Recently, a new motor came, and the manufacturer did not give a specific parameter of inductance and resistance. There is no way to study if the parameters are identified. Thinking about parameter identification, it was also a topic that was going to be done a long time ago. Recently, life has fluctuated greatly, and I really don’t want to do too complicated things anymore. I just immerse myself in it and fill in the holes.
1. Recursive least squares method
The least square method was first proposed by Gauss in the research work of the body motion orbit report, and it is called the cornerstone of parameter identification theory. It is widely used in system identification and parameter estimation. I have to lament the greatness of mathematicians and the improvement of engineering technology. It is inseparable from the optimization of tools by these great mathematicians. So roughly what is the recursive least squares method? For an observable system, the L groups of input and output observation data can be expressed as {y(k),u(k),k=1,2,3....}.
Assuming that the input and output of the system can be expressed as:
Among them, y(k) is the output matrix of the system, phiT(k) is the observable intermediate matrix, theta(k) is the matrix of the parameters to be identified, and e(k) is the random variable matrix with an average value of 0.
Construct its objective function as:
Let its partial derivative be 0, then the recursive formula of the recursive least squares method can be expressed as:
Then this formula is the core algorithm of the recursive least squares method, where K(k) and P(k) are the intermediate variables of the recursive formula. Then as long as we can get y(k) and phi(k), we can start the recursive least squares, and the identification result is theta(k).
2. The input and output matrix of the motor
By directly analyzing the voltage model of its dq axis, the following relationship can be obtained: where wr is the electrical angular velocity of the motor.
Since what we want to do is online parameter identification, it must be discretized. The mathematical model after discretization is as follows:
Overall further collation can be obtained:
Then it can actually be extracted. The input and output matrices we need for the least square method are y(k) and phi(k). Extract it to get:
According to the above sorting, the equation of parameter identification is finally obtained, combined with the simulation framework we made before, to realize it.
