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

Abstract

A new approach for robust fixed-order H∞ controller design by convex optimization is proposed. Linear time-invariant singleinput single-output systems represented by nonparametric models in the frequency domain are considered. It is shown that the H∞ robust performance condition can be represented by a set of linear or convex constraints with respect to the parameters of a linearly parameterized controller in the Nyquist diagram. Multimodel and frequency-domain uncertainty can be considered straightforwardly in the proposed approach. The proposed method is compared with the standard H∞ control problem by a simulation example on an unstable system.

Fixed-order data-driven H∞ controller synthesis for flexible mechanical systems: Two-stage approach

“…The order of the synthesized sub-optimal H ' controller equals to the order of the generalized plant P in Figure 1 and the high order of the H ' controllers makes it difficult to implement this controller on real systems. Using DDC approaches, the fixed-order H ' controller synthesis problem can be formulated as a convex optimization problem (Karimi and Galdos, 2010;van Solingen et al, 2018). However, the main disadvantage of these methods is that the coefficients in the denominator of the transfer function of the controller should be predetermined without being included in the optimization problem.…”

“…By approximating the disc shaped region with a radius W 0 u jv ð ÞL jv, r ð Þ by a polygon with q . 2 vertices, constraints of the H ' controller synthesis problem in equation ( 20) can be expressed as convex constraints (Karimi and Galdos, 2010). If all vertices of the polygon in Figure 4 stay in the right side of the line d v ð Þ, then the constraints of the H ' controller synthesis problem are satisfied…”

“…In Khadraoui et al (2016), a DDC method is introduced for both stable and unstable systems, by using input/output data obtained from the closed-loop system identification tests performed with three different initial controllers. In Karimi and Galdos (2010), open-loop system identification input/output data is used to optimize parameters of linearly parametrized controller under convex H ' constraints. In this approach, convexification of the nonconvex robust performance constraints is performed with the help of the desired loop transfer function.…”

Design of a Fixed-Order Robust Controller to Damp Inter-Area Oscillations in Power Systems

“…The primary purpose of this paper is to design linearly parameterized robust controller to damp out the inter-area oscillations. Consider a linearly parameterized controller of the form given in (1) [8] [9]:…”

H∞/Predictive output control of a three-axis gyrostabilized platform

“…Research activities have been performed on this class of controllers. Similar strategies are the combination of model predictive robust control and sliding mode control, 1 solution of low rate of predictive control problem with the use of pre-calculation and scheduling system gains in bound of system performance, 2 the use of high gain adaptive control to fast adaptation which causes high-frequency disturbances with the use of scriptL2 robust control mechanism, 3 combination of predictive and fuzzy control with neural networks, 4 use of boundary real lemma as a linear inequality matrix with equality constraint to implementation of scriptH∞ controller, 5 a new method to design fix order scriptH∞ controller with the use of convex optimization for a linear time invariant MIMO, 6 design of fixed order scriptH∞ controller with the use of convex optimization in a SISO system, 7 use of combination of extended unified power quality conditioner and scriptH∞ loop shaping controller to accomplish zero steady state error of a controller which is robust to system uncertainties and insensitive to power supply frequency, 8 geometric structure of observable controllers to classify controllable and unobservable subspaces of scriptH∞ and scriptH2 controllers, 9 combination of linear predictive control with a kind of fuzzy controller to increase the dynamic performance of linear predictive control in relation to the nonlinear systems, 10 combination of predictive control in outer loop to position control and …”