Model-free control modeling of switching power supplies
An Integrated Approach to Modeling and Adaptive Control
In the reference, the following generic model is proposed:
y(k)-y(k-1)=φ(k-1)[u(k-1)-u(k-2)>(4-1)
Without loss of generality, it is assumed here that the time delay of the controlled dynamic system S is 1, y(k) is the one-dimensional output of the system S, and u(k-1) is the p-dimensional input. φ(k) is a characteristic parameter, which is estimated online by using some identification algorithm, and k is discrete time. We will see that φ(k) has obvious mathematical and engineering significance in the integration procedure of identification and control of real-time identification-real-time feedback correction.
Integration of real-time modeling and feedback control
Specifically, our integrated framework of modeling and feedback control is as follows:
(1) Based on observation data and general model
y(k)-y(k-1)=φ(k-1)[u(k-1)-u(k-2)]
Using an appropriate valuation method, an estimate φ(k-1) of φ(k-1) is obtained.
(2) To seek the forecast value φ*(k) of φ(k-1) one step forward, a simple method is to take
φ*(k)=φ*(k-1)
When seeking the control law, we still record φ*(k) as φ(k).
(3) Apply the control law to the system S to get a new output bey(k+1). So a new set of data {y(k+1), u(k)} is obtained.
Repeat (1), (2) and (3) on the basis of this new set of data to get new data {y(k+2), u(k+1)} and so on. As long as the system S satisfies certain conditions, under the action of this procedure, the output y(k) of the system s will gradually approach y0.
