K.F. Fong

Neural network modelling and control strategies for a pH process

Abstract The control of a pH process using neural networks is examined. The neural network as a universal approximator is used to good effect in this nonlinear problem, as is shown in the simulation results. In the modelling task, the dynamics of the process was carefully examined to determine a suitable structure for the net. In particular, a multilayer net consisting of two single hidden layers was constructed to reflect the Wiener model of the pH process. This led to much simpler training compared to similar modelling attempts by other researchers. For the control task, two schemes were simulated. In one approach, a net was used to deal with the static nonlinearity to achieve control over a wide working range. The dynamic controller used was the PID, with its parameters tuned on a relay auto-tuner. This control design was compared with the strong acid equivalent method. In the second approach, a direct model reference adaptive neural network control scheme was proposed. The training procedure uses the more efficient least squares algorithm developed by Loh and Fong.

Adaptive control of discrete time systems with concave/convex parametrizations

This note considers the adaptive control of a class of nonlinear discrete time system with concave/convex parametrizations. The solutions involved two tuning functions which are determined by a minmax optimization approach much like the continuous time counterparts found in the literature. Direct extension from the continuous time case do not work very well due to the premature termination of the adaptive algorithm before zero tracking error can be achieved. In this note, this problem is solved. The proposed algorithm is shown to be stable and achieves zero tracking error in steady state.

MRAC of nonlinear systems using neural networks with recursive least squares adaptation

A model reference adapative control of nonlinear systems using neural networks is presented. In this scheme, adaptive control is viewed as an identification process, in which the parameters to be identified are that of the controller and the plant model. The neural net controller is adapted using a variant of recursive least squares estimation which can be considered a generalization of backpropagation. Simulations show that, for a simple plant, adaptive control is stable.<<ETX>>

A frequency domain approach for fault detection

This paper considers the use of online frequency response estimates for change detection, which serves as a preliminary for fault detection and diagnosis. In general, a finite time frequency response estimator will always show some deviations from its nominal response even when a change has not occurred. The question we address is when does a fault detector decide if a change has occurred based on these estimates. The approach taken is based on statistical decision theory. When deviations from the nominal frequency response are detected, the detector decides with good statistical accuracy, whether a change has indeed occurred. The design is based on the Neymann-Pearson criterion, which allows for the specification of a constant false alarm rate. The performance of the detector and some practical considerations are discussed. Simulations axe used to illustrate the performance and properties of the detector.

Diagnosis of parametric faults with optimal partitioning of frequency response estimates

In this paper, a new frequency domain fault isolation method for linear time-invariant systems is proposed. A fault is assumed to be manifested in the change in one of the system parameters, which will in turn cause a change in the frequency response. Based on this changed frequency response, a fault detection is first made, then followed by a fault isolation which attempts to determine what fault has occurred. In practice, estimation of the frequency response is usually plaqued with noise, contributed from the estimation process as well as system and output noise. The statistical approach to the detection problem has been discussed in our earlier paper. Here, we explore the issue of fault isolation after the detection phase. The proposed method captures the changes in the frequency response by monitoring an observation vector constructed from at least two segments of the frequency response. The changes in frequency response due to corresponding changes in the system parameters are first mapped out as trajectories in the vector plane. When a fault is detected, it is then isolated by comparing it to the reference trajectories. Throughout the fault isolation phase, only the frequency response of the system is estimated and no attempt is made to estimate the system parameters.

Detecting spectral changes in the frequency domain

This paper considers the use of frequency response estimates for change detection. The class of faults considered affects the spectral properties of the system. Spectral changes are detected as deviations in the frequency response, through the choice of a suitable residual. Taking into consideration the statistical nature of a finite-time estimator, a X/sup -2/ detector is then designed for the residual. The performance of the fixed sample size detector is compared with a conventional cusum algorithm, and found to be better. The DC motor is used as an implementation example to illustrate the performance and properties of the detector.

ADAPTIVE CONTROL OF DISCRETE TIME SYSTEMS WITH CONCAVE/CONVEX PARAMETRIZATIONS

Abstract This paper considers the adaptive control of a class of nonlinear discrete time system with nonlinearly parametrized functions. In particular, the focus is on concave or convex parametrizations with unknown parameters. The solutions involved 2 tuning functions which are determined by a minmax optimization approach much like the continuous time counterparts found in the literature. Direct extension from continuous time case do not work very well due to the premature termination of the adaptive algorithm before zero tracking error can be achieved. In this paper, this problem is solved. The proposed algorithm can be shown to be stable and in some cases, achieve zero tracking error in steady state.

Discrete-time optimal control using neural nets

The authors show how neural networks can be incorporated in optimal control strategies by providing a mathematical formulation and numerical algorithms in terms of general gradient descent and backpropagation. They present techniques that use neural nets in nonlinear optimal control. It is shown that D.H. Nguyen and B. Widrows (1990) self-learning control is a special case of this technique. Control of an inverted pendulum using a neural net in nonlinear feedback is simulated, demonstrating the usefulness of the approach.<<ETX>>

Backpropagation using generalized least squares

The backpropagation algorithm is essentially a steepest gradient descent type of optimization routine minimizing a quadratic performance index at each step. The backpropagation algorithm is re-cast in the framework of generalized least squares. The main advantage is that it eliminates the need to predict an optimal value for the step size required in the standard backpropagation algorithm. A simulation result on the approximation of a nonlinear dynamical system is presented to show its rapid rate of convergence compared to the backpropagation algorithm.<<ETX>>