Output Feedback Variable Structure Control Research Articles

Robust Output Feedback Passivity-Based Variable Structure Controller Design for Nonlinear Systems

This paper examines the use of an output feedback variable structure controller with a nonlinear sliding surface for a class of SISO nonlinear systems in the presence of matched disturbances. With only the measurable system output, the discontinuous observer reconstructs the system states and ensures that the estimation errors exponentially approach zero. Using the estimation states, the proposed nonlinear sliding surface with variable damping ratio can simultaneously achieve low overshoot and short settling time. Then the passivity-based controller including a discontinuous term can guarantee that the closed-loop system asymptotically converges to the sliding surface. Compared with other sliding mode controllers, the proposed passivity-based control scheme has better transient performance and effectively reduces the control gain. Finally, simulation results demonstrate the validity of the proposed method.

Terminal adaptive output feedback variable structure control

Based on the Lyapunov stability theorem, an adaptive output feedback variable structure control (OFVSC) scheme is proposed in this study for a class of multi-input multi-output non-linear systems with matched and mismatched perturbations to solve regulation problems. First, a switching function is designed, and the system to be controlled is decomposed into two subsystems through a linear state transformation. Then the proposed OFVSC scheme is presented. A perturbation estimation algorithm is utilised in designing the proposed control scheme in order to overcome the problem of unmeasurable states. Adaptive mechanism is also employed so that the upper bounds of perturbations as well as perturbation estimation errors are not required to be known in advance. Furthermore, the resultant control system is capable of driving all the states into zero within a finite time and guaranteeing global stability. Finally, a numerical example is given for demonstrating the feasibility of the proposed control scheme.

Adaptive Variable Structure Control for Mismatched Uncertain Systems

This paper proposes an adaptive variable structure control (VSC) for a class of mismatched uncertain systems with unknown disturbances. First, a necessary and sufficient condition in terms of linear matrix inequalities is proposed to guarantee the system in sliding mode is asymptotically stable. Second, an adaptive output feedback variable structure controller is designed to force the system states reach the sliding surface and stay on it thereafter. Finally, the advantages and effectiveness of the proposed approaches are demonstrated via a numerical example.

A New Variable Structure Control Scheme for Mismatched Uncertain Large Scale Systems

In this paper, a new decentralized adaptive output feedback variable structure control scheme is designed for mismatched uncertain large-scale systems where the exogenous disturbance is unknown. The proposed approach uses output information completely in sliding surface and controller design. Therefore, conservatism is reduced and robustness is enhanced. Furthermore, the reduce order system in sliding mode is asymptotically stable under certain conditions. Finally, a numerical example is used to demonstrate the efficacy on the method.

Output Feedback Variable Structure Control Design for Uncertain Nonlinear Lipschitz Systems

This paper develops a full-order compensator-based output feedback variable structure control law for uncertain nonlinear Lipschitz systems having matched perturbations. Given that the sufficient condition is satisfied, the developed control scheme, with the observer-like technique incorporated into the design of the compensator, can achieve global exponential stabilization. An illustrative example is provided with simulation results to show the effectiveness of the proposed method.

Memoryless variable structure control for affine nonlinear systems using only output information

SummaryIn this paper, local stabilisation is considered for a class of affine nonlinear control systems with uncertainties involving time‐varying delay. It is not assumed that either the dimension of the inputs is equal to the dimension of the outputs or that the nominal system is linearisable or partially linearisable. The bounds on both the matched and mismatched uncertainties are nonlinear and time delayed. A static output feedback variable structure control is synthesized to stabilise the system uniformly asymptotically. A control strategy to enforce exponential stability is also derived. The Lyapunov–Razumikhin approach is used to deal with the effect of the time delay, and the bounds on the uncertainties are used in the control design to enhance the robustness. The designed control does not depend on the time delay, and thus, it is not required that the time delay is known. Finally, the obtained results are tested on a simple mechanical system through simulation. The simulation results show that the proposed approach is effective and feasible. Copyright © 2014 John Wiley & Sons, Ltd.

A New Robust Output Feedback Variable Structure Controller for Uncertain More Affine Nonlinear Systems with Mismatched Uncertainties and Matched Disturbance

In this note, a new robust nonlinear output feedback variable structure controller is first systematically and generally designed for the output control of more affine uncertain nonlinear systems with mismatched uncertainties and matched disturbance. A transformed integral output feedback sliding surface with a most simple form is applied in order to remove the reaching phase problems. The closed loop exponential stability and the existence condition of the sliding mode on the integral output feedback sliding surface is investigated with a corresponding output feedback control input in Theorem 1. For practical application the continuous implementation of the control input is made by the modified saturation function. The effectiveness of the proposed controller is verified through a design example and simulation study.

Delay-independent decentralised output feedback control for large-scale systems with nonlinear interconnections

In this paper, a stabilisation problem for a class of large-scale systems with nonlinear interconnections is considered. All the uncertainties are nonlinear and are subject to the effects of time delay. A decentralised static output feedback variable structure control is synthesised and the stability of the corresponding closed-loop system is analysed based on the Lyapunov Razumikhin approach. A set of conditions is developed to guarantee that the large-scale interconnected system is stabilised uniformly asymptotically. Further study shows that the conservatism can be reduced by employing additive controllers if the known interconnections are separated into matched and mismatched parts. It is not required that the subsystems are square. The designed controller is independent of time delay and thus it does not require memory. Simulation results show the effectiveness of the proposed approach.

Pre- and post-filtering approach to sensorless VSS speed control of a permanent magnet DC motor subject to Hammerstein and Wiener nonlinearities

In this paper, we propose a pre- and post-filtering approach to output feedback variable structure control of a permanent magnet DC servo motor under constant inertial load. The proposed control method is to regulate the motor speed by using the armature current measurement alone. Both the Hammerstein nonlinearity for the system input end and the Wiener nonlinearity for the output end are considered. With these static nonlinear functions carefully identified and their inverses fitted, the linearized model renders a simple dynamic mapping from the armature current to the sliding variable, which is designed as a dynamic function of the motor angular velocity. The pre-filter is the inverse of the Hammerstein function. The post-filter consists of two blocks in series: the inverse of the Wiener function and the concatenating dynamic filter, which is a linear relationship between the armature current and the sliding variable. The proposed method is robust against parameter variations in the electric subsystem such as the armature inductance and resistance.

Decentralised delay-dependent static output feedback variable structure control

In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. Then, a decentralised delay-dependant static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using the Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach.

Decentralised Output Feedback Variable Structure Control for Large Scale Time Delay Systems

In this paper, an output feedback stabilisation problem is considered for a class of large scale interconnected time delay systems with uncertainties. The uncertainties appear in both isolated subsystems and interconnections. The bounds on the uncertainties are nonlinear and time delayed. It is not required that either the known interconnections or the uncertain interconnections are matched. A decentralised delay dependent static output feedback variable structure control is synthesised to stabilise the system globally uniformly asymptotically using a Lyapunov Razumikhin approach. A case study relating to a river pollution control problem is presented to illustrate the proposed approach.

Application of variable-structure output feedback control to active front steering for understeer and oversteer conditions

This paper describes an approach to the design of Active Front Steering (AFS) based on Variable-Structure Output Feedback Control (VSOFC) with integral action to enhance vehicle stability during understeer and oversteer conditions. We determine the understeer and oversteer behaviour of the vehicle and we change the AFS control strategy based on the understeer and oversteer behaviour of the vehicle so that the road wheel steering angle is in the ideal position to provide the intended steering angle. The control law ensures not only that the vehicle trajectory follows a desired reference trajectory but also that its convergence rate can be specified. Finally we present simulation results to demonstrate the potential benefits of the control strategy under different driving scenarios.

Research on Multivariable Model Reference Variable Structure Control

This paper studies the output-feedback variable structure control for MIMO (multi-input multi-output) linear systems with generalized relative degree one. A new variable structure control scheme is proposed within the framework of model reference control. Under the assumption that the high frequency gain matrix of the plant can be transformed to a main diagonal dominant matrix via full rank transformation, it is shown that all signals of the closed-loop system are globally uniformly bounded and meanwhile, the tracking error converges to zero exponentially. Simulation results are presented to illustrate the effectiveness of the proposed scheme.

Global decentralised static output feedback sliding-mode control for interconnected time-delay systems

Global decentralised stabilisation of a class of interconnected time-varying delay systems is considered, where both known and uncertain interconnections involve time delay. Matched and mismatched interconnections are considered separately to reduce the conservatism. A composite sliding surface is designed and the stability of the associated sliding motion, which is governed by a time delayed interconnected system, is analysed based on the Razumikhin–Lyapunov approach. A decentralised static output feedback variable structure control which is dependent on time delay is synthesised to drive the interconnected system to the sliding surface globally. Simulation results show the effectiveness of the proposed approach.

A Dynamic Output Feedback Variable Structure Controller for Uncertain Systems with Unmatched System Matrix Uncertainty

In this paper, a variable structure dynamic output feedback controller with an transformed sliding surface is designed for the improved robust control of a uncertain system under unmatched system uncertainty, matched input matrix uncertainty, and disturbance satisfying some conditions. This paper is extended from the results of the static output feedback VSS in [9]. To effectively remove the reaching phase problems, an initial condition of the dynamic output is determined. The previous some limitations on the dynamic output feedback variable structure controller is overcome in this systematic design. A stabilizing control is designed to generate the sliding mode on the predetermined sliding surface S=0 and as a results the closed loop exponential stability is obtained and proved together with the existence condition of the sliding mode on S=0 for all unmatched system matrix uncertainties. To show the usefulness of the algorithm, a design example and computer simulations are presented.

A New Robust Discrete Static Output Feedback Variable Structure Controller with Disturbance Observer for Uncertain Discrete Systems

In this paper, a new discrete static output feedback variable structure controller based on a new dynamic-type sliding surface and output feedback discrete version of the disturbance observer is suggested for the control of uncertain linear systems. The reaching phase is completely removed by introducing a new proposed dynamic-type sliding surface. The output feedback discrete version of disturbance observer is derived for effective compensation of uncertainties and disturbance. A corresponding control with disturbance compensation is selected to guarantee the quasi sliding mode on the predetermined dynamic-type sliding surface for guaranteeing the designed output in the dynamic-type sliding surface from any initial condition for all the parameter variations and disturbances. Using Lyapunov function, the closed loop stability and the existence condition of the quasi sliding mode is proved. Finally, an illustrative example is presented to show the effectiveness of the algorithm.

A New Robust Discrete Integral Static Output Feedback Variable Structure Controller with Disturbance Observer and Integral Dynamic-Type Sliding Surface for Uncertain Discrete Systems

In this paper, a new discrete integral static output feedback variable structure controller based on the a new integral dynamic-type sliding surface and output feedback discrete version of the disturbance observer is suggested for the control of uncertain linear systems. The reaching phase is completely removed by introducing a new proposed integral dynamic-type sliding surface. The output feedback discrete version of disturbance observer is presented for effective compensation of uncertainties and disturbance. A corresponding control with disturbance compensation is selected to guarantee the quasi sliding mode on the predetermined integral dynamic-type sliding surface for guaranteeing the designed output in the integral dynamic-type sliding surface from any initial condition for all the parameter variations and disturbances. Using discrete Lyapunov function, the closed loop stability and the existence condition of the quasi sliding mode is proved. Finally, an illustrative example is presented to show the effectiveness of the algorithm.

A Two-stage Floating Raft Isolation System Featuring Electrorheological Damper with Semi-active Static Output Feedback Variable Structure Control

In this study, a semi-active static output feedback variable structure control (VSC) strategy is presented to control a two-stage electrorheological (ER) floating raft isolation system. A continuous semi-active static output feedback VSC controller is designed and a bypass ER damper is applied to achieve the best control effect more rapidly and accurately. The sliding surface parameters are determined in terms of the Routh—Hurwitz stability criterion. The optimal vibration attenuation of the intermediate mass is guaranteed due to the control rule that damping force only dissipates the vibration energy of the intermediate mass. The robustness of the control method with respect to parameter variations and the effectiveness of vibration isolation are demonstrated by numerical simulation results. It shows that the designed semi-active static output feedback VSC strategy realized by the ER damper can achieve better performance than that of optimally passive damping even if system parameter uncertainties exist. In addition, the experiment was carried out to demonstrate the practical effectiveness of the presented control scheme in this study. The experimental results are satisfied.

Post-filtering approach to output feedback variable structure control for single-input-single-output sampled-data systems

This study presents a dynamic post-filtering approach to a single-input-single-output sampled-data variable structure output feedback control problem. Given a sliding surface, Σ(x)=0 (x being the system state vector), designed through standard procedures with the assumption of full state accessibility, a dynamic filter, denoted post-filter, is employed to synthesise Σ(x) by means of output variable alone. In contrast with a state observer, the post-filter is invariant of the matched disturbances; and it requires only partial information of the system parameters. Thus, the robustness property of the variable structure system is retained. Let T be the sampling period. A sampled-data realisation of the post-filter is done by zero-order hold. Depending on the system relative degree, either Σk or Σk−1 can be obtained for implementing the variable structure control law. A discrete-time switching-type control law, which is originally designed to satisfy the continuous-time reaching condition, will lead to a quasi-sliding motion, forming a boundary layer of thickness O(T) about the sliding surface. The stability of the post-filter is ensured if the system output is in minimum phase and that the sliding mode dynamics are chosen properly.

Output feedback variable structure control of uncertain linear systems in the presence of actuator dynamics

AbstractA new output feedback variable structure control scheme is developed based on a novel passivity idea. This scheme may practically stabilize a class of higher‐relative‐degree uncertain linear systems, and realize output tracking and disturbance attenuation as well. The controller is composed of linear filters and a single relay, without employing real‐time exact differentiators. Under this framework, we also explain how actuator dynamics affect the closed loop behavior. A simulation example shows the simplicity and efficiency of this method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society