Application of Lyapunov matrix inequality based unsymmetrical saturated control to a multi-vectored propeller airship

Abstract

The problem of the design of a controller for a multi-vectored propeller airship is addressed. The controller includes anti-windup that takes into account unsymmetrical actuator constraints. First, a linear transformation is applied to transform the unsymmetrical constraints into symmetric constraints with an amplitude-bounded exogenous disturbance. Then, a stability condition based on a quadratic Lyapunov function for the saturated closed-loop system is proposed. The condition considers both amplitude-bounded and energy-bounded exogenous disturbances. Thus, the controller design problem is transformed into a convex optimization problem expressed in a bilinear matrix inequality form. Two controller design methods were applied: one-step controller and traditional anti-windup controller. The one-step method obtains the controller and the anti-windup compensator in one step while the anti-windup controller method separates this process into the linear controller design and the compensator design. Simulation results showed that both controllers enlarge the stability zone of the saturation system and have good tracking performance. It is shown that the anti-windup controller design method not only has a larger region of stability, but the demanded actuator output exceeds the constraints less and has a smaller anti-windup coefficient matrix compared to the one-step method.

Keywords

Multi-vectored propeller airship unsymmetrical saturation one-step controller anti-windup controller Lyapunov matrix inequality

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References

Fossard

Normand-Cyrot

. Nonlinear systems: Stability and stabilization, London: Chapman & Hall, 1996.

Tarbouriech

Garcia

Glattfelder

. Advanced strategies in control systems with input and output constraints, New York: Springer Verlag, 2007.

Shtessel Y, Buffington J, Pachter M, et al. Reconfigurable flight control on sliding modes addressing actuator deflection and deflection rate. In: AIAA guidance, navigation, and control conference and exhibit, Boston, MA, USA, 10–12 August 1998, paper no. AIAA-98-4112, pp.127–137.

Queinnec I, Tarbouriech S and Garcia G. Anti-windup design for aircraft control. In: Proceedings of IEEE conference on control applications (CCA), Munich, Germany, 2006, pp.2541–2546.

Lin

. Controlled invariance of ellipsoids: Linear vs. nonlinear feedback. Syst Control Lett 2004; 53: 203–210.

Benzaouia

. Saturated switched systems, New York: Springer Verlag, 2012.

Suárez

Alvarez-Ramirez

Solis-Daun

. Linear systems with bounded inputs: Global stabilization with eigenvalue placement. Int J Robust Nonlinear Control 1997; 7: 835–845.

Bemporad A, Teel AR and Zaccarian L. L₂ anti-windup via receding horizon optimal control. In: 2002 American control conference, Anchorage, AK, USA, 8–10 May 2002, pp.639–644.

Hindi H and Boyd S. Analysis of linear systems with saturation using convex optimization. In: Conference on decision and control, Tampa, OR, USA, 1998, pp.903–908.

10.

Wada

Saeki

. An LMI based scheduling algorithm for constrained stabilization problems. Syst Control Lett 2008; 57: 255–261.

11.

Palmeira

AHK

Gomes da Silva

Tarbouriech

et al.

Sampled-data control under magnitude and rate saturating actuators. Int J Robust Nonlinear Control 2016; 26: 3232–3252.

12.

Jungers

Tarbouriech

. Anti-windup strategies for discrete-time switched systems subject to input saturation. Int J Control 2016; 89: 1–29.

13.

Tarbouriech

Garcia

Gomes da Silva

et al.

Stability and stabilization of linear systems with saturating actuators, London: Springer, 2011.

14.

Garcia

Tarbouriech

Gomes da Silva

et al.

Finite L₂ gain and internal stabilization of linear systems subject to actuator and sensor saturations. IET Control Theory Appl 2009; 3: 799–812.

15.

Gomes da Silva

Tarbouriech

. Local stabilization of discrete-time linear systems with saturating controls: An LMI-based approach. IEEE Trans Autom Control 2001; 46: 119–125.

16.

Kapila

Grigoriadis

. Actuator saturation control, New York: Marcel Dekker, 2002.

17.

Lin

. Control systems with actuator saturation: Analysis and design, Boston, MA: Birkhäuser, 2001.

18.

Oliveira MZ, Gomes da Silva JM Jr, Coutinho D, et al. Anti-windup design for a class of multivariable nonlinear control systems: An LMI-based approach. In: 50th IEEE conference on decision and control and European control conference (CDC-ECC), Orlando, FL, USA, 12–15 December 2011.

19.

Grimm

Hatfield

Postlethwaite

et al.

Antiwindup for stable linear systems with input saturation: An LMI-based synthesis. IEEE Trans Autom Control 2003; 48: 1509–1525.

20.

Tarbouriech

Turner

. Anti-windup design: An overview of some recent advances and open problems. IET Control Theory Appl 2009; 3: 1–19.

21.

Sussmann

Sontag

Yang

. A general result on the stabilization of linear systems using bounded controls. IEEE Trans Autom Control 1994; 39: 2411–2425.

22.

Gomes da Silva

Tarbouriech

. Anti-windup design with guaranteed regions of stability: An LMI-based Approach. IEEE Trans Autom Control 2005; 50: 106–111.

23.

Boyd

El Ghaoui

Féron

et al.

Linear matrix inequalities in system and control theory, Philadelphia, PA: SIAM, 1994.

24.

Benzaouia

Benhayoun

Mesquine

. Stabilization of systems with unsymmetrical saturated control: An LMI approach. Circuits Syst Signal Process 2014; 33: 3263–3275.

25.

Chen

Zhang

Duan

. Control system design of a multi-vectored thrust stratospheric airship. Proc IMechE, Part G: J Aerospace Engineering 2014; 228: 2045–2054.