## IMPROVING THE PERFORMANCE OF AN INADEQUATELY TUNED PID CONTROLLER BY INTRODUCING A POLYNOMIAL MODEL BASED INCREMENT IN PID CONTROL VALUE

Mathematical Modeling, Vol. 2 (2018), Issue 1, pg(s) 8-12

In control literature, one can easily find a variety of different examples for industrial control, where contemporary control algorithms are implemented. Surprisingly, there are not many known examples where the state-of-the-art control algorithms have been implemented in real-time control systems. Instead, researchers usually implement algorithms that are proven to be reliable, fast and easy to implement. One control solution that has been proven to satisfy all previously mentioned attributes is PID. However, despite all its good assets it has two major deficiencies. One of them is that it can’t adapt on the diversities caused by the variation occurring in the model parameters and still it can’t control nonlinear systems due to multiple operating points present there. Therefore, to deal with those weaknesses an improvement in PID control structure has been introduced in the form of supervisory mechanism (SM) which as a main constitute part has a quadratic polynomial model. Thus, the control value of the newly proposed PID algorithm is formed of two terms, the first one is the value calculated by standard PID and the second one is the value calculated by the SM. The quadratic model forming part of the SM is obtained based on the past value of the error. Nevertheless, the use of quadratic model introduces additional complexity into the PID controller. Furthermore, the quadratic model should be updated fast enough and also it has to describe the data adequately. These aspects are analyzed and discussed in details in this paper. Moreover, an algorithm is introduced which will guarantee that the data used for calculation of the quadratic model is suitable.

## IMPROVING THE PRECISION OF PLANT RESPONSE BY MODELING THE STEADY STATE ERROR

Industry 4.0, Vol. 2 (2017), Issue 4, pg(s) 161-164

Nowadays, one of the most common problems in control system theory that should be tackled is how to improve the precision of a plant in steady state, under a change in the target value of the plant. Well known fact is that the models we use for designing controllers are not ideal. Thus, when the controller is applied to the real plant there is difference in between the expected and obtained results. Likewise, the controllers should be designed to be at the same time robust to uncertainties and also fast enough to drive the system to the desired value. The purpose of this paper is to describe and finally implement the approach in which the idea is to improve the precision of the system in steady state by adding an additive term to the control value calculated by the predesigned PID controller. The PID controller is designed in advance, and has poorly tuned integral term. Afterwards, when the desired target value is changed the PID controller is not aware of that change, so its performance starts to drop and as a result the steady state error starts to increase. Therefore, to preserve the exactness of the plant’s output an additive term to the control signal is calculated out of a polynomial second order model derived from the error values obtained in the previous measurements of the plant. The results from MATLAB simulations have shown that the PID controller could not keep up good performance when the target value of the system is changed. Hence, by adding an additive term to the control signal we gave to PID the needed ‘awareness’ and as a result of that we could improve the steady state error by small margin.