Self-tuning algorithms for predictive functional controller

In this paper we explore possibilities to use simple step response-based identification methods for self tuning of the predictive functional controller (PFC). The methods tested are: tangent method (Fig. 2), area method (Fig. 3) and improved area method. Two versions of the improved area method were tested, one using the normal least squares (Eq. 17) and the other least squares with the instrumentation matrix (Eqs. 18 and 19). The methods were automated and adapted for gaining the PFC parameters. The PFC algorithm is described by Eq. 1 and block scheme in Fig. 1. To tune the PFC, we need five parameters. The first three are from the first order model with delay (gain, time constant and delay) that approximates the real process and the other two are T-r (desired time constant) and H (the time horizon where the model and the process response coincide) that come from the derivation of the algorithm. Parameters of the model are attained from the identification methods. Parameters T-r and H are then tuned in accordance with the gained model parameters from Eq. 24 for better controllable processes and from Eq. 25 for poorly controllable processes. Because of the space limitation the results are given only for two simulated processes (see Eqs. 20 and 21) and for two real processes for the DC motor and laboratory air conditioner. The methods were evaluated by comparing their estimates to the real processes using criterion functions given by Eqs. 22 and 23. The Tabs. 1 and 2 shoe values of the criterion functions. In the first table, there are results from experiment where the Gaussian noise of variance 0.01 was added to the output of the process. In the second table, the noise variance was 0.001. Results of the experiment on the real processes are given in Tab. 3. Our conclusion is that simple identification methods, such as the tested ones, can give us enough accurate parameters for the tuning of the PFC.