Automatic loop-shaping of QFT robust controllers

Abstract

This paper introduces a methodology to design automatically QFT (Quantitative Feedback Theory) robust controllers for SISO (single input-single output) plants with model uncertainty. The method generalizes previous automatic loop-shaping techniques, avoiding restrictive assumptions about the search space. This methodology applies two strategies: a) Evolutionary Algorithms, and b) Genetic Algorithms (GA). In both cases the objective is to search the QFT robust controller that fulfils the control specifications for the whole set of plant models within the uncertainty. Each strategy has been applied to a benchmark in order to validate the techniques.

Simultaneous automated design of structured QFT controller and prefilter using nonlinear programming

“…However, this process limits the convergence of the algorithm because such a discretized description cannot be differentiated, while efficient optimization algorithms (local or global) require differentiating at least once the constraints. Second, QFT bounds have been used directly using population‐based optimization algorithms: use a simple constraint that is either 0 or 1 depending on the bound satisfaction, while uses a more elaborated constraint that compute a distance to the bound satisfaction.…”

“…The same issue has been overcome in by computing explicitly the poles and enforcing the greatest real part to be negative. Such an iterative procedure cannot be used directly in standard solvers for nonlinear programming.…”

“…Here, we have considered another QFT benchmark example to test the quality of the new methodology. The uncertain transfer function for flight control problem is given as follows : where the uncertainties introduced in the parameters k , a , and t d are as follows: Samples from these plant uncertainty intervals are chosen as follows: …”

QFT Based Control for Twin Rotor MIMO System

“…The method consists [7], [8], [9] in assuming an initial value of the controller function G( jω), and adjusting the loop function L o ( jω) that verifies the imposed restrictions and minimizes the control effort. The adjustment is made by shifting the loop curve vertically and horizontally on the magnitude-phase plane, until it is situated in such a way as to have the lowest gain possible.…”

Automatic loop shaping of QFT applied to an active control design

“…In [6] the controller synthesis problem is posed as interval constraint satisfying problem and solved with interval constraint solver. In [7] a methodology that applies two techniques to design QFT controllers is proposed. The first one is based on evolutionary algorithms and the second is based on genetic algorithms.…”