SEARCH-FREE ALGORITHM FOR PARAMETRIC OPTIMIZATION OF PI CONTROLLER WITH SEMI-PERMANENT INTEGRATION

PURPOSE. It is a well known fact that proportional integral (PI) and proportional integral derivative (PID) controllers when applied in automatic systems with a large delay (when the delay value exceeds the highest values of controlled object time constants) do not provide acceptable quality of transients. This makes us address to some classes of regulators compensating the negative impacts of delay. This article deals with the known for its advantages PID controller with semi-permanent integration that belongs to the class of regulators with a variable structure that do not use a sliding mode. On the basis of the minimum integral-square criterion this work forms the algorithm of an automatic parametric optimization (APO) that calculates the optimal adjustment vector of the PI-controller with semi-permanent integration in an automatic system for the object with a large delay when adjustable parameters of the controller are independent from the moment of switching. METHODS. Due to the fact that the controller applied belongs to the class of regulators with a variable structure and the study is devoted to an object with delay, the use of analytical approaches to the adjustment of such regulator is extremely difficult. Therefore, an algorithmic method should be used to solve the problem of controller parametric optimization. This study also employs a gradient procedure which enables to calculate gradient components using the functions of sensitivity with their known advantages. RESULTS AND THEIR DISCUSSION. The formed APO algorithm has determined the optimal parameters of the PI controller with semi-permanent integration for a given object with a large delay at the minimal integral-quadratic criterion. The validity of the found vector of controller adjustment generated by the APO algorithm is confirmed by the calculation of Hessian matrix and proven by the computing methodology. CONCLUSIONS. The APO algorithm solves the set problem of parametric optimization with the accuracy sufficient for practice. Received positive experience in the optimization of PI-controller with semi-permanent integration allows to apply it to other regulators with variable structure that do not use the sliding mode. In future it will allow to extend the use of the gradient algorithm based on the sensitivity functions for this class of controllers with variable structure under different laws of controller structure switching.

proportional integral (PI) controller, sensitivity, time delay, parametric optimization problem, integral-quadratic criterion

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