A Class of Predictive Adaptive Controls

A new class of control systems termed predictive adaptive controls is developed and the performance characteristics are investigated analytically and experimentally. The concepts of signal prediction, interval control, and synthesis of the control variable by a sum of orthonormal polynomials in t are introduced and developed in relation to adaptive control. A modified least squares integral index of performance is formulated and used as the criterion for system optimization. Control of dynamic processes is subdivided into intervals of a specified length T and prediction is used to obtain estimates of future values of system error. Minimization of the index of performance leads to a family of control laws which specify the structure of the controller. The resulting control configuration is optimum in a specific mathematical sense and is readily realizable with available physical components. The adaptive capability is achieved through time-varying gains which are specific functions of the unit impulse response of the dynamic process being controlled. Predictor design is presented in terms of the classical Wiener-Lee theory, and a relationship for control interval length as a function of prediction accuracy is developed. Preliminary design of the controller is considered from the viewpoints of relative weighting of system error and control effort, control interval length T, and the number of terms needed In the orthonormal polynomial sum approximation of the control variable. A method of obtaining an engineering estimate of the latter quantity is developed and 11 lustrated by three examples, two of which are investigated experimentally. Two applications of predictive adaptive control are investigated on an analog computer. The two dynamic processes used are a first-order process whose parameter varies over a range of ten to one and a second-order process whose parameter varies in such a manner that the process is unstable at one extremum and heavily damped at the other. The results of three basic experiments which evaluate the steady-state adaptability transient response, and statistical signal response of the two systems are reported. It is found that all three aspects of system performance improve with decreasing control interval length, but that the minimum value of the interval length which can be used is limited by the accuracy of the time-varying gain and controller circuitry. Improved performance which can be achieved by increasing the relative weighting of System error and control effort, is limited by saturation considerations. Theoretical, results that .point to the need., for keeping the control interval length short to preserve stability, prediction accuracy, and loss of control doe to process parameter drift are substantiated by the experimental results. For the two systems investigated it is found that satisfactory control Is achieved If the interval length is chosen so that process parameter drift Is no more than 4% per control interval, A figure of 5% was estimated originally, : A one-term approximation of the control variable is used to control .the first-order process- and Is found to give satisfactory performance. A four-term approximation Is found to give adequate control of the second- order process whereas the three-term approximation does not. These results bear out the predictions made in the-theoretical analyses

A Survey of the Philosophy and State of the Art of Adaptive Systems

This is a preliminary report on the state of the art of adaptive control. It in no way attempts to review all of the various adaptive systems which have been proposed or constructed® Probably the most complete effort in this direction is WADC TR 59-49# The Proceedings of the Self Adaptive Flight Control Systems Symposium, Edited by P. C. Gregory® Rather this report attempts a synthesis of the present philosophy on adaptive control and is essentially a definition of the problem® The report attempts to subdivide the adaptive control problem into three subdivisions and to assess present progress in each of these areas. Ideas that have been proposed by various authors are brought together and given unified treatment® In making this organization# various gaps in the present state of the art have become apparent and these are under intensive survey presently at Purdue. The initial portion of the project# consisting of this organization terminated several months ago and at present the project personnel are engaged on original research along the lines indicated by the monthly progress reports to WADD. Further interim reports will discuss these items and in accordance with present Air Force practice the final report will contain all of the information of the interim reports and will thus be self sufficient

The use of the Nintendo Wii in motor rehabilitation for virtual reality interventions:a literature review

Several review articles have been published on the use of Virtual Reality (VR) in motor rehabilitation. The majority of these focus on the effectiveness of VR on improving motor function using relatively expensive commercial tools and technologies including robotics, cybergloves, cybergrasps, joysticks, force sensors and motion capture systems. However, we present the case in this chapter that game sensors and VR technologies which can be customized and reconfigured, such as the Nintendo Wii, provide an alternative and affordable VR intervention for rehabilitation. While the performance of many of the Wii based interventions in motor rehabilitation are currently the focus of investigation by researchers, an extensive and holistic discussion on this subject does not yet exist. As such, the purpose of this chapter is to provide readers with an understanding of the advantages and limitations of the Nintendo Wii game sensor device (and its associated accessories) for motor rehabilitation and in addition, to outline the potential for incorporating these into clinical interventions for the benefit of patients and therapists