A New Non - linear Multi - variable Multiple - Controller incorporating a Neural Network Learning Sub - Model

A new non-linear multi-variable multiple-controller incorporating a neural network learning sub-model is proposed. The unknown multivariable non-linear plant is represented by an equivalent stochastic model consisting of a linear timevarying sub-model plus a non-linear neural-network based learning sub-model. The proposed multiple controller methodology provides the designer with a choice of using either a conventional Proportional-Integral-Derivative (PID) self-tuning controller, a PID based pole-placement controller, or a newly proposed PID based pole-zero placement controller through simple switching. The novel PID based pole-zero placement controller employs an adaptive mechanism, which ensures that the closed loop poles and zeros are located at their pre-specified positions. The switching decision between the different non-linear fixed structure controllers can be done either manually or by using Stochastic Learning Automata. Simulation results using a non-linear Multiple Input Multiple Output (MIMO) plant model demonstrate the effectiveness of the proposed multiple controller, with respect to tracking setpoint changes. The aim is to achieve a desired speed of response, whilst penalizing excessive control action, for application to non-minimum phase and unstable systems. INTRODUCTION Conventional PID controllers have been proven to be robust, easy to implement using analogue or digital hardware, and remarkably effective in regulating a wide range of processes. For most simple processes, PID control can provide satisfactory closed loop performance. However, the problems of large time-delays, time-varying processes, large nonlinearities and non-negligible disturbances call for more advanced control algorithms. In the last two decades much progress has been seen in the theory of self-tuning and other adaptive control systems, which automatically adjust controller parameters online in response to changes in the process or the environment. Over a longer period of about three decades, a lot of attention was paid to the problem of designing pole-placement controllers and self-tuning regulators. Various self-tuning controllers based on classical pole-placement ideas were developed and employed in real applications, e.g. [1, 2]. The popularity of pole-placement techniques may be attributed to the following [3]: 1) In the regulator case they provide mechanisms to over-come the restriction to minimum-phase plants of the original minimum variance self-tuner of [1]. 2) In the servo case, they provide the ability to directly introduce bandwidth and damping ratio as tuning parameters. In many industrial sectors, machines and processes might be improved using optimal control and optimisation (e.g., the steel industry, food industry, chemical industry, textile industry). A difficult problem in the control of these industrial processes is due to the inherent non-linearities of their models and these problems cannot be solved by traditional “generalised minimum variance control” techniques. The application of linear control theory to these problems relies on the key assumption of a small range of operation in order for the linear model assumption to be valid. When the required operating range is large, a linear controller may not be adequate. For this reason, it seems appropriate to extend “generalised minimum variance” control to plants with non-linear models and with plant/model mismatch. A possible way this can be achieved is by incorporating the inherent non-linearity of the process into the control design process using a so-called learning model. Over the last decade or so, there has been much progress in the modelling and control of non-linear processes, using black-box type learning models, such as neural networks [4, 5]. This is due to their proven ability to learn arbitrary non-linear mappings. Other advantages inherent in neural networks include their robustness, parallel architecture and fault tolerant capabilities. Neural networks have been shown to be very effective for controlling complex non-linear systems, when there is no complete model information, or when the controlled plant is considered to be a “black box” [5]. In the following a new control algorithm is developed which builds on the works of Zayed et al. [3, 6] and Zhu et. al. [7], in which the unknown non-linear plant is represented by an equivalent model, consisting of a linear sub-model plus a nonlinear sub-model. Models of a similar type have previously been shown to be particularly useful in an adaptive poleplacement based control framework by Zhu et al.[7]. In this work, the parameters of the linear sub-model are identified by a standard recursive identification algorithm, and in addition a conventional multi-layered neural network is utilized as the non-linear learning sub-model (see figure (1)).