Feedforward feedback controller design for uncertain systems

Abstract

We describe an optimization method for design of combined feedforward and feedback controllers when the plant model is uncertain. It b demonstrated that the feedback design and the feedforward design have to be made jointly for the performance to be optimal. The uncertainties used in the synthesis are given as intervals for the parameters with corresponding probability density functions. These are used in the evaluation of the objective function, which is the expected value of the effect of load disturbances. The minimization is subject lo constraints on the sensitivity function and the controller response to reference signals and meusurement noise. By changing the constraints the trade-oN between performance, robustness and actuation is elucidated in the same manner as for plants with no explicit uncertainties. Depending on the problem character, i.e. S E 0 or MIMO, number of uncertain parameters and size of nominal closed loop in the uncertainty formulation, three different methods to guarantee the constraints are suggested A direct evaluation, Horowitz-Sidi bounds with a Homwitz-Sidi test, or use of the structured singular value far robust performance. We also derive a second order approximation of the objective function to use when the number of uncertain parameters is high. The methods are illustrated on a nonlinear and uncertain control problem, namely the external carbon addition in predenitrification wastewater treatment plants.

Joint synthesis of dynamic feed-forward and static state feedback for platoon control

“…Suitable state feedback gains are then constructed as in (25) with α = ρ/(ρ + 1). Proof: We first express (31) as κ T k M κ k < 0 by using (29). By applying the Schur complement lemma, we then express the sufficient condition M ≺ 0 as in (32) …”

“…This structure facilitates a separate treatment of feed-forward synthesis, which is usually performed in the second step. Nevertheless, a joint synthesis is more preferable in view of the fact that controller design usually involves multiple objectives that can better be handled simultaneously [29].…”

Nonconservative Robust Control: Optimized and Constrained Sensitivity Functions

“…With this in mind, (2) and (3) can be simplified to (5) (6) where and are based on the nominal plant. If, for some reason, is expected to depend significantly on the uncertainties, an approximation of the expected value taking the covariance of the parameters into consideration can be used (see [19]). …”

“…The same methods may naturally be applied to single-input, single-output (SISO) systems as well. However, for many SISO cases, the QFT-based method presented here is superior to the use of structured singular values [19]. For systems where the same uncertain parameter occurs in many places of a system model, the dimension of the nominal closed-loop system matrix , resulting from linear fractional transformations, may become very large.…”

“…For systems where the same uncertain parameter occurs in many places of a system model, the dimension of the nominal closed-loop system matrix , resulting from linear fractional transformations, may become very large. This can make structured singular value determinations unfeasible, while the method presented here is quite insensitive to this [19]. This paper is organized as follows.…”