Showing papers by "Richard H. Middleton published in 2002"

Optimal tracking performance for SIMO systems

Abstract: This note studies the optimal tracking problem for linear time-invariant single-input-multiple-output systems responding to a step reference signal. An integral square error criterion is used as the measure for tracking performance. Explicit expressions are developed for the optimal tracking error. These results characterize how nonsquare plants may pose additional difficulties for tracking, other than those resulted from nonminimum phase zeros and unstable poles.

Cheap control performance of a class of nonright-invertible nonlinear systems

Abstract: For strict-feedback nonlinear systems, this paper shows that it is impossible to reduce to zero the optimal cost in the regulation of more states than the number of control inputs in the system, even using an unrestricted control effort. By constructing a near-optimal cheap control law, we characterize the infimum value of the optimal regulation cost as the optimal value of a reduced-order regulator problem. We illustrate our results with an example on the optimal control of a magnetic suspension system.

On the robustness of multivariable algebraic loops with sector nonlinearities

Abstract: The paper is motivated by multivariable 'anti-windup' schemes Such schemes are often described in a form that includes a multivariable algebraic loop Multivariable algebraic loops may be particularly problematic in terms of well-posedness (the existence and uniqueness of the solutions) and robust stability Conditions for well-posedness of such loops have been analysed previously Here we extend this analysis to consider robust stability of the algebraic loop with small time-delays It is shown that sufficient conditions for robustness of the algebraic loop can be directly incorporated into an LMI based static anti-windup controller synthesis In addition, an alternative implementation of the algebraic loop is shown to have robustness without altering the LMI set up

Cheap control tracking performance for non-right-invertible systems

Abstract: There exists a well-known fundamental limitation upon the achievable setpoint tracking performance of a non-right-invertible plant. This limitation manifests itself, for example, in the cost associated with the cheap control tracking problem. In this paper, we provide a new interpretation of this limitation. We show that the cheap control cost may be decomposed into the sum of two terms. The first of these depends upon certain non-minimum phase zeroes that include the non-minimum phase plant zeroes. The second term depends upon the extent to which the plant direction varies with frequency. To state these results, we first develop a co-ordinate transformation that may be used to define the notion of frequency dependent plant direction and to display the relevant non-minimum phase zeroes. We also show that the cheap control cost is connected to an integral relation that constrains the performance of any stable closed-loop system (not necessarily under cheap control) for which the plant has a single control input and two performance outputs. Copyright © 2002 John Wiley & Sons, Ltd.

Best achievable tracking performance in sampled-data control systems

Abstract: In this paper we study the problem of tracking a step reference signal using sampled-data control systems. We investigate the best achievable tracking performance, where the performance is deemed best for it is the minimal attainable by all possible sampled-data stabilizing controllers. Our primary objective is to investigate the fundamental tracking performance limit in sampled-data systems, and to understand whether and how sampling and hold in a sampled-data system may impose intrinsic barriers to performance. For this purpose we derive an analytical expression for the optimal tracking performance. The result shows that a performance loss is generally incurred in a sampled-data system, in comparison to the tracking performance achievable by continuous-time controllers. This loss of performance, as so demonstrated by the expression, can be attributed to the non-minimum behaviors and the aliasing effects generated by samplers and hold devices.

Best achievable tracking performance in sampled-data control systems

Abstract: In this paper we study the problem of tracking a step reference signal using sampled-data control systems. We investigate the best achievable tracking performance, where the performance is deemed best for it is the minimal attainable by all possible sampled-data stabilizing controllers. Our primary objective is to investigate the fundamental tracking performance limit in sampled-data systems, and to understand whether and how sampling and hold in a sampled-data system may impose intrinsic barriers to performance. For this purpose we derive an analytical expression for the optimal tracking performance. The result shows that a performance loss is generally incurred in a sampled-data system, in comparison to the tracking performance achievable by continuous-time controllers. This loss of performance, as so demonstrated by the expression, can be attributed to the non-minimum behaviors and the aliasing effects generated by samplers and hold devices.

Nonminimum phase zeros in the general feedback configuration

Abstract: Design limitations due to nonminimum phase plant zeros have been extensively studied for unity feedback systems. We now study these limitations in a general feedback architecture that allows for arbitrary exogenous and control inputs and performance and measured outputs. Motivation to do so is that many feedback systems have more complex architectures than the single input, single output architecture typically used to study design limitations. While it is difficult to make concrete statements without assuming additional structure, it is also possible to demonstrate that certain design limitations are present in very general circumstances. The results are applied to the problems of command tracking and disturbance attenuation for a military tank.

A new method based on wavelet packet transformation to reduce narrow band noise in on-site PD measurement

Abstract: The suppression of interference is crucial in onsite Partial Discharge (PD) monitoring. This paper presents a new algorithm to reduce narrow band noise coupled into PD measurements. The algorithm is based on wavelet packet analysis and is capable of automatically detecting narrow band interference without requiring prior knowledge of detailed noise characteristics. Simulations are provided as well as some results obtained during laboratory experiment and on-line PD measurements for a power transformer. The efficiency of reducing narrow band noises is measured by comparing the frequency spectrum before and after filtering with the new method.

Towards quantitative time domain design tradeoffs in nonlinear control

Abstract: This paper analyzes the feasibility of quantifying design tradeoffs on the transient step response of a class of nonlinear systems. This feasibility analysis builds on available tools for the characterization of performance limitations in the optimal quadratic response of the class of strict feedback nonlinear systems. We present results that show that, as in linear systems, for certain classes of nonminimum, phase systems, the closed loop transient step response must display undershoot. A lower bound on this undershoot can be computed based on the settling time of the system, and this bound increases as the settling time is decreased.

steady-state error can be eliminated by including an integral term in the linear part of the controller (19).

Abstract: IX. SUMMARY A new approach has been proposed for adaptive output feedback control of uncertain nonlinear systems using neural networks. A simple linear observer was introduced to estimate the derivatives of the tracking error. These estimates are used as inputs to the neural network and in the adaptation laws as an error signal. Ultimate boundedness of all error signals was proven by Lyapunov’s direct method. Simulations of a second-order system illustrated the theoretical results.

Robustness of decoupling with almost redundant inputs

Abstract: Control design for an ill-conditioned plant is known to be problematic. One reason a plant may be ill-conditioned is that its control inputs may be almost redundant, in the sense that they have an almost identical effect upon the controlled outputs. In this paper we study robustness problems that may occur when a controller that decouples, or partially decouples, the plant is used with a plant that has almost redundant inputs.