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.

A dynamic output feedback variable structure controller for linear systems with mismatched uncertainties is studied. The proposed controller consists of nonlinear and linear parts. The linear part with full dynamics completely handles mismatched uncertainties and on the other hand, the nonlinear part is simplified as possible. By using the Lyapunov theory and linear matrix inequality method, the condition of existence of dynamic output feedback variable structure control law is derived and transformed as the feasibility problem described by linear matrix inequality, which can be solved by Matlab LMI toolbox to obtain the variable structure control for a class of system. A simulation example is given to illustrate that the analysis method and the result are valid and feasible.

Bifurcation analysis on a turning system with large and state-dependent time delay

This paper considers the problem of output feedback stabilization of multiple time delay uncertain systems with series nonlinearities. We develop a delay-dependent method for designing linear dynamic output feedback controllers which ensures global uniform asymptotic stability for the range of allowable delay times. The proposed stabilization method, which is based on the comparison theorem and some analytical methods, is employed to treat this problem. The most striking feature of the results presented is their simplicity in testing the stabilization of multiple-time-delay systems with series nonlinearities and this can be used to estimate the size of the delay time. Examples are used to illustrate the less conservative results of the proposed methods compared with existing methods in the literature.

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

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.

This paper addresses the problem of global output feedback stabilization for a class of upper-triangular systems with delay in the input. By using a linear observer, a linear dynamic output feedback control law is explicitly constructed to globally stabilize the system. To dominate the nonlinear perturbing terms and handle the case with a larger input delay, a tunable scaling gain is introduced to the controller by using a coordinates change. With the help of appropriate Lyapunov-Krasoveskii functional and feedback domination approach, it is shown that upper-triangular nonlinear system with arbitrary large input delay can be globally stabilized by the proposed output feedback controller with appropriate gains.

This paper presents the design, tuning and performance analysis of a new predictive fuzzy controller structure for higher order plants with large time delays. The designed controller consists of a fuzzy proportional‐integral (PI) part and a fuzzy predictor. The fuzzy predictive PI controller combines the advantages of fuzzy control while maintaining the simplicity and robustness of a conventional PI controller. The dynamics of the prediction term are adaptive to the system’s time delay. The prediction term has two parts: a fuzzy predictor that uses the system time delay as an input for calculating the prediction horizon and an exponential term that uses the prediction horizon as its positive power. The prediction term also introduces phase lead into the system which compensates for the phase lag due to the time delay in the plant, thereby stabilizing the closed‐loop configuration. The performance of the proposed controller is compared with the responses of the conventional predictive PI controller, showing many advantages of the new design over its conventional counterpart.

A novel active disturbance rejection control (ADRC) solution and a particular tuning method are presented for a class of time delay system (TDS) with uncertainty. First, the complicated process dynamics is modeled as a simple first order plus large time delay (FOPTD) plant, with the difference between the actual dynamics and its model treated as disturbances to be rejected. Then the reduced order linear extended state observer (RLESO) with input delay is proposed to estimate the time delay state and disturbance. It is shown how the time delay could be eliminated from the characteristic equation of the closed-loop system by manipulations of controller parameters. Secondly, the one parameter tuning (OPT) technique is developed where all controller parameters are made function of a single coefficient. In comparison with optimal proportional-integral-derivative (PID) controller and twice optimum controller (TOC), the simulation results show that the proposed method not only has better accuracy and faster response, but also ensures better robustness and adaptability against uncertain model parameters and external disturbances, especially for the plant with very large time delays.

Output feedback stabilization of nonlinear dual-rate sampled-data systems via an approximate discrete-time model

A SEMI-GLOBAL OUTPUT FEEDBACK STABILIZATION SCHEME FOR A CLASS OF NON UNIFORMLY OBSERVABLE SYSTEMS

This paper investigates the problem of output feedback stabilization for a class of stochastic feedforward nonlinear systems with time-varying input delay. The drift and diffusion terms satisfy the linear growth condition and are dependent on unmeasurable states and the delayed input. First, we use a change of coordinates to introduce a scaling gain into the system. Then, based on the high-gain observer technique, a delay-free output feedback controller with the scaling gain is developed. Based on the Lyapunov–Krasovskii method and the idea of feedback domination, it is shown that the closed-loop system can be rendered globally asymptotically stable in probability via appropriately choosing the scaling gain. Finally, two examples are presented to illustrate the effectiveness of the proposed scheme.

We study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output feedback controller and prove that the closed-loop system is bounded in probability. Under an infinite-horizon risk-neutral cost criterion, the controller designed can guarantee an arbitrarily small long term average cost. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large, and the risk-neutral cost is guaranteed to be zero. With special care, the controller preserves the equilibrium of the nonlinear system.

In this paper, we deal with the problem of output feedback stabilization for a class of linear hybrid systems. This problem is addressed by characterizing the structural properties of such a class of systems. Namely, reachability, controllability, stabilizability, observability, constructibility, and detectability are framed in terms of algebraic and geometric conditions on the data of the system. Two canonical forms, recalling the classical Kalman decompositions with respect to reachability and observability, are given. By taking advantage of this characterization, duality between control and observation structural properties is established and necessary and sufficient conditions for the existence of a linear time-invariant output feedback compensator are stated. Compared with previous results, no assumption is needed on the plant about minimum phaseness, relative degree, or squareness.