On the control of systems with input saturation or periodic disturbances
Abstract: This thesis deals with two important problems in control theory and practice. The first problem is the windup problem in controllers where there exist non-linearities between the controller output and the process input. The first four parts of the thesis address this issue and in particular, anti-windup compensators to avoid controller windup are studied. The second problem, which is studied in Part V of the thesis, is the rejection of periodic disturbances and the tracking of periodic setpoints. In Part I we investigate a number of different anti-windup compensators available in the literature, and expose the observer property inherent in a class of such compensators. This observer property enables us to unify these anti-windup compensators as special cases of a general observer based anti-windup compensator. In Part II, a particular anti-windup compensator known as the conditioning technique is investigated, and an inherent weakness (short sightedness) in this method is demonstrated. To overcome the effect of the short sightedness and other limitations in the conditioning technique, a generalization is proposed, and its relationship to the other methods is investigated. In Part III, we have investigated the convergence properties of adaptive poleplacement controllers when there exists input saturation. The analysis is facilitated by using the anti-windup compensator based on the generalization proposed for conditioning technique in Part II. The analysis is limited to stable processes. Part IV addresses the problem of controller windup and the problem of directional change in controls for multi-input multi-output processes with input saturation. To avoid the windup problem, first the generalization in Part II for the conditioning technique is extended to the multivariable case. Then, using the geometric interpretation of the conditioning technique, further modifications based on inequality constraint optimization are introduced to reduce the effect of the directional change in control on output performance. In Part V, as an alternative to the controllers based on the internal model principle, a feedforward controller is derived to achieve complete decoupling of periodic disturbances and perfect tracking of periodic setpoints, even when the process is nonminimum phase. In particular, it is shown that this feedforward controller which is indeed a finite impulse response filter, can be obtained by solving a Diophantine identity. When the measurements are corrupted by noise, a tuned filter is utilized to improve the performance. To achieve fast disturbance estimation, especially when the shape of the periodic signal is slowly varying, a time-varying tuned filter is also proposed. However, the proposed tuned filter is strictly limited to the case where the disturbances are purely periodic in discrete-time.
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