Mathematical Models for Modelless Control of Switching Power Supplies
Overview of model-free control of switching power supply
With the high-speed development of power electronics technology, power electronic equipment and people's work, life is increasingly close relationship, and electronic equipment are inseparable from a reliable power supply. Switching power supply is the use of modern power electronics technology, control the switching transistor turn on and off time ratio, to maintain a stable output voltage of a power supply, switching power supply is generally composed of pulse width modulation (pWM) control IC and MOSFET. The vast majority of switching power supply control part is in accordance with the analogue signal to design and work, the disadvantage is that the anti-interference ability is very poor. Due to the rapid development of computer control technology, the processing and control of digital signals show obvious advantages: easy computer processing and control, the flexibility of the design is greatly improved, the software debugging is convenient, etc., the emergence of pID control.
Switching power supply without model control mathematical model
In the control law design in general, the need to establish a mathematical model of the dynamic system. The classical approach requires that this mathematical model must be established in advance, at least its structure must be determined in advance. The more accurate the model, the better. In model-free control law design, the restriction of the control law requirement that the mathematical model be as precise as possible in advance is broken.
Our modelling procedure is accompanied by feedback control. The initial mathematical model can be imprecise, but it is necessary to ensure that the designed control law has a certain degree of convergence. The model-free control law we design is modelled and controlled at the same time, and when new observations are obtained, it is modelled and controlled again. This continues so that the mathematical model obtained each time becomes progressively more accurate, and the performance of the control law improves as a result. We call this procedure the integration of real-time modelling and feedback control.
Switching Power Supply Modelless Control Modelling
Integration of modelling and adaptive control
In Ref. the following generalised 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 lag 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 the characteristic covariate, which is estimated online using some kind of discrimination algorithm, and k is the discrete time. We will see that φ(k) has clear mathematical and engineering significance in the real-time discrimination-real-time feedback correction procedure of discrimination and control integration.
Integration of real-time modelling and feedback control
Specifically, our framework for modelling and feedback control integration is as follows:
(1) Based on the observed data and the generalised model
y(k) - y(k-1) = φ(k-1) [u(k-1) - u(k-2)
The valuation φ(k-1) of φ(k-1) is obtained using appropriate valuation methods.
(2) A simple way to seek the forecast value φ＊(k) for a step forward of φ(k-1) is to take
φ＊(k) = φ＊(k-1)
In seeking the control law, we still write φ＊(k) as the community φ(k).
(3) Applying the control law to the system S yields the new output bey (k+1). A new set of data ｛y(k+1),u(k)} is obtained.
Repeating (1), (2) and (3) on the basis of this new set of data results in a new set of data, y(k+2),u(k+1)}}, and so on. As long as the system S satisfies certain conditions, the output y(k) of the system S will gradually approach y0 under the effect of this procedure.
