Abstract
In this chapter, the explicit solution for tuning the PID controller parameters in the presence of integrating process is presented. The presence of one integrator coming from the plant along with one integrator coming from the PID-type control action results in a type-II control loop according to Sect. 2.5. The proposed control law is developed again in the frequency domain and lies in the principle of the symmetrical optimum criterion which, strictly speaking, is the application of the Magnitude Optimum criterion in type-II control loops. Therefore, the desired control action requires again that the magnitude of the closed-loop transfer function is equal to the unity in the widest possible frequency range. For the proof of the control law, a general transfer function process model is adopted consisting of \(n\) poles, \(m\) zeros plus unknown time delay \(d\). The final solution determines explicitly the P, I, and D parameters as a function of all time constants involved within the control loop and irrespective of the process complexity. The potential of the proposed method is tested both (1) on benchmark process models (integrating process with dominant time constants, integrating non-minimum phase process, integrating process with long time delay). The proposed control action is tested also for the control of the actual DC link voltage in an AC/DC grid connected converter. In all cases, an extensive comparison test is presented between the conventional current state-of-the-art PID tuning and the proposed control law, justifying the potential of the proposed method.
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Notes
- 1.
In this case, a grid connected converter controls the DC Link which is then used by the motor side converter which finally drives the motor.
- 2.
In the case of the island network, auxiliary small diesel generators are completely switched off since they are consuming expensive oil, and the energy is coming from the main diesel engine of the ship which drives the propeller.
- 3.
Grid of the vessel supporting the electrical load of the vessel.
- 4.
SFOC: stator field-oriented control, RFOC: rotor field-oriented control.
- 5.
In many real-world applications, \(k_\mathrm{p}\) stands for the plant’s dc gain at steady state.
- 6.
This kind of instability is justified by the Routh theorem. For a polynomial of the form \(D\left( s \right) = {a_n}{s^n} + {a_{n - 1}}{s^{n - 1}} + \cdots + {a_1}s + {a_0}\), necessary condition for \(D\left( s \right) \) to be stable is \(a_j>0\), \(j=0,1,2,\ldots \) Since in (4.6) \(a_1=0\), then according to the Routh theorem, the denominator \(D(s)\) of \({ T}(s)\) is unstable.
- 7.
Let it be noted that the conventional tuning has never been tested to non-minimum phase processes within the academic literature.
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Papadopoulos, K.G. (2015). Type-II Control Loops. In: PID Controller Tuning Using the Magnitude Optimum Criterion. Springer, Cham. https://doi.org/10.1007/978-3-319-07263-0_4
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DOI: https://doi.org/10.1007/978-3-319-07263-0_4
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