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Controlling of Second-Order Two-Channel Object with Delay

The control of multi-channel objects is relevant for many areas of science and technology. The presence of multiple links from each input to each output inside the object complicates the control problem extremely. Solving this problem by creating separate loops from each exit to each input is impossible. To solve this problem, a multichannel controller is necessary, that is, a controller containing the demanded transfer functions from each of its inputs to each output. There are many methods for calculating multi-channel controllers, but the overwhelming majority of them can be used only for the simplest models of the object. If each transfer function in the matrix model of the object contains delay links, none of the analytical methods for calculating the regulator is acceptable. This problem can be solved only by numerical optimization methods. In this paper, the method of numerical optimization of a regulator for a multi-channel object is proposed and investigated in the case when the transfer function of each channel is a product of a second-order filter and a pure delay link. A simple application of the numerical optimization method yields a system in which transient processes are characterized by overshoot exceeding 50%. The paper suggests a modification of the cost function for calculating the regulator by the method of numerical optimization. The effectiveness of the suggested solution is demonstrated, recommendations on the use of the proposed method are given.