Fixed-order Controller Design for State Space Polytopic Systems by Convex Optimization
نویسندگان
چکیده
In this paper, a new method for fixed-order controller design of systems with polytopic uncertainty in their state space representation is proposed. The approach uses the strictly positive realness (SPRness) of some transfer functions, as a tool to decouple the controller parameters and the Lyapunov matrices and represent the stability conditions and the performance criteria by a set of linear matrix inequalities. The quality of this convex approximation depends on the choice of a central state matrix. It is shown that this central matrix can be computed from a set of initial fixed-order controllers computed for each vertex of the polytope. The stability of the closed-loop polytopic system is guaranteed by a linear parameter dependent Lyapunov matrix. The results are extended to fixed-order H∞ controller design for SISO systems.
منابع مشابه
Fixed-Order Controller Design for Systems with Polytopic Uncertainty via Convex Optimization
Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex innerapproximation of the whole non-convex set of stabilizing controllers and depends on the choice of a central polynomial. It is shown that with an appropriate choice of the central polynomial, the set of all s...
متن کاملFixed-Order Controller Design for Polytopic Systems Using Rank Deficiency in a Sylvester Matrix
Fixed-order controller design for LTI-SISO polytopic systems is investigated using rank deficiency constraint on the controller Sylvester resultant matrix. It is shown that the non-convexity of fixed-order controller design problem can be contracted in a rank deficiency constraint on Sylvester resultant matrix of the controller. Then, an improved convex approximation of the rank deficiency cons...
متن کاملRobust H∞ Controller Design Using Frequency-Domain Data via Convex Optimization
A new robust controller design method that satisfies the H∞ criterion is developed for linear timeinvariant single-input single-output (SISO) systems. A data-driven approach is implemented in order to avoid the unmodeled dynamics associated with parametric models. This data-driven method uses fixed order controllers to satisfy the H∞ criterion in the frequency domain. The necessary and sufficie...
متن کاملRobust Fixed-order Gain-scheduling Autopilot Design using State-space Stability-Preserving Interpolation
In this paper, a robust autopilot is proposed using stable interpolation based on Youla parameterization. The most important condition of stable interpolation between local controllers is the preservation of stability so that each local controller can ensure stability for an open neighborhood around a nominal point. The proposed design used fixed-order robust controller with parameter-dependent...
متن کاملOff-line Robustification of Model Predictive Control for Uncertain Multivariable Systems
This paper proposes an off-line state-space control methodology for enhancing the robustness of multivariable Model Predictive Control (MPC) through the convex optimization of the Youla parameter. The Youla parameter-based optimization strategy allows convex specifications in closed-loop representation, focusing on the robustification of an initial controller using LMIs (Linear Matrix Inequalit...
متن کامل