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A cascaded PID controller is depicted in following image (courtesy of controlglobal.com): enter image description here

The primary PID tracks the setpoint $SP_1$ and delivers a setpoint $SP_2$ to the secondary PID.

I wondered if it could be a problem if the secondary PID does not have a nice behaviour w.r.t. tracking its setpoint, while the total result of the cascaded PID controller is OK. This would mean that the overall tracking of $SP_1$ is OK, which is the goal of the total controller, while some internal controllers are not tuned too well.

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In general, poor performance of PID2 will cause poor performance in PID1, in both disturbance rejection and setpoint tracking.

There are some special instances where poor performance of PID2 in the form of high frequency oscillation is attenuated by G1, so the performance of PID1 is not significantly affected.

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