Modelling of a model-free control system for a switching power supply unit
In the references, the following general models are proposed:
y(k)-y(k-1)=φ(k-1)[u(k-1)-u(k-2)>(4-1)
Without loss of generality, it is assumed that the time delay of the controlled dynamic system S is 1, y (k) is the one-dimensional output of system S, and u (k-1) is the p-dimensional input. Phi (k) is the characteristic parameter, which is estimated online using some identification algorithm, and k is the discrete time. We will see that in the integrated process of real-time identification real-time feedback correction identification and control, phi (k) has significant mathematical and engineering significance.
Integrated real-time modeling and feedback control
Specifically, our integrated framework for modeling and feedback control is as follows:
(1) Based on observational data and general models
y(k)-y(k-1)=φ(k-1)[u(k-1)-u(k-2)]
By using appropriate valuation methods, the estimated value of phi (k-1) was obtained.
(2) A simple method to seek the forward predicted value of phi (k-1) is to take the
φ＊(k)=φ＊(k-1)
When seeking control laws, we still denote phi * (k) as social phi (k).
(3) Apply the control law to system S and obtain a new output Bey (k+1). So a new set of data {y (k+1), u (k)} was obtained.
On the basis of this new set of data, repeat (1), (2), and (3) to obtain new data {y (k+2), u (k+1)} and continue like this. As long as system S meets certain conditions, under the action of this procedure, the output y (k) of system S will gradually approach y0.
