Preview Control for a Class of Linear Continuous Time-Varying Systems

Abstract

A design method of an optimal preview controller for a class of linear continuous time-varying systems is presented in this paper. By differentiating both the output error signal and the two sides of the state equation, an augmented error system is constructed, which contains the error signal, the state vector and the derivative of the state vector. Then the performance index function is introduced and the control problem is solved by optimal control theory. Thus the optimal preview control input for the original time-varying system is found. The proposed controller includes the previewable future signal, so the response speed is accelerated. Meanwhile, the integrators in the controller make the output vector track the target signal better. The numerical simulations illustrate the validity of the proposed method.

Preview repetitive control with equivalent input disturbance for continuous‐time linear systems

“…Remark Assumption 1 is reasonable, which is a necessary hypothesis when designing an RC law [1–3]. Assumption 2 is a quite standard hypothesis introduced to consider the PC problem [21–24]. It indicates that the reference signal's values are known in the future.…”

“…In [21], by applying LQR technique, a state‐feedback controller with tracking error integral and preview compensation was derived. The obtained result was extended to continuous time‐varying systems and time‐invariant descriptor systems in [22] and [23], respectively. Taking the identical equation of the derivative of the control input as a part of the augmented systems, the optimal preview controller in finite horizon was deduced in [24, 25].…”

Estimation and rejection of periodic disturbance in a preview repetitive control system

“…In order to meet the continuous-time system of previewable requirements, Katayama and Hirono derived a type 1 servomechanism with both integral of tracking error and preview action by constructing an augmented error system and using linear quadratic regulator (LQR) technology [12]. The optimal PC problems for continuous-time systems and time invariant descriptor systems have been studied [13,14], respec-tively. For the PC control problem of continuous-time linear systems with input delay, Liao et al used variable substitution and state augmentation techniques to achieve time delay elimination and preview future information [15,16].…”

Optimal preview repetitive control for impulse-free continuous-time descriptor systems

“…As a result, the difficulty and complexity are greatly increased. By differentiating both the output error signal and the two sides of the state equation, the optimal PC problem of continuous-time systems is solved in [18][19][20]. By taking the derivative of the control input, a new optimal PC was deduced [21].…”