Development of novel hybrid metaheuristic algorithms for identification and control in the delta domain

Abstract

The thesis develops five novel hybrid metaheuristic algorithms as per Talbi’s taxonomy of hybrid metaheuristics. Firefly algorithm is integrated with bacterial foraging, flower pollination, pattern search and grey wolf optimizer respectively to develop high performance computing algorithms. Two types of test functions, namely unimodal and multi-modal of relatively high dimension are considered to validate each of the hybrid propositions. The results obtained are compared with the parent as well as some standard and latest heuristics reported in the literature. The results show great promise for the hybrid algorithms developed in terms of convergence speed and accuracy. These firefly-based hybrid algorithms has further been applied for identification of linear dynamic systems with static nonlinearities in the delta domain unifying continuous and discrete time analyses at high sampling rate. A test system with different polynomial nonlinearities has been considered for hammerstein and wiener system identification in continuous, discrete and delta domain. Delta operator modelling provides a unified approach for system identification matching continuous and discrete-delta results at high sampling frequency. Pseudo random binary sequences (PRBS), contaminated with white noise of fixed signal-to-noise (SNR), have been taken up as the input signal to estimate the unknown model parameters as well as static nonlinear coefficients. The hybrid algorithms not only outperform the parent heuristics of which they are constituted but also prove better as compared to some of the standard and latest heuristic techniques available in the literature. Delta operator parameterization presents a unified framework in analysis and design of discrete-time systems, in which the resultant model converges to its continuous-time counterpart at high sampling limit. Capitalizing this unique property of delta operator, the new firefly-based hybrid algorithms have been utilized for model order reduction of high dimensional linear discrete-time system applying constraints to ensure stability, minimum phase feature and matching of dc gain. It has been shown that the reduced discrete-time model inherits all the dominant characteristics of the higher order discrete-time model and with the increase of sampling frequency it converges to the continuous-time reduced model. Four test systems viz. single-input single-output, fractional order, time delay and multi-input multi-output systems are taken up to establish the usefulness of the proposed methods. The hybrid techniques not only yield better matching in the delta domain, but also deliver quality solutions and provide faster convergence than the parent and some standard heuristic methods. The performances of the reduced systems are also compared with their respective original systems as well as reduced systems reported in the literature in terms of time-domain and frequency-domain parameters. The proposed topologies also proved its superiority in terms of some benchmark error indices well established in the literature of systems and control. Further, the controller design of the reduced models developed using approximate model matching in the Truxal framework applying the proposed hybrid metaheuristic algorithms in the complex delta domain. The plant model, cascaded with a PID controller, is compared with a reference model to obtain the unknown controller parameters. The tuned controller parameters in the delta domain closely match those obtained from the continuous-time approach. Thus, a unified framework of controller design has been developed. The hybrid algorithms performed better in terms of error index and transient parameters as compared to the standard heuristics reported in the literature. An additional case study has also been considered for order reduction and speed control of permanent magnet synchronous motor drive in the delta domain. Thus, the proposed hybrid methods not only prove their mettle to solve unconstrained higher dimension optimization problems but also prove their worth for system identification, model order reduction and controller design in the complex delta domain. These methods may be further applied to handle multi-objective real time applications.