The polynomial method of controller synthesis based on the reference and disturbing signals

Abstract

Linear controlled objects with one input and one output (single input - single output, SISO), and objects with multiple inputs and multiple outputs (multi-input – multi-output, MIMO) have different formalized controller synthesis algorithms. At the same time, objects with an unequal number of inputs and outputs, in many cases, are built by the developer intuitively, when changing the existing calculation algorithms for each control object, therefore, the development of a formalized calculation algorithm for this type of objects is relevant. Within the framework of this work, it is proposed to extend the synthesis technique for multichannel objects, which is the polynomial synthesis technique, to objects with a smaller number of inputs compared to the number of outputs, namely, to objects with one input and several outputs (single input – multi-output, SIMO). The reasoning developed in the work is an example of calculating an electromechanical tension control system in the material transportation zone of the production line, which has one input – the voltage supplied to the electric motor and four outputs–- the armature current, the rotation speed of the electric motor shaft, the rotation speed of the roll, the tension in the zone under consideration and the elastic moment. The tension in the considered zone is an adjustable coordinate. The use of the polynomial synthesis method for objects with a non-square matrix function made it possible to place the poles of a closed system in a given position, and the transfer function does not contain zeros according to the assignment. It was also possible to set the disturbance-stimulated zeros of the closed system in such a way that a second-order astatism is obtained.