Optimal loop-shaping for systems with large parameter uncertainty via linear programming

Abstract

This paper describes an optimization method for designing feedback systems subject to large parameter uncertainty. Following the design philosophy of the Quantitative Feedback Theory (Horowitz andSidi 1972, 1978) the objective is to minimize the magnitude of the open loop LOW) at high frequencies subject to: (a) low and intermediate-frequency bounds capturing the closed-loop robust-performance objectives; (b) a universal-frequency bound on LCjw) which limits the effects of disturbances; and (c) realization constraints on L(s) in the form of Bode's integral. This last relation is discretized at a number of frequencies and defines, together with ( a ) and (b), the overall set of linear constraints in a resulting linear programming optimization problem.

Optimal design of PID controllers using the QFT method

“…PID (or "three-term") controllers are widely used in industry because they are simple and easy to tune. Our algorithm can be used to provide an adequate QFT design, or as the first step for designing a more complex controller [1]. In addition, the algorithm can easily tackle a large number of constraints and can be also be applied to multivariable systems, using the standard QFT approach [7], [6].…”

Fixed-order H∞ controller design for nonparametric models by convex optimization

“…Frequency-domain approaches lead usually to low-order controllers and the design procedures need some expertise and are based on trial and error. Although recently optimization ap-proaches are used to compute controllers in the QFT framework [10,11,12], H 2 and H ∞ control criteria for spectral models have not been considered.…”

Automated Synthesis of Fixed Structure QFT Controller using Interval Constraint Satisfaction Techniques

“…Traditionally, this synthesis was done manually by the designer, relying on design experience and skill. Recently, several researchers have attempted to automate this step, see, for instance, Bryant and Halikias (1995); Chait et al (1999); Gera and Horowitz (1980); Garcia-Sanz and Guillen (2000); Nataraj and Tharewal (2007); Nataraj and Kubal (2007); Thomspon and Nwokah (1994).…”

“…Such a template approximation leads to overbounding in the constraints derived for the optimization. Bryant and Halikias (1995) addressed the problem of automatic loop shaping using linear programming techniques wherein the QFT bounds are approximated by a series of linear approximations. However, their method also leads to conservatism in describing nonlinear QFT bounds by linear inequalities.…”