Development of PI-controller optimal tuning method

2019;
1
National University of Life and Environmental Sciences of Ukraine
2
National University of Life and Environmental Sciences of Ukraine
3
National University of Life and Environmental Sciences of Ukraine
4
National University of Life and Environmental Sciences of Ukraine

Aim. The research aims to develop a method of optimal PI-controller tuning, which allows to take into account the constraints and to minimize the undesirable indicators of the automatic control quality. Method. In order to carry out the investigation, the problem of optimal PI-controller tuning was stated in a general form. The analysis of the elements of the problem has been conducted. It allowed substituting the elements to the requirements of individual minimization criteria. Development of the general (complex) criterion, which includes these criteria, was conducted with taking into account weight coefficients. They considerably differ from each other. It allowed created the desired topology of the general criterion. Results. Based on the problem of optimal PI-controller tuning with constraints, a method has been developed that ensures the stability of the automatic control, met the constraints and minimizes the complex optimization criterion. The implementation of the method is connected with the MISO-function, which should be minimized during the calculation process and which is based on the mathematical model of the plant. The method does not impose hard constraints on the mathematical properties of the problem (for example, the continuity of optimization criteria). Scientific novelty. For the first time, the method of optimal PI-controller tuning with constraints has been developed, which may be used for plants of arbitrary order. In addition, the method allows minimization of several optimization criteria, provided that the importance of each must be estimated by some numerical indicator. The developed method allows taking into account the conditions of stability. It can also be generalized for PID-controllers and controllers of arbitrary structure (including nonlinear ones). Practical significance. Significant reduction of the mean integral error is stated. It relates to the cases of the developed method application (in comparison with other engineering methods of PI-controllers tuning). The comparison has been made between those methods, which allow obtaining zero overshoot during setpoint reaching. For example, for a plant described by the transfer function G(s)=1/(s+1)2, the mean integral error decreased by 1.87… 3.14 times, for a plant with the transfer function G(s)=1/(s+1)3 this criterion decreased by 1.32… 2.10 times. The method may also be applied to the problems of minimization of other undesirable indicators of integral or positional type.

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