Contributions to the control of input-saturated systems: time delay and allocation function cases

Abstract

Saturating actuators are ubiquitous to real-world processes. Currents and voltages in circuits,motors speed in robotics systems, the concentration of agents in chemical reactions, and so on,are all variables limited in amplitude. The consideration of such limitations in otherwise open-loop linear systems introduces some special challenges to the control engineer/ mathematician.From the ’80s to the early years of the new millennium, control researchers have spent effortsin developing mathematical tools based on the Lyapunov theory for the stability analysis andstabilization of such systems. Although one could say that a mature stage of the subject hasbeen achieved, some interesting problems still arise for the control of input saturated systems,especially when considered in conjunction with other challenging issues.Time delays are another subject of main interest in control systems. In this thesis,we are mainly interested in the predictor/ model-based control of such systems. Specially, weaddress dead-time compensators (DTCs), which are a class of controllers derived from Smith’sidea developed in the ’50s. The contributions in this part are split throughout two chapters: i)First, we develop a DTC structure for systems with saturating inputs through the addition of ananti-windup strategy. The interesting facts about the proposed strategy are that we show that dueto thecompensationof the delay in the nominal case, the strategy can be used in a very practicalmanner (with easy to follow tuning rules) and can also be applied in a unified way to delay-freesystems. ii) Secondly, in the case of time-varying delays, a new strategy for the characterizationand analysis of the system region of attraction in the presence of saturating inputs is presented.By means of convex optimization problems, we establish relations between the controller tuningvariables, bounds on the time-varying delay and sizes of the estimated region of attraction. Bothchapters in this part are developed in the discrete-time domain.The problem of over-actuated/ input-redundant systems is also approached in the finalpart of the thesis. This subject is closely related to aerospace and robotics applications, whereredundancy of actuators is often necessary. Besides the controller and anti-windup subsystems, athird subsystem, designated “allocation function", needs to be designed in order to distribute thedesired control effort among the multiple actuators. The contribution in this part is related tothe development of convex conditions for the co-design of a dynamic allocator subsystem alongwith static anti-windup. Furthermore, we show that the developed conditions are always feasibleunder certain assumptions. The development in this part is made in the continuous-time domain.The contributions in this thesis are, therefore, related to the analysis, control and anti-windup strategies for input saturated systems in conjunction with either time delays or allocation functions. Thus, we intend by no means to argue that we have developed novel general methodologies to the study of the mature field of the saturation nonlinearity. However, thecontributions reported here are of importance for the special covered cases