Date: 05/10/2011

Author: Salvador Alcántara Cano

Tittle: Analytical design of feedback compensators based on Robustness/Performance and Servo/Regulator trade-offs (Utility in PID control applications)

Director: Carles Pedret


The concept of (negative) feedback, albeit simple, is extremely powerful, and has since the Industrial Revolution changed our world dramatically. Nowadays, control systems are everywhere. In process industry, for example, they keep the manipulated variables close to the set-points in spite of disturbances and changes in the plant. Moreover, feedback provides the only means to stabilize unstable processes. This way, the feedback mechanism is essential for improving product quality and energy efficiency, which yields better (sustainable) economy.

The theme of this thesis is on analytical design of feedback compensators through linear control theory. The restriction to the Linear Time Invariant (LTI) case is not severe in the sense that most processes are well modeled locally by LTI systems. The operating range of the controller can then be extended using gain scheduling or adaptation. Within this work, the standard single-loop feedback configuration is assumed. Among the control objectives, stability and robustness are important considerations because of the presence of uncertainty in practice. Apart from that, the controller faces servo (set-point tracking) and regulation (disturbance rejection) objectives.

In the considered scenario, it is well-known that there is an inherent compromise between robustness and performance. In general, the servo and regulation objectives are  also conflicting and sometimes a balance is desirable. An example is in cascade configurations: the inner loop should be tuned based on tracking as it receives the set-points from the master loop. However, the inner loop may also need acceptable load disturbance suppression capabilities. Another good example is found in Model Predictive Control (MPC) applications due to frequent changes of set-points by the server. Finally, there may be a trade-off between the response to disturbances entering at the input and at the output of the plant, which can be understood as a servo/regulator trade-off too.

The goal of this thesis is to provide model-based design procedures in terms of the Robustness/Performance and Servo/Regulator trade-offs, and give insight into how the tuning depends on the process parameters. In the presented methods, the designer is not required to choose weighting functions nor reference models as in other approaches, and the involved parameters have a clear meaning to facilitate the tuning process. Because PID controllers are prevalent in industry, application to PID tuning is considered most of the times. Although numerical methods for controller derivation may yield superior performance than analytical ones, the latter category has been preferred for several reasons. First, analytical procedures help understand the problem at hand. Second, when applied to low-order models, well-motivated tuning rules which are simple and easy to memorize can be obtained. These features are very desirable from the operator's point of view, and for teaching purposes too.

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