanical actuator based on discrete-time variable structure controller with Kalman filter is designed. In order to improve the perfect of the mechanical actuator mathematical model, the hinge moment is considered, and the coefficients of its transfer function are appropriately amended. For practical application, the Kalman filter is introduced to reduce the white noise in control process. The calculative results show that the precision of track and control is improved obviously.

Fault-tolerant variable structure control of an overactuated Dynamic Positioning vessel after thruster failures

In this paper the application of a fault-tolerant control technique for the dynamic positioning of an over-actuated offshore supply vessel to handle abrupt fault on the actuators is proposed. The fault detection is a combination of two model-based techniques: Parity Space Approach and Luenberger observer. Dynamic positioning is provided by a bench of reconfigurable discrete time variable structure controllers, selected by a logic supervisor, based on the fault isolation logic, while an extended Kalman filter is designed for wave filtering. Reported simulations for a scaled model of an offshore supply vessel show that dynamic positioning can be achieved using the proposed solution in case of actuators faults.

Discrete Time Variable Structure Control for the Dynamic Positioning of an Offshore Supply Vessel

This paper presents a Discrete-Time Variable-Structure Control (DTVSC) for the dynamic positioning system of a marine supply vessel. The DTVSC guarantees robustness with respect to disturbances and parametric variations. Two wave-filtering approaches are employed: the Extended Kalman filter (EKF) and the multi-rate Kalman filter (MREKF). The proposed solution is compared with a PID-based control and a passive non-linear wave filter. The reported simulations show that the proposed solution produces better performances and it is robust in the presence of input disturbances and model uncertainties.

An Improved Design Scheme of Variable Structure Control for Discrete-time Systems

摘要: 在分析了几种离散变结构趋近律趋近过程的基础上, 提出了一种改进的趋近律, 该方法能够大幅度削弱抖振, 使系统运动最终趋于原点且不存在稳态振荡, 能使系统的准滑动模态保持步步穿越切换面的基本属性, 改善了趋近过程. 关键词: 离散时间系统 / 变结构控制 / 离散趋近律 / 抖振

Reconstructing Sliding Surfaces for SISO Variable Structure Output Feedback Control Systems Using Inverse Method

There exists a dynamic mapping relationship between the sliding variable and the output variable in a linear, time-invariant (LTI), single-input-single-output (SISO) system. This relationship is invariant of the matched disturbances, which lies in the control space. In this note, a continuous-time dynamic inverse compensator is proposed to reconstruct the sliding variable from the system output. This inverse compensator is stable and causal provided that the original SISO system is minimum phase and that the input-output relative degree is less than or equal to one. In case the system relative degree is greater than one, a digital approximation for the inverse compensator is introduced to track the sliding variable in discrete-time to the accuracy of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> is the sampling period. Thus the discrete-time variable structure control (VSC) law can be implemented without full state accessibility.

Time-Varying Sliding Mode Control for Discrete-Time Nonlinear Uncertain Coupled Systems via Sliding Mode Prediction

In this paper, a novel time-varying sliding mode control (SMC) algorithm based on sliding mode prediction for a class of discrete-time nonlinear uncertain coupled systems is presented. After giving a kind of time-varying sliding mode function, a sliding mode prediction model is used to predict the future information of sliding mode. By employing feedback correction and receding horizon optimization approaches which are extensively applied in predictive control strategy, the desired discrete-time variable structure control law is obtained. Under the influence of uncertainties whose boundaries are unknown, the closed-loop systems are proofed to be robustly stable. Numerical simulation results illustrate that compared with conventional SMC method, under the algorithm proposed in this paper, chattering is eliminated, the control signals have smaller peak values, and the closed-loop system possesses stronger robustness.

Improving existing “reaching law” for better discrete control of seismically-excited building structures

In this paper, a novel “composite reaching law” was explained in details: 1) the equation of discrete motion for a control system; 2) the design of discrete-time variable structure control. In addition, the model of a three-storey shear-type building structure was used to verify the effectiveness of the discrete variable structure control method. The results of numerical example analysis of the model show that the control law can effectively reduce the peak value of seismic response of the building structure and the chattering effect of the control system.

GUARANTEED COST CONTROL OF UNCERTAIN LINEAR SYSTEMS VIA DISCRETE-TIME VARIABLE STRUCTURE CONTROL

This paper presents a design of realizing the guaranteed cost control problem for uncertain linear systems via discrete-time variable structure control (VSC) scheme. The uncertainties in the system are assumed to be norm-bounded and time-varying. Based on the discrete-time VSC technique, the proposed controller can drive the system into a pre-specified switching surface to obtain the desired dynamic performance and the chattering phenomenon is eliminated. Sufficient conditions for the existence of guaranteed cost control are presented, and the problem of designing guaranteed cost control is converted to a convex optimization problem with linear matrix inequality (LMI) constraints. Finally, simulation results demonstrate the efficacy of the proposed control methodology.

Binary ABR flow control over ATM networks with uncertainty using discrete-time variable structure controller

A binary available bit rate (ABR) scheme based on discrete-time variable structure control (DVSC) theory is proposed to solve the problem of asynchronous transfer mode (ATM) networks congestion in this paper. A discrete-time system model with uncertainty is introduced to depict the time-varying ATM networks. Based on the system model, an asymptotically stable sliding surface is designed by linear matrix inequality (LMI). In addition, a novel discrete-time reaching law that can obviously reduce chatter is also put forward. The proposed discrete-time variable structure controller can effectively constrain the oscillation of allowed cell rate (ACR) and the queue length in a router. Moreover, the controller is self-adaptive against the uncertainty in the system. Simulations are done in different scenarios. The results demonstrate that the controller has better stability and robustness than the traditional binary flow controller, so it is good for adequately exerting the simplicity of binary flow control mechanisms.

Control of spatiotemporal chaos in coupled map lattice by discrete-time variable structure control

A discrete-time sliding mode controller is introduced for controlling spatiotemporal chaos modeled by coupled map lattices. The controller which is designed based on Lyapunov function satisfies reaching law such that tracking problem is solved. This method can apply for all types of coupled map lattices. Simulation results reveal the feasibility of the control method.

Approximation law for discrete-time variable structure control systems

Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.