Shyh-Pyng Shue

Design of Automatic Landing Systems Using Mixed H/H Control

Mixed H2/HX control technique is employed to develop controllers for auto-landing systems for a commercial airplane. A linear model of the aircraft in longitudinal motion is established using the appropriate aerodynamic coefficients. With the control actuator, tracking errors, and altitude motion, the aircraft is shown to be governed by an augmentation system along with its filter model. Two kinds of optimal and robust control requirements are designed, which need to be satisfied simultaneously. One of requirements is with respect to an optimal trajectory selection for landing routes. The H2 method is used to minimize a cost function such that the optimal gain for trajectory optimization can be obtained. The other requirement is with respect to the disturbance attenuation. The Hm technique is employed to obtain the necessary formulation for the robust control gain to minimize the affection of the disturbance to the performance output. An algorithm is developed based on the convex theory for the mixed H2I Hn control and filter gains, which provides a suboptimal solution. A large commercial aircraft (Boeing 747-200) is employed to illustrate the potential of the proposed method. It is shown that the glide slope capture motion and flare maneuver of the aircraft are accomplished quite well, and the amplitudes of all maneuver are within FAA requirements. L INTRODUCTION Control of aircraft under difficult maneuvers is a problem of both theoretical and practical interest. Control under one of these difficult maneuvers, that of landing, is discussed and addressed in this paper. Design of automatic landing systems has been achieved using both robust and optimal control methods [1-3]. Reference [1] employed the #„ synthesis to design an automatic landing controller for an F-14 aircraft. Design of landing systems encountering windshear is given in

Optimal feedback control of a nonlinear system - Wing rock example

A procedure is presented for optimizing a state feedback control law for a nonlinear system with respect to a positive performance index. The Hamilton-Jacobi-Bellman equation is employed to derive the optimality equations wherein this performance index is minimized. The closed-loop Lyapunov function is assumed to have the same matrix form of state variables as the performance index. The constant interpolated terms of these matrix forms are easily determined so as to guarantee their positive definitenesses. The optimal nonlinear system is asymptotically stable in the large, as both the closed-loop Lyapunov function and performance index are positive definite. An unstable wing rock equation of motion is employed to illustrate this method. It is shown that the wing rock model using nonlinear state feedback is asymptotically stable in the large. Both optimal linear and nonlinear state feedback cases are evaluated.

Robust Hinfinity state feedback control of discrete time-delay linear systems with norm-bounded uncertainty

This paper studies, via a linear matrix inequality approach, the problem of Hinfinity control for discrete time-delay linear systems with parametric uncertainty. The system under consideration is subjected to both time-varying norm-bounded parameter uncertainty and time delay in the state. First, the problem of robust stability of the underlying system is investigated. Next, we address the problem of robust Hinfinity state feedback control in which both robust stability and a prescribed Hinfinity performance are required to be achieved irrespective of the uncertainty and time delay. It is shown that the above problem can be solved if a linear matrix inequality has a symmetric positive definite solution.

Robust disturbance attenuation with stability for a class of uncertain singularly perturbed systems

In this paper, the problem of robust stability and robust disturbance attenuation is investigated for a class of singularly perturbed linear systems with norm-bounded parameter uncertainties in both state and output equations. Based on the slow and fast subsystems, a composite linear controller is designed such that both robust stability and a prescribed H infinity performance for the full-order system are achieved, irrespective of the uncertainties. Our results show that the above problem can be converted to an H infinity control problem for a related singularly perturbed linear system without parameter uncertainty. Thus, the existing results on H infinity control of singularly perturbed systems can be applied to obtain solutions to the problem of robust H infinity control for the uncertain systems, which is independent of the singular perturbation epsilon when epsilon is sufficiently small. An example is given to show the potential of the proposed technique.

Controller design for bilinear systems with parametric uncertainties

This paper studies the problem of robust control of a class of uncertain bilinear continuous-time systems. The class of uncertain systems is described by a state space model with time-varying norm-bounded parameter uncertainty in the state equation. We address the problem of robust H∞ control in which both robust stability and a prescribed H∞ performance are required to be achieved irrespective of the uncertainties. Both state feedback and output feedback controllers are designed. It has been shown that the above problems can be recast into H∞ syntheses for related bilinear systems without parameter uncertainty, which can be solved via a Riccati inequality approach. Two examples are given to show the potential of the proposed technique.

Mixed H2/H∞ Method Suitable for Gain Scheduled Aircraft Control

The formulations of mixed H2/H1 gain scheduling control of aircraft in longitudinal motion aredeveloped. The coefe cients of a linear model of aircraft are estimated from the aircraft geometry. Based on e ight Mach number, gain scheduling is applied with the mixed H2/H1 . It is shown that the state equation of aircraft can be mathematically simplie ed to the standard mixed H2/H1 problem. The advantage of decoupling the aircraft system based on phugoid (slow) and short period (fast) modes is to allow the slow model with its disturbance to be controlled by the H2 method, whereas the fast system with the fast disturbance is to be stabilized by the H1 technique. A comparison of this method with the standard H1 control is made using aircraft coefe cients derived for a large commercial airplane. It is shown that the current method will provide better performance for the given aircraft while the condition on the disturbance attenuation is also satise ed. The actual model controlled by the estimated controller and by the real controller is also discussed. It is shown that the estimated controller performs as well as the controller derived from the actual model.

H∞ control of interconnected nonlinear sampled-data systems with parametric uncertainty

This paper studies the problem of robust control design for a class of interconnected uncertain systems under sampled measurements. The class of system under consideration is described by a state space model containing unknown cone bounded nonlinear interaction and time-varying norm-bounded parameter uncertainties in both state and output equations. Our attention is focused on the design of linear dynamic output feedback controllers using sampled measurements. We address the problem of robust H∞ control in which both robust stability and a prescribed H∞ performance are required to be achieved irrespective of the uncertainties and nonlinearities. The H∞ performance measure involves both continuous-time and discrete-time signals. It has been shown that the above problems can be recast into H∞ syntheses for related N decoupled linear sampled-data systems without parameter uncertainties and unknown nonlinearities, which can be solved in terms of Riccati differential equations with finite discrete jumps. A num...

Robust Aircraft Control Design for Glideslope Capture in Windshear Using Gain Scheduling

Design of a robust automatic landing controller for the glideslope capture under windshear conditions is presented in this paper. Ha robust technique is employed to develop the necessary formulations for the aircraft control gain. Gain scheduling control inputs are determined so as to recover the glideslope trajectory in all stages of windshear. It is shown that the aircraft lift affected by the windshear can be separated into three parts: ballooning due to head wind, downburst, and combination of downburst with tail wind. In order to adjust the loss or increase in lift due to windshear, the robust gain scheduling controller is designed based on the change in aircraft lift caused by the windshear. Simulation results show that the glideslope capture of the landing aircraft can be recovered under different kinds of windshear. L INTRODUCTION

On the Control of Linear Systems Using Nonlinear Optimal Feedback

Abstract Optimal nonlinear feedback control of a linear system is presented in this paper. The non-negative cost function is designed to Find the optimal nonlinear controller. The Hamilton-Jacobi-Bellman (HJB) inequality is employed to achieve this objective. It is shown that the closed loop Lyapunov function (CLLF) is required to have an even order such that the CLLF is always positive with non-positive time derivative. Therefore, the second method of Lyapunov theory is satisfied. This will allow the controlled system to be stable in the large and the problem of saturation in the control input is reduced. An undetectable marginally stable case is solved for illustration.

OPTIMAL CONTROL OF SINGLE-INPUT SINGULARLY PERTURBED SYSTEMS VIA WEIGHT SELECTION WITH PRESPECIFIED POLES

Optimal pole placement method for singleinput singularly perturbed systems is presented in this paper. With prespecified poles, the optimal state weight can be determined by linear formulations for single-input controllable singularly perturbed systems. In order to reduce the magnitude of the state feedback control input, and to achieve better performance for the closed loop system, pre-selection of the closed loop poles can be used to attain these goals. It is shown that the singularly perturbed system can be decoupled into two subsystems by the two time scale method. These two subsystems can be transformed into two second canonical forms such that the optimal control method can be applied to find the desired state weighting matrices through prespecified closed loop poles for the slow and fast modes. It is shown that the differences between the closed loop and open loop characteristic polynomials reduce the algebraic Riccati equations (ARE) to the linear algebraic formulas. An example of control of longitudinal motion of a large commercial aircraft is given to illustrate the proposed technique.