An adaptive robust approach to actuator fault-tolerant control in presence of uncertainties and input constraints

Shreekant Gayaka, Purdue University

Abstract

In this work, we develop adaptive robust schemes for actuator fault-tolerant control in presence of uncertainties and input saturation. The type of faults considered in the present work encompass hardover-failure, loss in efficiency and stuck actuators. The two chief ways in which the system performance can degrade following an actuator-fault are undesirable transients and unacceptably large steady-state tracking errors. Adaptive control based schemes are ideal for handling the jump in parameter values following an actuator fault, and can guarantee good final tracking accuracy. However, such schemes may not be able to suppress the transients due to sudden change in system parameters. Furthermore, the performance of adaptive control based schemes deteriorate significantly in presence of unknown modeling errors and disturbances. Robust control based schemes, on the other hand, can guarantee desired transient response due to the sudden jump in system parameters and attenuate the effect of modeling uncertainties on the tracking error. But, in face of large parametric uncertainties due to actuator faults, the final tracking accuracy of robust control based schemes may degrade as they cannot reduce the extent of parametric uncertainties. In the present work, we claim that an adaptive robust fault-tolerant control scheme can solve both the problems, as it seamlessly integrates adaptive and robust control design techniques. Comparative simulation studies are performed using linear and nonlinear aircraft models to illustrate the superior performance of the proposed scheme over robust MRAC and robust backstepping based adaptive control designs respectively. One of the standard assumptions made in the design of adaptive fault-tolerant control is that the healthy actuators have sufficient control authority despite faults to recover desired closed-loop performance. In reality, however, the controller could generate large control commands to suppress the undesired transients, leading to actuator saturation. Furthermore, in direct adaptive schemes, the estimator may fail to generate reliable parameter estimates due to saturation. This could further degrade the performance of a actuator fault-tolerant control. As a first step towards developing an approach which can deal with input constraints, we propose a conceptually different technique for global stabilization of a chain of integrators. A novel and elegant approach to solve this problem was proposed by Teel [1] using saturation functions and coordinate transformation. With Teel’s work as foundation, many results have been proposed to improve the performance of tracking/stabilizing controllers for chain of integrators. Naturally, all such approaches also inherited the limitations of Teel’s approach. Most importantly, in presence of uncertainties, such a transformation would considerably shrink the region where the controller is unsaturated, and in some cases, may even render the task of designing a stabilizing controller impossible. We combine the backstepping based design with saturation functions to develop a simple controller which does not rely on coordinate transformation and meets all the desired objectives. Furthermore, necessary and sufficient conditions for the existence of the proposed control law, as well as a systematic way of choosing the controller parameters is also presented. Comparative simulation studies are performed on a third order integrator chain which shows the effectiveness of the proposed scheme. Finally, an actuator fault-tolerant controller is designed which combines the proposed backstepping based saturation functions approach with a least-square estimator. The indirect scheme ensures that the adaptation mechanism is not affected adversely due to actuator saturation. Simulation studies performed on a hypersonic aircraft model demonstrate the effectiveness of the proposed scheme in addressing actuator faults in presence of input constraints.

Degree

Ph.D.

Advisors

Yao, Purdue University.

Subject Area

Mechanical engineering

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