Investigation of the Numerical Optimization Toolkit for Control of the Oscillatory Unstable Object

The numerical optimization method for calculating regulators has been used more frequently. The toolkit of the method includes various regulator structures, including pseudolocal loops regulators, regulators with a reference model, or with a Smith's predictor, with a bypass channel, regulators using the open model, etc. The arsenal of cost functions for optimization is also quite diverse. It includes the integral of the error module or the squared error and often this value is recommended to be multiplied by the time from the moment of the transient process. In addition, recommendations that use the compound aim functions are known. In this case, it is recommended to use an error growth detector (an overshoot detector) including a reverse overshoot and some other terms that increase the cost function, which allows adjusting the optimization result in the desired direction. It seems that this arsenal of funds is sufficient for any case encountered in practice. This paper investigates the possibility of solving the control problem for an oscillatory unstable object using all known methods for solving ones. It is shown that for some object models it is extremely difficult to obtain a satisfactory solution, and the set of known methods based on numerical optimization is insufficient. In this case, an object of the third order, containing negative coefficients in the polynomials of the numerator and denominator were chosen. The possibilities of using a PID-regulator, a bypass channel, or the open model of the object are investigated. The best solution among the robust ones is still characterized by a reverse overshoot of 70 %, which demonstrates the complexity of the solved problem and the inadequacy of the known tools in the form of regulator structures set and techniques for formation of a aim function. The method of additional control of the complex system obtained by using an external I-regulator is proposed. The efficiency of this method is shown with regard to the method of numerical optimization of the this regulator coefficients is not operational, and the factor for an external integrator is easily found empirically.