Dynamic Gain Scheduled Control Research Articles

Gain-Scheduled Control of Linear Differential Inclusions Subject to Actuator Saturation

This paper focuses on the problem of robust stabilization of linear differential inclusions subject to actuator saturation. A continuous set of nonlinear controllers is constructed by a parameter-dependent convex hull Lyapunov function to avoid actuator saturation for known worst-case disturbances. The controller, which can achieve the best closed-loop performance while complies the saturation bound, is selected at each time, based on the closed-loop states. Thanks to the application of the continuous dynamic gain-scheduled control law, the internal stability and guaranteed disturbance attenuation can be obtained simultaneously. A quarter-car active suspension system is studied to demonstrate the benefit of the proposed method.

H∞Optimization-based robust decoupling control algorithm in linear parameter varying systems using Hadamard weighting

This article proposes a novel gain scheduled control technique for a class of linear parameter varying (LPV) systems with main emphasis on reducing the cross coupling interaction in dynamics using the Hadamard weight. By employing the Hadamard and the conventional [Formula: see text] performance weighting, an extended [Formula: see text] closed loop norm LPV theorem is derived that involves traditional [Formula: see text] weights for input output shaping control and Hadamard weight for decoupling control. Furthermore, a robust dynamic output feedback gain scheduled control law is designed to solve the control optimization problem in the proposed theorem using the linear matrix inequality (LMI) approach. It is shown that the proposed theorem is suitable for the multivariable control of multiple input multiple output (MIMO) coupled non-linear systems. In particular, in presence of cross coupled dynamics, external disturbances, changing operating conditions and time varying parameters. The effectiveness of the proposed technique is demonstrated in simulation as well as validated with experiments.

Output feedback stabilization of spacecraft autonomous rendezvous subject to actuator saturation

This paper studies the output feedback dynamic gain scheduled control for stabilizing a spacecraft rendezvous system subject to actuator saturation. By using the parametric Lyapunov equation and th...

Dynamic gain-scheduled control and extended linearisation: extensions, explicit formulae and stability

A controller designed for linearisations at various trim/operating points of a nonlinear system using linear approaches is not necessarily performing well or stable once scheduled with a state under dynamic conditions; the key idea of using this scheduled control law design is to retain states close to the current, usually dynamically varying, operating point. Dynamic gain scheduling (DGS) is a technique aimed to resolve this controller scheduling issue for rapidly changing dynamics and states. It entails scheduling the control law gains with a fast-varying state variable rather than with a slowly varying state. It has been successfully applied to the aircraft system models, allowing also for nested loops. The aim of this paper is to extend DGS to a more general setting allowing for more complex multi-input dynamics incorporating the more simple static scheduling within the same controller. Hence, given a linear design, suitable transformations are provided which allow fast scheduling of multi-variable controllers. Important parallels to the approach of extended linearisation are drawn. Theoretical results are shown, providing explicit formulae related to nonlinear dynamic inversion control. Several examples of varying nonlinear complexity are presented in order to emphasise the characteristics of the approach.

Dynamic gain scheduled control of a Hawk scale model

AbstractWhen designing flight control laws using linearisations of an aircraft model about different flight conditions, some form of scheduling of the resultant gains will often be required to implement the controller over wide operating regions. In practice, the controller gains are often scheduled against relatively slowly-varying system states such as altitude or velocity. However, it may also be desirable to schedule gains against rapidly-varying states such as angle-of-attack, thereby generating a cyclic dependence through hidden coupling terms. Previous published work at Bristol has developed a numerical method of accounting for this dependence when scheduling state feedback gains against coupled states. The resulting ‘dynamic gain schedule’ is shown to significantly improve the transient response of the aircraft model during rapid manoeuvring and to reduce the chances of control surface actuator position limit saturation. In this paper, the novel design process, using eigenstructure assignment, is applied to a mathematical second-order longitudinal aircraft model which represents an approximate BAe Hawk wind-tunnel model. The dynamic gain scheduled controller is shown to work extremely well in practice when applied to the closed-loop experimental rig. Despite the highly nonlinear characteristics of the model aerodynamics and tailplane actuation system, as well as unmodelled high turbulence levels, dynamic gain scheduling demonstrates stable closed loop control even in regions where the nonlinearities are such that conventional gain scheduling fails to produce a stable response.

Tailored Dynamic Gain-Scheduled Control

This paper advances the theoretical basis and application of dynamic gain-scheduled control, a novel method for the control of nonlinear systems, to an aircraft model. Extensions of this method involving multivariable gain scheduling and continuation tailoring are developed. The idea behind this method is to schedule the control law gains with a fast-varying state rather than with a slow-varying state or an input parameter. This approach is advantageous because it is then possible to schedule the gains with a state that is dominant in the mode that we are most interested in controlling. The use of this type of gain scheduling is shown to improve the transient response of the aircraft model when stepping between trim conditions and to reduce control surface movement, thus reducing the potential for saturation problems. Hidden coupling terms that introduce unwanted dynamics when scheduling gains with a fast state (rather than the input design parameter) are eliminated directly by applying a transformation to the classical parameter-scheduled gain distributions that are calculated using optimal control theory. A highly nonlinear unmanned combat air vehicle model is used to demonstrate the design process.

Dynamic gain-scheduled control of the ICE 101-TV

AbstractThis paper shows the theoretical development and application of dynamic gain scheduled control – a novel method for the control of nonlinear systems – to an aircraft model. The idea behind this method is to schedule the control law gains with a fast varying state variable rather than with a slow varying state or an input parameter. This is advantageous as it is then possible to schedule the gains with a state variable that is dominant in the mode that we are most interested in controlling. The use of this type of gain scheduling is shown to improve the transient response of the aircraft model when stepping between trim conditions and to overcome some of the problems associated with conventional gain scheduled controllers (such as control surface position limit saturation). ‘Hidden coupling terms’ that introduce unwanted dynamics when scheduling gains with a fast state (rather than the input design parameter) are eliminated directly by applying a transformation to the classical parameter-scheduled gain distributions which are calculated using eigenstructure assignment. A second order longitudinal model and a 5th order longitudinal/lateral model of the ICE 101-TV tailless delta-wing aircraft configuration are used to demonstrate the design process.

Dynamic gain scheduled process control

Gain scheduled control techniques are widely used in the chemical and aerospace industries but suffer from the limitation to slowly changing scheduling variable ( ξ). A dynamic gain scheduling (DGS) algorithm is proposed to specifically address this constraint. The control synthesis is based on algebraic transformations of the composite nonlinear controller obtained using the input–output linearization (IOL) and internal model control (IMC) formalisms. The controller is reduced to linear form and implemented in a dynamic gain scheduling approach, scheduled in the two-dimensional ξ and ξ ̇ space. In this fashion, the time variation of the scheduling variable is explicitly accounted for. The algorithm is demonstrated on a simple isothermal continuous stirred tank reactor and a complex, highly nonlinear low-density polyethylene polymerization reactor. Simulation results for the polymerizer case study show that the DGS controller provides satisfactory control during polymer grade changes, outperforms IOL control for disturbance rejection, and is stable under noisy measurements. Performance under parametric uncertainty as well as uncertainty with respect to unmodeled dynamics is also evaluated. Structured singular value analysis for nonlinear and time-varying uncertainty facilitated the determination of theoretical stability of the DGS loop. Finally, extensions to multiple-input–multiple-output systems and systems with higher relative degrees are discussed.