Marc Bodson

Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency

Abstract Two algorithms are presented for the rejection of sinusoidal disturbances with unknown frequency. The first is an indirect algorithm where the frequency of the disturbance is estimated, and the estimate is used in another adaptive algorithm that adjusts the magnitude and phase of the input needed to cancel the effect of the disturbance. A direct algorithm that uses the concept of a phase-locked loop is also presented in which frequency estimation and disturbance cancellation are performed simultaneously. Approximate analyses are presented for both schemes and the results are found useful for the selection of the design parameters. Simulations are given which demonstrate the validity of the analytical results and the ability of the algorithms to reject sinusoidal disturbances with unknown frequency. The indirect algorithm is found to have a larger capture region for the parameter estimates, whereas the direct algorithm has superior convergence properties locally about the optimum parameter estimates

Multivariable adaptive algorithms for reconfigurable flight control

The application of multivariable adaptive control techniques to flight control reconfiguration is considered. The objective is to redesign automatically flight control laws to compensate for actuator failures or surface damage. Three adaptive algorithms for multivariable model reference control are compared. The availability of state measurements in this application leads to relatively simple algorithms. The respective advantages and disadvantages of the adaptive algorithms are discussed, considering their complexity and the assumptions that they require. An equation-error based algorithm is found to be preferable. Simulations obtained using a full nonlinear model of a twin-engine jet aircraft are presented. The results demonstrate the ability of the adaptive algorithms to maintain trim after a failure, to restore tracking of the pilot commands despite the loss of actuator effectiveness, and to coordinate the use of the remaining active control surfaces in order to guarantee the decoupling of the rotational axes. A new adaptive algorithm with a variable forgetting feature is also used and is found to yield a useful alternative to covariance resetting as a solution to covariance wind-up in least-squares algorithms.

Evaluation of Optimization Methods for Control Allocation

The performanceand computational requirements ofoptimization methodsfor control allocation areevaluated. Two control allocation problems are formulated: a direct allocation method that preserves the directionality of the moment and a mixed optimization method that minimizes the error between the desired and the achieved momentsaswellasthecontroleffort.Theconstrainedoptimizationproblemsaretransformedinto linearprograms so that they can be solved using well-tried linear programming techniques such as the simplex algorithm. A variety of techniques that can be applied for the solution of the control allocation problem in order to accelerate computations are discussed. Performance and computational requirements are evaluated using aircraft models with different numbers of actuators and with different properties. In addition to the two optimization methods, three algorithms with low computational requirements are also implemented for comparison: a redistributed pseudoinverse technique, a quadratic programming algorithm, and a e xed-point method. The major conclusion is that constrained optimization can be performed with computational requirements that fall within an order of magnitude of those of simpler methods. The performance gains of optimization methods, measured in terms of the error between the desired and achieved moments, are found to be small on the average but sometimes signie cant.Avariety ofissuesthataffecttheimplementation ofthevariousalgorithmsin ae ight-controlsystem are discussed.

High-performance nonlinear feedback control of a permanent magnet stepper motor

The permanent magnet stepper motor is considered for use in high-performance positioning systems. A model-based control law is developed using the exact linearization methodology and implemented on an industrial setup. The practical issues of speed estimation and voltage saturation are considered and resolved through the use of a nonlinear observer and field-weakening, respectively. The results of the implementation of the control algorithm for an industry-specified point-to-point move of a linear positioning table are presented and discussed. >

High-performance induction motor control via input-output linearization

We have shown that a current-command input-output linearization controller can achieve high-performance motion control, that is, the precise tracking of a fast point-to-point position reference. Specifically, this controller was shown to provide the means of decoupling the speed and flux dynamics in an induction motor. This decoupling of speed and flux was exploited to simultaneously track the position/speed reference and an optimal flux reference. This flux reference was used to obtain the optimal (max/min) motor torque at any given speed without violating voltage and current limits. Experimental results were presented to demonstrate the effectiveness of this scheme.<<ETX>>

Real-time estimation of the parameters and fluxes of induction motors

A novel method for the real-time estimation of the parameters and fluxes of induction motors is presented. The method is based on a standard model of the induction motor, expressed in rotor coordinates. It is assumed that current and position (or velocity) measurements are available. The interesting features of the method are: that it does not rely on special tests such as the locked rotor test or the no-load test (instead, a broad range of motor responses can be used); the method provides estimates of the rotor fluxes together with the estimates of the parameters; and measures of the uncertainties in the estimated motor parameters are provided. Results for both simulated and experimental data are provided.<<ETX>>

Active noise control for periodic disturbances

Proposes an active noise control algorithm for periodic disturbances of unknown frequency. The algorithm is appropriate for the feedback case in which a single error microphone is used. A previously proposed algorithm for the rejection of sinusoidal noise sources is extended for the cancellation of multiple harmonics. Unlike many other approaches, the estimates of the frequencies of the separate harmonics are tied together within the algorithm to account for the integer multiplicative relations between them. The dynamic behavior of the closed-loop system is analyzed using an approximation that is shown, in simulations, to provide an accurate representation of the systems behavior. Experimental results on an active noise control testbed demonstrate the success of the method in a practical environment.

Adaptive identification and control for manipulators without using joint accelerations

We present a new scheme for the adaptive control of mechanical manipulators along with proof of convergence. This work is an extension of our earlier work [Craig, Hsu and Sastry] [1]. The new scheme does not require the measurement of joint accelerations and needs less computation. We illustrate the theory with some simulations.

Advanced methods for repeatable runout compensation [disc drives]

This paper presents and compares experimental results from two types of periodic disturbance compensation methods. The repeatable runout (RRO) cancellation techniques studied in this paper are adaptive feedforward cancellation (AFC) and repetitive control. Two modifications (phase advance and a feedthrough term) to the basic AFC structure are also studied experimentally. Of the AFC methods, the feedthrough technique is superior, but the repetitive controller provides better RRO rejection. Overall it is found that the removal of repeatable runout improved the tracking precision by as much as 53%. >

Differential-geometric methods for control of electric motors

SUMMARY The di⁄erential-geometric techniques of nonlinear control developed over the last 20 years or so include static and dynamic feedback linearization, input—output linearization, nonlinear state observers and disturbance decoupling. The theory has now reached a level of maturity where control practicioners are making e⁄ective use of the techniques for electric motors. Indeed, DC and AC motors have well-defined nonlinear mathematical models which often satisfy the structural conditions required of the di⁄erential-geometric theory. In this paper, the application of various di⁄erential-geometric methods of nonlinear control is shown by way of examples including DC motors (series, shunt and separately excited), induction motors, synchronous motors and DC—DC converters. A number of contributions are surveyed which show the benefits of the methods for the design of global control laws by systematic means. ( 1998 John Wiley & Sons, Ltd.