Output feedback variable structure control design for a class of uncertain linear systems

This note has studied the invariance of dynamic output feedback variable structure control systems (VSCS) for square, invertible plants. Based on a result of Diong and Medonic (1992), we show that such systems can be made invariant to disturbance and uncertainty, with stability, only if the plant being controlled is minimum-phase. Thus if dynamic output feedback VSC is to be applied to this class of plants, then it is almost always necessary to robustify the sliding mode dynamics against the residual disturbance and uncertainty. One approach was given by Diong and Medonic, and other methods are being studied. The invariance of dynamic output feedback VSCS for other classes of plants is also under investigation. >

The output feedback variable structure control problem is considered for a class of single input single output uncertain linear plants with arbitrary relative degree and with parameter perturbations, unmodeled dynamics and bounded disturbance simultaneously. A novel passivity-based control scheme composed of linear feedback and variable structure control is proposed. If exact differentiations of system output provided, this scheme results in asymptotic stability; if a class of singular perturbation based linear differentiators adopted, it leads to an arbitrarily small regulation/tracking error.

The problem of output feedback variable control of discrete-time linear systems with unmatched uncertainties is studied in this paper. The output feedback control doesn't need state available and estimated state. First, the sliding surface is designed by using linear matrix inequality (LMI) technique when there exists the unmatched uncertainties. The sufficient condition for the existence of stable sliding surface is derived in terms of LMIS. Then the design of sliding mode control is presented according to the reachability condition. Finally, an illustrative example is presented to show the feasibility and effectiveness of the proposed method.

In this paper, the Linear Matrix Inequality (LMI) method is used to solve the problem of making observer-based control solutions for a class of uncertain linear systems. The study yields both control and observer gains derived from feasible LMI solutions. To illustrate the effectiveness of our approach, we present a practical example, showcasing the practicality and applicability of the proposed solutions.

Linear matrix inequality (LMI) methods, novel techniques in solving optimisation problems, were introduced as a unified approach for vehicle's active suspension system controller design. LMI methods were used to provide improved and computationally efficient controller design techniques. The active suspension problem was formulated as a standard convex optimisation problem involving LMI constraints that can be solved efficiently using recently developed interior point optimisation methods. An LMI based controller for a vehicle system was developed. The controller design process involved setting up an optimisation problem with matrix inequality constraints. These LMI constraints were derived for a vehicle suspension system. The resulting LMI controller was then tested on a quarter-car model using computer simulations. The LMI controller results were compared with an optimal PID controller design solution. The LMI controller was further tested by incorporating a nonlinear term in the vehicle's suspension model; the LMI's controller degraded response was enhanced by using gain-scheduling techniques. The LMI controller with gain-scheduling gave good results in spite of the unmodelled dynamics in the suspension system, which was triggered by large deflections due to off-road driving.

Output feedback variable structure control design using dynamic compensation for linear systems

This letter addresses the semi-global output regulation problem for continuous-time linear systems with input saturation and unknown dynamics. First, we employ a low-gain technique to design a state-feedback linear control law such that the control input operates within the linear region of the actuator. Then, taking it as the linear part, we construct a composite nonlinear feedback (CNF) control law, consisting of both linear and nonlinear parts, to improve the transient performance of the closed-loop system. Without requiring prior knowledge of the system dynamics or an initial stabilizing control policy, we propose a novel adaptive dynamic programming (ADP) learning algorithm. This algorithm learns both the linear part and the nonlinear part of the CNF control law using the same set of data. In addition, the algorithm uses single-layer filters, eliminating the need for integral operations during the learning process. Finally, the effectiveness of the proposed algorithm is demonstrated by an illustrative example.

Joint planning of electric vehicle battery swapping stations and distribution grid with centralized charging

Observer-Based Output Feedback Variable Structure Control with Application to a Two-Link Manipulator

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.

This chapter examines some aspects of the output-feedback control problem for nonlinear uncertain plants, with special emphasis on possible applications of recent results about higher order sliding modes (HOSMs). This regime is established when the simultaneous, finite-time, zeroing of an output quantity (the sliding quantity), and of a certain number of its derivatives, is ensured. In this work, for any step of an output feedback variable structure control design, namely, the definition of the sliding variable, the synthesis of the control law, and the state estimation, a survey of proposals characterized by a finite-time convergence transient is presented. Some different types of sliding surfaces in the state space, such that the associated constrained motion is characterized by a finite-time converging dynamics, are recalled. The use of a discontinuous control to make them attractive and invariant is then analyzed. Finally, real-time differentiators based on HOSMs for estimating the output derivatives are considered. The twofold objective of the present chapter is to survey the most recent results on HOSMs and to highlight their possible role in improving existing approaches, to motivate and to draw possible lines for future research.

Decentralised delay-dependent static output feedback variable structure control

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.

In this paper, global decentralised stabilisation of a class of interconnected 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 delay 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 synthesized to drive the interconnected system to the sliding surface globally. Simulation results show the effectiveness of the proposed approach.

Two state feedback sliding mode control schemes are developed for position control for brushless DC motor drives. The first controller design achieves the desired swiftness of response. In addition to swiftness, the second controller drastically reduces system’s chattering by adding the guaranteed cost constraint. The proposed controller consists of two parts, linear and non-linear. Linear matrix inequalities (LMIs) optimisation is used to design the linear part that achieves the desired dynamic performance: it is robust against system uncertainties, and is based on a new sufficient condition for the existence problem; the non-linear part is created to guarantee that the sliding surface is attained. System uncertainty due to changes in drive’s load inertia is represented with norm- bounded structure. The main advantages of this technique are that: the LMI algorithm includes an optimal part to preclude high control efforts, and the control burden is heavily placed on the linear part to improve the chattering problem of the conventional sliding mode control.