Lena Valavani

Robustness of adaptive control algorithms in the presence of unmodeled dynamics

This paper reports the outcome of an exhaustive analytical and numerical investigation of stability and robustness properties of a wide class of adaptive control algorithms in the presence of unmodeled dynamics and output disturbances. The class of adaptive algorithms considered are those commonly referred to as model-reference adaptive control algorithms, self-tuning controllers, and dead-beat adaptive controllers; they have been developed for both continuous-time systems and discrete-time systems. The existing adaptive control algorithms have been proven to be globally assymptotically stable under certain assumptions, the key ones being (a) that the number of poles and zeroes of the unknown plant are known, and (b) that the primary performance criterion is related to good command following. These theoretical assumptions are too restrictive from an engineering point of view. Real plants always contain unmodeled high-frequency dynamics and small delays, and hence no upper bound on the number of the plant poles and zeroes exists. Also real plants are always subject to unmeasurable output additive disturbances, although these may be quite small. Hence, it is important to critically examine the stability robustness properties of the existing adaptive algorithms when some of the theoretical assumptions are removed; in particular, their stability and performance properties in the presence of unmodeled dynamics and output disturbances. A unified analytical approach has been developed and documented in the recently completed Ph.D. thesis by Rohrs [15] that can be used to examine the class of existing adaptive algorithms. It was discovered that all existing algorithms contain an infinite-gain operator in the dynamic system that defines command reference errors and parameter errors; it is argued that such an infinite gain operator appears to be generic to all adaptive algorithms, whether they exhibit explicit or implicit parameter identification. The practical engineering consequences of the existence of the infinite-gain operator are disastrous. Analytical and simulation results demonstrate that sinusoidal reference inputs at specific frequencies and/or sinusoidal output disturbances at any frequency (including d.c.) cause the loop gain of the adaptive control system to increase without bound, thereby exciting the (unmodeled) plant dynamics, and yielding an unstable control system. Hence, it is concluded that none of the adaptive algorithms considered can be used with confidence in a practical control system design, because instability will set in with a high probability.

Active control of rotating stall in a low-speed axial compressor

The onset of rotating stall has been delayed in a low-speed, single-stage, axial research compressor using active feedback control. Control was implemented using a circumferential array of hot wires to sense propagating waves of axial velocity upstream of the compressor. Using this information, additional circumferentially traveling waves were then generated with appropriate phase and amplitude by «wiggling» inlet guide vanes driven by individual actuators. The control scheme considered the wave pattern in terms of the individual spatial Fourier components. A simple proportional control law was implemented for each harmonic. Control of the first spatial harmonic yielded an 11 percent decrease in the stalling mass flow, while control of the first, second, and third harmonics together reduced the stalling mass flow by 23 percent

A Frequency-Domain Estimator for Use in Adaptive Control Systems

The paper presents a frequency-domain estimator which can identify both a nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which we call a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.

Evaluation of Approaches to Active Compressor Surge Stabilization

Recent work has shown that compression systems can be actively stabilized against the instability known as surge, thereby realizing a significant gain in system mass flow range. Ideally, this surge stabilization requires only a single sensor and a single actuator connected by a suitable control law. Almost all research to date has been aimed at proof of concept studies of this technique, using various actuators and sensor combinaltons. In contrast, the work reported here can be regarded as a step toward developing active control into a practical technique. In this context, the paper presents the first systematic definition of the influence of sensor and actuator selection on increasing the range of stabilized compressor performance

Paper: Some design guidelines for discrete-time adaptive controllers

There have been many algorithms proposed for adaptive control which will provide globally asymptotically stable controllers if some stringent conditions on the plant are met. The conditions on the plant cannot be met in practice as all plants will contain high frequency unmodeled dynamics. This paper uses a linearization analysis of a nonlinear adaptive controller to demonstrate analytically some design guidelines which alleviate some of the problems associated with adaptive control in the presence of unmodeled dynamics. The points made are further demonstrated by simulation results.

Optimal and robust controllers for periodic and multirate systems

The problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete-time periodic systems. The solution consists of solving an equivalent time-invariant standard l/sup 1/ optimization problem subject to an additional constraint. This constraint assures the causality of the resulting periodic controller. By the duality theory, the problem is shown to be equivalent to a linear programming problem, which is no harder than the standard l/sup 1/ problem. Also, it is shown that the method of solution presented applies exactly to the problem of disturbance rejection in the case of multirate sampled data systems. Finally, the results are applied to the problem of robust stabilization of periodic and multirate systems. >

A frequency-domain estimator for use in adaptive control systems

The paper presents a frequency-domain estimator which can identify both a nominal model of a plant as well as a frequency-domain bounding function on the modeling error associated with this nominal model. This estimator, which we call a robust estimator, can be used in conjunction with a robust control-law redesign algorithm to form a robust adaptive controller.

A Lyapunov Based Nonlinear Control Scheme for Stabilizing a Basic Compression System Using a Close-Coupled Control Valve

The use of a closed loop control to allow surge free operation of a compression system beyond its uncontrolled surge line is addressed. In contrast to previous analyses which used a linearized model, the approach described here directly addresses the nonlinear nature of the compressor characteristic using a Lyapunov based control law design formulation. The proposed approach is fairly generic, and should be of interest for gas turbine engine, as well as other applications.

High performance linear-quadratic and H-infinity designs for a 'supermaneuverable' aircraft

Recent efforts by the National Aeronautics and Space Administration Langley Research Center have focused on expanding the flight envelope of the F/A-18 aircraft. Of particular concern has been the low speed, high angle-of-attack regime over which the conventional aerodynamic controls of the F/A-18 lose their effectiveness. In order to address this problem the F18 high alpha research vehicle was developed. This aircraft is essentially a modified F/A-18 which possesses thrust vectoring capabilities and hence increased maneuverability in this flight regime. The linear-quadratic-Gaussian with loop-transfer-recovery and H(infinity) design methodologies are used to design high performance controllers for the F18 at an operating point within the expanded envelope. In addition, how the control redundancy of the F18 can be used to maintain nominal performance, as well as nominal stability, in situations where failures occur, is shown.

Robustness studies in adaptive control

This paper examines robustness issues in Model Reference Adaptive Control systems in the presence of unmodeled dynamics and output disturbances. We present an approximate technique, trend analysis, by which we can study the evolution of the parameter error trajectory under periodic excitation. This analysis provides new insights upon the size and spectral content of the excitation sufficient to guarantee local stability.