Mohammed M’Saad

Introduction to Adaptive Control

Adaptive Control covers a set of techniques which provide a systematic approach for automatic adjustment of the controllers in real time, in order to achieve or to maintain a desired level of performance of the control system when the parameters of the plant dynamic model are unknown and/or change in time.

Robust Parameter Estimation

In the previous chapters, we assumed that: 1. The true plant model and the estimated plant model have the same structure (the true plant model is described by a discrete time model with known upper bounds for the degrees n A , n B + d). 2. The disturbances are zero mean and of stochastic nature (with various assumptions). 3. For parameter estimation in closed loop operation, the controller a. has constant parameters and stabilizes the closed loop. b. contains the internal model of the deterministic disturbance for which perfect state disturbance rejection is assured. 4. The parameters are constant or piece-wise constant. 5. The domain of possible parameters values is in general not constrained (exception: recursive maximum likelihood and adaptive filtered closed loop output error).

Adaptive Regulation—Rejection of Unknown Disturbances

This chapter addresses the problem of attenuation (rejection) of unknown disturbances without measuring them by using a feedback approach. In this context, the disturbance model is unknown and time varying while the model of the plant is known (obtained by system identification) and almost invariant. This requires an adaptive approach. The term “adaptive regulation” has been coined to characterize this control paradigm. Direct and indirect adaptive regulation strategies using the internal model principle and the Youla-Kucera parameterization will be presented. The evaluation of the methodology is done in real time on an active vibration control system using an inertial actuator.

Recursive Plant Model Identification in Open Loop

Iterative combination of identification in closed loop and robust control redesign leads to a two time scale adaptive control system very appealing in practice. The chapter is dedicated to the presentation of recursive algorithms for plant identification in closed-loop operation and their application. Two classes of algorithms will be presented, analyzed and evaluated experimentally: closed-loop output error algorithms and filtered open-loop recursive identification algorithms. Specific techniques for model validation in the context of identification in closed loop will also be presented. The performance of the various algorithms will be illustrated by simulation and by their application to the identification in closed loop and controller re-design of a flexible transmission control system.

Discrete-Time System Models for Control

We will consider single-input single-output time invariant systems described by input-output discrete-time models of the form:

Robust Digital Control Design

y(t) = - \sum\limits_{i = 1}^{{n_A}} {{a_i}y} (t - i) + \sum\limits_{i = 1}^{{n_B}} {{b_i}u} (t - d - i)

Indirect Adaptive Control

(2.1.1) where t denotes the normalized sampling time (i.e., \( t = \frac{t}{{{T_S}}} \), TS sampling period) , u(t) is the input, y(t) is the output, d is the integer number of sampling periods contained in the time delay of the systems, ai and bi are the parameters (coefficients) of the models.

Direct Adaptive Control

The principles of adaptive control with switching are presented. This method insures high control performance in the presence of large and abrupt parameter variations. The stability of this type of adaptive control is studied and shown to be guaranteed with a minimum dwell-time between switchings. An application of adaptive control with switching and tuning to a flexible transmission system is presented. The advantages of this scheme with respect to classical adaptive control and fixed robust control are illustrated via some experimental results. The use of CLOE adaptation in the adaptive control with switching will also improve the performance of the system in the tuning phase.