β Scribed by C. Canudas de Wit
No coin nor oath required. For personal study only.
EFFORTS CONFINED to the analysis, synthesis and design of control theory usually assume a complete knowledge of the model describing the dynamic behaviour of the system and a particular distribution of the disturbances acting on the system. In real-life situations, the exact order of the system model, the precise knowledge of the parameters associated to this model and the nature of the noise and disturbances are, in general, far to be exactly determined. Other types of uncertainties such as actuator nonlinearities, time delays and parameter variations may also be a cause of model mismatches.
Adaptive control theory provides an answer to the problem of system stabilisation under parameter uncertainties. However, as was shown in Rohrs's example (Rohrs et al., 1985), adaptive systems suffer of an substantial lack of robustness to unmodelled dynamics. Methods for achieving stable adaptation by modifying the adaptive laws are now available. These modifications seek to guarantee boundedness of all signals in the presence of unrnodelled dynamics and/or in the presence of bounded external disturbances. Examples of such modifications are: dead-zone (Egardt, 1979), parameter projection (Egardt, 1979;Kreisselmeier and Narendra, 1982), a-modification (Ioannou and Kokotovic, 1983) and ermodification (Narendra and Annaswamy, 1987). In order to implement these ideas some a priori information is required either on the amplitude of the external disturbance, on the norm of the parameter vector, on the system relative degree or on the "richness" of the information vector. This is the type of a priori knowledge to which the book refers.
After a general introduction in Chapter 1, the authors devote Chapters 2 and 3 to the study of adaptive systems subject to parasite uncertainties as a consequence of the use of reduced order models as a basis for the control design. Singular perturbation models are used for this purpose. The system under analysis is divided into two subsystems, one fast and the other slow. The parasite states are thus modelled by the fast subsystem whereas the slow subsystem describes the nominal dynamics disturbed by the fast modes. In the continuous-time case (Chapter 2) the authors apply the el-modification algorithm (version bounded disturbances) to the problem of unmodelled dynamics (which are statedependent). The authors have used the first version of the el-modification algorithm using the hypothesis of relative degree (which is restrictive) rather than the second one which seems to be more appropriate to the problem at hand. Local results are instead obtained. Chapter 3 deals with the discrete time case and proposes three additional modifications for assuring both signals and parameters boundedness. The first modification is similar to the a-modification (Ioannou and Kokotovic, 1983), where the same type of hypothesis on the relative degree between model and plant is assumed. The last two modifications are strongly inspired by the el-modification (Narendra and Annaswamy, 1987).
The analysis presented in Chapters 2 and 3 is based on one of the existing methods dealing with the robustness of the adaptive algorithms. A general treatment on the topic can be * Control of Partially-known Dynamical Systems (Lecture Notes in Control and Information Sciences) by A. A.
π SIMILAR VOLUMES
An alternative adaptive scheme to achieve output tracking for a class of minimum-phase dynamically input-output linearizable nonlinear systems with parametric uncertainties is considered. The proposed approach is based upon a combination of the adaptive backstepping design method and a sliding mode
Reduction of structural vibration in actively controlled dynamical system is usually performed by means of convenient control forces dependent of the dynamic response. In this paper the existent studies will be extended to dynamical systems subjected to non-normal delta-correlated random process wit