Robust pi controller design satisfying sensitivity and uncertainty specifications

Abstract

This note presents a control design method for determining proportional-integral-type controllers satisfying specifications on gain margin, phase margin, and an upper bound on the (complementary) sensitivity for a finite set of plants. The approach can be applied to plants that are stable or unstable, plants given by a model or measured data, and plants of any order, including plants with delays. The algorithm is efficient and fast, and as such can be used in near real-time to determine controller parameters (for online modification of the plant model including its uncertainty and/or the specifications). The method gives an optimal controller for a practical definition of optimality. Furthermore, it enables the graphical portrayal of design tradeoffs in a single plot, highlighting the effects of the gain margin, complementary sensitivity bound, low frequency sensitivity and high frequency sensor noise amplification.Index Terms-Design, gain and phase margin, linear systems, proportional-integral (PI) control, robustness.

Tuning of PI compensators for integrating systems with large parametric uncertainty

“…A common design specification is to place an upper bound on the sensitivity function for every frequency [7], that is…”

“…The gain and phase margins can be seen as special case of sensitivity bound specification, since a sensitivity bound specification implies certain values for the gain and phase margins [7].…”

“…In this work, the optimization problem will be based on the non-convex optimization problem proposed in [5], where the integral gain is maximized with some constraints on the sensitivity and the complementary sensitivity functions. The formulation of the design problem with parametric uncertainty is not new, and has been previously approached in a number of works [6], [7], [8], [9]. However, in all these previous works, the design method comes up with a numerical or graphical procedure to obtain the optimum value of the compensator parameters, since, in general, the resulting non-convex optimization problem with parametric uncertainty is very hard to solve for general plants.…”

Robust PI compensators design for FOPDT systems with large uncertainty

“…The formulation of the design problem with paramet ric uncertainty is not new, and has been previously ap proached in a number of works [8][9][10][11][12][13]. In general, this design problem is very hard to solve, since it is necessary to consider all the plants of a given plants set (represent ing the parametric uncertainty).…”

Optimal Design Method of Pi Controller for Multiple Processes and Coupled Liquid Level System

“…In [14], a method is proposed to design robust PI/PID controller via iterative linear matrix inequalities algorithm (ILMI). In [15], a method is proposed to design the robust PI controller with sensitivity specifications through ILMI.…”