Self-tuning PID self-tuning control 】 【

Self-calibration PID is a kind of self-calibration control. Its core idea is to use online identification to identify changes in system parameters, and then use the idea of ​​pole configuration to calculate PID parameters to achieve the purpose of automatic adjustment.

Recursive least squares with forgetting factor

In the previous article, the recursive least squares method was derived and experimented.However, due to the accumulation of previous data, the simple recursive least squares method may not be able to track the system parameters very well when the system parameters change rapidly. Therefore, a forgetting factor can be added to better track the changes of the system parameters.:

Calculate PID

After the system parameters are obtained by parameter identification, the PID parameters can be calculated according to the previous pole configuration idea.Follow the previous transfer function reference: G = b0 / (a0*s^2 + a1*s + a2)

For this second-order system, the closed-loop characteristic equation after adding the PID transfer function is third-order, so the expected third-order characteristic equation can be set as follows:

(s + alpha)(s^2 + 2*drag*wn + wn^2)

According to the closed-loop transfer function, the characteristic polynomial can be calculated, and then the PID parameters can be calculated according to the expected characteristic polynomial above.

Experiment

The experimental program is divided into three groups. One group is the PID parameters that have been debugged, but the system parameters have not changed; the second group, after the fifth second, changes the system parameters every cycle, and the cycle is 0.001 seconds; the third group usesSelf-calibration PID, also after the fifth second, changes the system parameters every cycle.The experimental results are as follows:

It can be seen that the self-calibration PID has a certain effect, but the overall feeling of the optimization effect is not large, but it can be regarded as providing an idea, and it is also possible that the calculation method of the PID parameters needs to be optimized.