Abstract
A systematic automatic tuning method for PID-type controllers in Single Input–Single Output processes is proposed. The method is inspired from the Magnitude Optimum design criterion and (1) considers the existence of a poor process model and (2) requires only access to the output of the process and not to its states (3) requires an open-loop experiment on the plant itself for initializing the algorithm. The application of the Magnitude Optimum criterion for tuning the PID controller in the case of a known single input–single output linear process model and regardless of its complexity shows that the step response of the control loop exhibits a certain performance in terms of overshoot (4.4 %), settling and rise time as it was already shown in Chap. 3 and Sect. 3.2. The proposed method exploits this feature and tunes the PID controller parameters, so that the aforementioned performance is achieved. Since the proposed control law is not restricted to specific plants regarding their complexity, a performance comparison in Sects. 7.3 and 7.4.3 discusses the closed-loop frequency response when the controller is tuned optimally according to Sect. 3.3 and when the controller is tuned automatically according to Sect. 7.2.
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Notes
- 1.
Stator or rotor field oriented vector control.
- 2.
Overshoot, settling and rise time remain unaltered.
- 3.
The controller’s unmodeled dynamics \({T_{{\Sigma _{\text {c}}}}}\) are negligible compared to the plant’s unmodeled dynamics \({T_{{\Sigma _{\text {p}}}}}\), \({T_{{\Sigma _{\text {c}}}}}\ll {T_{{\Sigma _{\text {p}}}}}\).
- 4.
In this case, only an open-loop experiment is required to the process for initializing the algorithm and no other information.
- 5.
In this case, the transfer function is assumed accurately modeled.
- 6.
\(T_x\) is a design parameter.
- 7.
This time constant was chosen sufficiently large, so that \(\tau \rightarrow 0\).
- 8.
The amplitude of these pulses is small enough, so that the output of the control loop \(y(t)\) does not diverge far from its operating point.
- 9.
The PI controller can be avoided and a simple bang-bang control with a hysteresis band in the output overshoot reference can be introduced.
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Papadopoulos, K.G. (2015). Automatic Tuning of PID Regulators for Type-I Control Loops. In: PID Controller Tuning Using the Magnitude Optimum Criterion. Springer, Cham. https://doi.org/10.1007/978-3-319-07263-0_7
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DOI: https://doi.org/10.1007/978-3-319-07263-0_7
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