HONU and Supervised Learning Algorithms in Adaptive Feedback Control

HONU and Supervised Learning Algorithms in Adaptive Feedback Control

Peter Mark Benes (Czech Technical University in Prague, Czech Republic), Miroslav Erben (Czech Technical University in Prague, Czech Republic), Martin Vesely (Czech Technical University in Prague, Czech Republic), Ondrej Liska (Technical University of Kosice, Slovakia) and Ivo Bukovsky (Czech Technical University in Prague, Czech Republic)
DOI: 10.4018/978-1-5225-0063-6.ch002
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Abstract

This chapter is a summarizing study of Higher Order Neural Units featuring the most common learning algorithms for identification and adaptive control of most typical representatives of plants of single-input single-output (SISO) nature in the control engineering field. In particular, the linear neural unit (LNU, i.e., 1st order HONU), quadratic neural unit (QNU, i.e. 2nd order HONU), and cubic neural unit (CNU, i.e. 3rd order HONU) will be shown as adaptive feedback controllers of typical models of linear plants in control including identification and control of plants with input time delays. The investigated and compared learning algorithms for HONU will be the step-by-step Gradient Descent adaptation with the study of known modifications of learning rate for improved convergence, the batch Levenberg-Marquardt algorithm, and the Resilient Back-Propagation algorithm. The theoretical achievements will be summarized and discussed as regards their usability and the real issues of control engineering tasks.
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Introduction

Due to the ever-growing complexity of our technological society, adaptive control has become a rapidly growing area of study in the field of modern engineering and computational science. Stretching back through the last several decades, the industry has proven that further optimisation and increased efficiency has grown to not only become a desirable feature, but a necessity to keep up with factors associated with increase in production rates, technological changes and further demands for increase in flexibility. The works from Alexandrov and Palenov (2014) highlight the trend in our modern industry for application of adaptively tuned Proportional-Integral-Derivative (PID) controllers as many processes indeed feature certain non-stationary parameters which can tend to drift in association with time. In this day various PID controllers manufactured within the industry incorporate a form of adaptive control, namely, the ABB-COMMANDER 351, Honeywell – UDC series and Foxboro – 700 series controllers. Their employed algorithms are classified under two key terms. Direct methods, are those where the controller parameters are immediately updated via a law that is in dependence of the controlled systems state, namely logical or rule-based, or further fuzzy logic based methods for updating the PID controller parameters. The latter, being an indirect approach where the engineering system or plant is parameterised with respect to a vector of unknown parameters, solved by on-line identification. The ultimate goal across both approaches is to retune the controller coefficients in order to preserve the desired controller objective or desired behaviour, even when certain non-stationary phenomena may be incorporated in a form of new or novel dynamics within an engineering system. In our day a leading trend in adaptive PID algorithms can be found in frequency adaptive control, here two approaches may be employed. The first features a sent single harmonic input test signal through the process. With application of a Fourier filter, the process dynamics may be singled out. The second approach, features two harmonic test signals, with the ultimate goal being an estimation of the model parameters, which may be further used for computation of the new PID controller coefficients.

Since as early as the 1960s, adaptive control has taken big leaps not only in the sense of adaptive tuning methods for conventional forms of industrial controllers, but also the conception of entirely different architectures of adaptive control methods. The motivation for such complex and advanced methods due largely to the necessity for control of processes featuring non-linear dynamics and furthermore non-linear uncertainties at their inputs. Pioneered by H. P. Whitaker and P. V. Osborn from the Massachusetts Institute of Technology, USA. Model Reference Adaptive Control (MRAC) particularly has featured an ever-growing increase in regards to its areas of application within the engineering field, with extensive studies focussing on not only theoretical but also practical application of newly proposed methods for controller parameter adjustment. In this current time, more emphasis in research has been pushed towards utilising soft computing techniques as such that of fuzzy and neural network based methods of MRAC adaptive control, however research in MRAC design with variable structures and advanced controller adjustment technique, whether they be directly or indirectly applied to the process are readily being extended to this field. With the design of model reference based adaptive control (MRAC) techniques, stability is key in ensuring convergence of the prescribed adaptive parameters as well as the process output value to its desirable set point. Several key works necessary to mention are from Patino and Liu (2000) and Wu, Wu, Luo, Zhu, and Guan (2012), these works encompass MRAC controller design via Lyapunov function based criteria as part of their respective adaptive control laws as a means of ensuring stability of convergence of the applied adaptive parameters. However, one drawback that can lead from such methods is the amount of adaptive parameters necessary to employ the control algorithm, which can increase the complexity and overall computational demand of such form for real time implementation.

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