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

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

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

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

Multivariable Anti-Windup and Bumpless Transfer: A General Theory

A general theory is developed to address the anti-windup/bumpless transfer (AWBT) problem. Analysis results applicable to any linear time invariant system subject to plant input limitations and substitutions are presented. Quantitative performance objectives for AWBT compensation are outlined and several proposed AWBT methods are evaluated in light of these objectives. A synthesis procedure which highlights the performance trade-offs for AWBT compensation design is outlined

Static anti-windup compensator design for locally Lipschitz systems under input and output delays

This paper proposes a static anti-windup compensator (AWC) design methodology for the locally Lipschitz nonlinear systems, containing time-varying interval delays in input and output of the system in the presence of actuator saturation. Static AWC design is proposed for the systems by considering a delay-range-dependent methodology to consider less conservative delay bounds. The approach has been developed by utilizing an improved Lyapunov-Krasovskii functional, locally Lipschitz nonlinearity property, delay-interval, delay derivative upper bound, local sector condition, L2 gain reduction from exogenous input to exogenous output, improved Wirtinger inequality, additive time-varying delays, and convex optimization algorithms to obtain convex conditions for AWC gain calculations. In contrast to the existing results, the present work considers both input and output delays for the AWC design (along with their combined additive effect) and deals with a more generic locally Lipschitz class of nonlinear systems. The effectiveness of the proposed methodology is demonstrated via simulations for a nonlinear DC servo motor system, possessing multiple time-delays, dynamic nonlinearity and actuator constraints

Advanced Anti-Windup Techniques for the Limitation of the Effects of the Actuator Saturation

In this thesis an industrial issue is analysed. The issue consist on the undesirable effect of actuator sturation. Two approaches are given to solve the issue: an accurate inertia identification algorithm based on the DFT coefficient; and advanced anti-windup compensators. The principle of the modern anti-windup (DLAW and MRAW, LMI-based design approach), and a systematic design design procedure for the observer-based anti-windup are given. Simulation and test results are also given.ope

A novel robust disturbance rejection anti-windup framework

This is an Author's Original Manuscript of an article submitted for consideration in the International Journal of Control [copyright Taylor & Francis] and is available online at http://www.tandfonline.com/10.1080/00207179.2010.542774In this article, we propose a novel anti-windup (AW) framework for coping with input saturation in the disturbance rejection problem of stable plant systems. This framework is based on the one developed by Weston and Postlethwaite (W&P) (Weston, P.F., and Postlethwaite, I. (2000), ‘Linear Conditioning for Systems Containing Saturating Actuators’, Automatica, 36, 1347–1354). The new AW-design improves the disturbance rejection performance over the design framework usually suggested for the coprime-factorisation based W&P-approach. Performance improvement is achieved by explicitly incorporating a transfer function, which represents the effect of the disturbance on the nonlinear loop, into the AW compensator synthesis. An extra degree of freedom is exploited for the coprime factorisation, resulting in an implicitly computed multivariable algebraic loop for the AW-implementation. Suggestions are made to overcome the algebraic loop problem via explicit computation. Furthermore, paralleling the results of former work (Turner, M.C., Herrmann, G., and Postlethwaite, I. (2007), ‘Incorporating Robustness Requirements into Antiwindup Design’, IEEE Transactions on Automatic Control, 52, 1842–1855), the additive plant uncertainty is incorporated into the AW compensator synthesis, by using a novel augmentation for the disturbance rejection problem. In this new framework, it is shown that the internal model control (IMC) scheme is optimally robust, as was the case in Turner, Herrmann, and Postlethwaite (2007) and Zheng and Morari (Zheng, A., and Morari, M. (1994), ‘Anti-windup using Internal Model Control’, International Journal of Control, 60, 1015–1024). The new AW approach is applied to the control of dynamically substructured systems (DSS) subject to external excitation signals and actuator limits. The benefit of this approach is demonstrated in the simulations for a small-scale building mass damper DSS and a quasi-motorcycle DSS