Parametric control systems design with applications in missile control

Abstract

This paper considers parametric control of high-order descriptor linear systems via proportional plus derivative feedback. By employing general parametric solutions to a type of so-called high-order Sylvester matrix equations, complete parametric control approaches for high-order linear systems are presented. The proposed approaches give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices, and produce all the design degrees of freedom. Furthermore, important special cases are particularly treated. Based on the proposed parametric design approaches, a parametric method for the gain-scheduling controller design of a linear time-varying system is proposed and the design of a BTT missile autopilot is carried out. The simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.high-order linear systems, parametric approaches, Sylvester matrix equations, BTT missile

Direct parametric control of fully-actuated second-order nonlinear systems—descriptor case

“…Necessity. Suppose that there exist a constant matrix V ∈ R 2n×(n+n0) , and a pair of gain matrices K 0 (θ, x,ẋ) and K 1 (θ, x,ẋ) ∈ R n×n , satisfying the relation (11) and the condition (17). Denote…”

“…Secondly, it follows from Lemma 1 that there exists a matrix Z satisfying (17) if and only if there exists a matrix Z satisfying…”

“…The above relation, together with (31), states that there exists a matrix Z satisfying (17) if and only if there exists a matrix Y 0 ∈ R n0×n0 which makes…”

Direct parametric control of fully-actuated second-order nonlinear systems—The normal case

“…Suppose that there exist a constant nonsingular matrix V ∈ R 2n×2n , and a pair of gain matrices K 0 (θ, x,ẋ) and K 1 (θ, x,ẋ) ∈ R n×n , satisfying the relation (19). Denote…”

“…The derivation of the above direct parametric control system design approach really originated from the author's work on parametric control of second-and highorder linear systems (e.g., [15]- [19]) as well as solutions to second-and high-order Sylvester matrix equations (e.g., [20]- [22]). It was firstly found out during the research that, for a fully-actuated high-order linear system, the parametrization of the controller can be immediately written out without any computation, and then it was further discovered that the approach also suits systems with nonlinear and time varying coefficients.…”