Did I do the PID control design correctly in matlab? if it's wrong, where should I change

Answer 1

[Sam Chak]

Hi @Mücahit

The block diagram in Fig. 4 represents a variant of the PID control scheme, known as I-PD control, wherein both the proportional and derivative actions are shifted to the feedback path. This adjustment aims to mitigate the proportional kick and derivative kick resulting from sudden changes in the setpoint . The architecture is almost similar to the Linear-Quadratic-Integral (LQI) control, as illustrated in the figure below.

If the signal Zsr represents the state-dependent output , then the block diagram in your Simulink model bears a resemblance to the I-PD scheme depicted in Fig. 4. Whether the designed output-feedback I-PD control scheme can induce adequate changes in the system's behavior to meet the performance specifications is another matter. Ultimately, the control principle aims to influence the values of the system's states to drive the system's output towards a desired value specified by .

[Sam Chak]

My point is that the output-feedback I-PD control scheme typically offers adequate compensation if the controlled state variable is also the system's output , where . However, since the output is a linear combination of the state variables, given by , a mathematical analysis is necessary to determine whether the I-PD controller independently influences the values of and , respectively.

[Paul]

Figure 4 in the question doesn't match equation (10) in the question. The former has the derivative control on the feedback y, but the latter has the derivative control on the error signal e, at least as far as I read it.

[Sam Chak]

Furthermore, if the error signal is defined as as depicted in the block diagram, then the derivative action in Eq.(10) may destabilize the system.