Comparison of Some optimization Techniques in Robust process Control Design
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Date
2015
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Publisher
Obafemi Awolowo University
Abstract
The research explored standard ways of quantifying uncertainties in systems and assessing controller performance in the frequency domain; examined four robust process control design strategies implementing them on typical multivariable systems. This was with the view of delineating their advantages and disadvantages.
The mathematical models of selected multivariable systems were obtained from the literature. Different sources of uncertainties were identified for each system. Nominal models were arrived at by considering the average plant using the Nyquist plots of different operating points in some instances, while the model of the nominal operating point in some other instances were chosen. In the previous case, the frequency plots of deviations of the different operating points from the nominal model were used to model the uncertainty weights whereas in the latter instance, specific ranges of perturbations were modelled to be attributed to the systems at low and high frequencies. The optimization techniques considered are Method of Inequalities (MoI), MATLAB Optimization Toolbox commands fmincon and fminsearch, and H∞ and µ synthesis strategies. Decentralized controllers were designed using IMC tuning relations (or SIMULINK auto-tuning facility) and fixed-structure H∞ design strategy. The former was optimized using MoI, fmincon and fminsearch at different instances. Optimal centralized controllers were also designed using H∞ and µ synthesis strategies. The performance of each controller was assessed by calculating the Structured Singular Value for robust stability and performance, the IAE values during unit step changes and observing other transient response characteristics such as rise-time, settling time, overshoot, interaction and disturbance rejection.
The results show that the efficiency of MoI decreases with increasing number of parameters to be optimized unlike fmincon which works better with more parameters and may rather appear “aggressive” on simple systems with few parameters to be optimized; such systems attain good rise-time but may not eventually settle fast as desired. Meanwhile, both strategies require starting parameters for optimization. Centralized H∞ and µ syntheses were reliable strategies for obtaining robust controllers even for complex systems (systems of large dimensions, high order, great interactions and/or time-delayed terms) but in most cases resulted in controllers of high order. Controller order reduction was undertaken whenever closed loop performance degradation was not significant. Fixed-structure H∞ controllers were found to be good alternatives but as expected, their performance did not exactly match those of the full controllers. In general, controllers synthesized with H∞ and µ strategies under a given bandwidth (ω_B^*) constraint were found to have slower responses compared to those optimized with MoI and fmincon with the same constraint.
The study concluded that optimal ω_B^* values are best obtained for simple systems by optimizing alongside with controller parameters using MoI while for complex systems, much improvement may not be achievable upon the value obtained from the sensitivity plot of initial controller. It is also concluded that H∞ and µ syntheses should be reserved for complex systems for which multiloop MoI optimization, fmincon optimization and fixed-structure H∞ synthesis fail to attain desired performance.
Description
xxii,225 pages.
Keywords
Robust, Process Control Design, multivariable systems, Low Frequencies, High Frequencies
Citation
Adeyemo,S.O(2015).Comparison of some optimization techniques in robust process control design.Obafemi Awolowo University.