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On the Selection of Tuning Methodology of FOPID Controllers for the Control of Higher Order Processes
Saptarshi Das, Suman Saha, Shantanu Das, Amitava Gupta
TL;DR
The paper addresses how FOPID tuning methodologies should be selected for higher-order processes. It compares frequency- and time-domain designs, introduces NIOPTD-based reduction for robust frequency-domain tuning, and reports different practical trade-offs between robustness, speed, disturbance suppression, noise rejection, and control effort.
Problem
Higher-order-process FOPID design requires comparing tuning strategies because their robustness, speed, disturbance suppression, noise filtering, and control-effort properties differ.
Method
The paper introduces NIOPTD-I and NIOPTD-II reduced-order templates, uses simultaneous nonlinear equation solving for robust frequency-domain tuning, and optimizes time-domain integral performance indices.
Results
Frequency-domain tuning provides greater robustness, high-frequency noise rejection, and lower control signal, whereas time-domain tuning is faster and better suppresses load disturbances.
Takeaways & Limitations
Neither methodology is unconditionally superior: frequency-domain tuning favors robustness and actuator demands, while time-domain tuning favors speed and load-disturbance suppression.
Takeaways & Limitations
Future work is needed for fractional-order modeling of open-loop unstable plants and processes with several minimum- or non-minimum-phase zeros.
Abstract
from arXiv · showhide
In this paper, a comparative study is done on the time and frequency domain tuning strategies for fractional order (FO) PID controllers to handle higher order processes. A new fractional order template for reduced parameter modeling of stable minimum/non-minimum phase higher order processes is introduced and its advantage in frequency domain tuning of FOPID controllers is also presented. The time domain optimal tuning of FOPID controllers have also been carried out to handle these higher order processes by performing optimization with various integral performance indices. The paper highlights on the practical control system implementation issues like flexibility of online autotuning, reduced control signal and actuator size, capability of measurement noise filtration, load disturbance suppression, robustness against parameter uncertainties etc. in light of the above tuning methodologies.
3. Frequency domain design of FOPID controllers
The paper develops flexible fractional-order reduced models for higher-order processes and uses them to tune robust FOPID controllers in the frequency domain. NIOPTD-II reduces modeling error and supports iso-damped designs based on simultaneous nonlinear equation solving.
- Frequency-domain tuning: The robust tuning solves five simultaneous nonlinear equations for the five FOPID parameters using phase-margin, crossover, iso-damping, complementary-sensitivity, and sensitivity specifications.The sensitivity specification represents load-disturbance suppression, while complementary sensitivity represents high-frequency noise attenuation.
- Reduced-order modeling: FOPTD and SOPTD reductions can produce large modeling errors for higher-order linear processes, limiting their suitability for robust FOPID design.
- Reduced-order modeling: NIOPTD-I and NIOPTD-II introduce flexible real-valued system orders, extending conventional integer-order reduced-model structures.The additional orders α and β are allowed to take any real value.
- Reduced-order modeling: The reduction procedure minimizes an H2-norm-based frequency-domain modeling error between the original and compressed process models.Candidate structures are compared using the minimum objective-function value.
- Reduced-order modeling: NIOPTD-II produces lower modeling error than the alternative reduced-order structures and is therefore selected for frequency-domain FOPID tuning.The resulting reduced models are reported for the higher-order test-bench plants.
- Frequency-domain tuning: Wide phase flatness around gain crossover frequencies produces iso-damped responses, allowing loop-gain increases to speed the response while maintaining overshoot.The reported closed-loop behavior supports robustness to gain variation and modeling uncertainty.
4. Time domain design of FOPID controllers
The time-domain method optimizes FOPID parameters against selected integral performance indices while enforcing stable, finite closed-loop responses. Its trade-offs against frequency-domain tuning depend on the chosen process and application priorities.
- Method: The method searches FOPID parameters by minimizing a selected time-domain integral performance index without requiring model reduction.Optimization is constrained to stable and finite closed-loop systems.
- Performance indices: Time-weighted error indices penalize later oscillations more heavily, helping reduce settling time, while higher error powers penalize large overshoot.The paper considers IAE, ITAE, ISE, ITSE, ISTES, and ISTSE criteria.
- Performance indices: The study compares individual indices with a weighted composite objective because combining objectives can average their individual strengths and deteriorate closed-loop performance.Setting all but one composite weight to zero recovers single-index tuning.
- Optimization: The optimization uses numerical integration and constrained Nelder–Mead search, with repeated perturbed initial guesses to reduce the risk of reporting a local minimum.Stability and finiteness checks restrict the parameter search.
- Selection of index: IAE performs best for plant 1P, but the most suitable index depends on the process model and should not be selected a priori.Optimal parameters for one higher-order process may not remain optimal for another.
- Comparison: Compared with time-domain tuning, frequency-domain design offers iso-damping robustness and better high-frequency noise rejection, whereas time-domain design better suppresses load disturbances.The time-domain approach also avoids model reduction, while frequency-domain design can reduce actuator requirements through lower control signals.
6. Conclusion
The paper finds that frequency-domain and time-domain FOPID tuning offer different practical advantages, so methodology selection depends on the process-control application. It also identifies future work for broader fractional-order process classes.
- Frequency-domain tuning provides greater iso-damping robustness, better high-frequency noise rejection, and lower control signals than time-domain optimal tuning.The lower control signal can reduce actuator size.
- Time-domain optimal tuning is faster and better suppresses load disturbances, but has lower robustness and poorer high-frequency noise filtration.Its larger control signal may saturate the actuator and cause integral wind-up.
- The paper contributes NIOPTD-I and NIOPTD-II templates, reduced-complexity frequency-domain tuning, stability-preserved time-domain tuning, and practical comparisons.The comparisons address noise filtration, control signal, actuator size, load disturbance rejection, and online or offline applicability.
- Future work includes fractional-order modeling of open-loop unstable plants and controllers for processes with several minimum- or non-minimum-phase zeros.