Date: 15/11/2012

Author: Víctor Alfaro Ruíz ?

Tittle: Trade-off Issues in 2DoF PID Control Design: Performance, Robustness, and Fragility

Advisor: Ramon Vilanova Arbós

Abstract:?? The proportional integral derivative (PID) is, with no doubt, the control algorithm most applied in industrial control used most of the time as proportional integral (PI) control.

The controller must be matched (tuned) to the controlled process considering: control system performance, its response to changes in its inputs, set-point and disturbance; its robustness, its capabilities to keep the system stable in case of changes in the controlled process dynamics; control effort use and characteristics; and controller fragility, the effect of a change on the controller parameters.

In this thesis, a general design procedure for two-degree-of-freedom (2DoF) PI/PID controllers is proposed based in the specification of the different control system closed-loop transfer functions that include parameters that affect the performance/robustness trade-off.  Considering than the control system robustness requirement, is controlled process dependent, and more important, that it cannot be avoided, the robustness level, measured with the maximum sensitivity, is used as the design parameter.

The proposed controller design methodology denoted as Model Reference Robust Tuning (MoReRT) is applied to tune 2DoF PI controllers for first- and second-order over damped, integrating, inverse response, and unstable controlled processes.  

An extension of the MoReRT to 2DoF PID controllers is also considered.
The proposed MoReRT method starts with the selection of regulatory control and servo control closed-loop transfer functions targets.  These transfer functions state the desired shapes for the disturbance and set-point step responses.

The responses targets specification takes into account the controlled process model characteristics, particularly its non-minimum phase components and order.  They depend also on the design parameters that affect the control system performance, control effort, and robustness.

Controller parameters are obtained by optimizing a cost functional that evaluate the difference between the target total response and the one obtained with the controller to tune.  Design parameters are adjusted to obtain a robustness level target.

The accomplishment of the robustness target level for all the controlled process models considered (over damped, integrated, and unstable) is one of the distinctive characteristics of the proposed MoReRT design method.

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