Neural network implementation of controllers for multi-channel objects synthesized by polynomial method

Abstract

The implementation of neural network multichannel controllers synthesized by polynomial matrix decomposition is analysed. Objects and controllers are assumed to be linear; these allow them to be described by matrix transfer functions. The transfer function of the object is converted to the right polynomial matrix inter-simple decomposition. The transfer function of the controller is sought in the form of a left polynomial matrix of inter-simple decomposition that allows leading the characteristic matrix to the form of a linear matrix polynomial equation with two matrix indeterminates. This equation is solved by leading to a matrix equation with numeric matrix indeterminates. Then the controller equation is converted to a discrete equation. The discrete sampling step is chosen small enough to allow the systems with continuous and discrete controllers have sufficiently close transient processes. The discrete controller is converted to a structure including delay elements, adder units and amplification coefficients. Then this structure is presented in the form of a set of neurons. The operation of the algorithm is illustrated by the example of the synthesis of an unstable inverted pendulum control, which includes two PID controllers. Possible increases in neuro controller performance are demonstrated. Two PID controllers are combined into one neural network in order to further optimization.