Guo-Qiang Zeng

Design of fractional order PID controller for automatic regulator voltage system based on multi-objective extremal optimization

Design of an effective and efficient fractional order PID (FOPID) controller, as a generalization of a standard PID controller based on fractional order calculus, for an industrial control system to obtain high-quality performances is of great theoretical and practical significance. From the perspective of multi-objective optimization, this paper presents a novel FOPID controller design method based on an improved multi-objective extremal optimization (MOEO) algorithm for an automatic regulator voltage (AVR) system. The problem of designing FOPID controller for AVR is firstly formulated as a multi-objective optimization problem with three objective functions including minimization of integral of absolute error (IAE), absolute steady-state error, and settling time. Then, an improved MOEO algorithm is proposed to solve this problem by adopting individual-based iterated optimization mechanism and polynomial mutation (PLM). From the perspective of algorithm design, the proposed MOEO algorithm is relatively simpler than NSGA-II and single-objective evolutionary algorithms, such as genetic algorithm (GA), particle swarm optimization (PSO), chaotic anti swarm (CAS) due to its fewer adjustable parameters. Furthermore, the superiority of proposed MOEO-FOPID controller to NSGA-II-based FOPID, single-objective evolutionary algorithms-based FOPID controllers, MOEO-based and NSGA-II-based PID controllers is demonstrated by extensive experimental results on an AVR system in terms of accuracy and robustness.

Design of multivariable PID controllers using real-coded population-based extremal optimization

Abstract The issue of designing and tuning an effective and efficient multivariable PID controller for a multivariable control system to obtain high-quality performance is of great theoretical importance and practical significance. As a novel evolutionary algorithm inspired from statistical physics and co-evolution, extremal optimization (EO) has successfully applied to a variety of optimization problems while the applications of EO into the design of multivariable PID and PI controllers are relatively rare. This paper presents a novel real-coded population-based EO (RPEO) method for the design of multivariable PID and PI controllers. The basic idea behind RPEO is based on population-based iterated optimization process consisting of the following key operations including generation of a real-coded random initial population by encoding the parameters of a multivariable PID or PI controller into a set of real values, evaluation of the individual fitness by using a novel and reasonable control performance index, generation of new population based on multi-non-uniform mutation and updating the population by accepting the new population unconditionally. From the perspectives of simplicity and accuracy, the proposed RPEO algorithm is demonstrated to outperform other reported popular evolutionary algorithms, such as real-coded genetic algorithm (RGA) with multi-crossover or simulated binary crossover, differential evolution (DE), modified particle swarm optimization (MPSO), probability based discrete binary PSO (PBPSO), and covariance matrix adaptation evolution strategy (CMAES) by the experimental results on the benchmark multivariable binary distillation column plant.

An improved multi-objective population-based extremal optimization algorithm with polynomial mutation

As a recently developed evolutionary algorithm inspired by far-from-equilibrium dynamics of self-organized criticality, extremal optimization (EO) has been successfully applied to a variety of benchmark and engineering optimization problems. However, there are only few reported research works concerning the applications of EO in the field of multi-objective optimization. This paper presents an improved multi-objective population-based EO algorithm with polynomial mutation called IMOPEO-PLM to solve multi-objective optimization problems (MOPs). Unlike the previous multi-objective versions based on EO, the proposed IMOPEO-PLM adopts population-based iterated optimization, a more effective mutation operation called polynomial mutation, and a novel and more effective mechanism of generating new population. From the design perspective of multi-objective evolutionary algorithms (MOEAs), IMOPEO-PLM is relatively simpler than other reported competitive MOEAs due to its fewer adjustable parameters and only mutation operation. Furthermore, the extensive experimental results on some benchmark MOPs show that IMOPEO-PLM performs better than or at least competitive with these reported popular MOEAs, such as MOPEO, MOEO, NSGA-II, A-MOCLPSO, PAES, SPEA, SPEA2, SMS-EMOA, SMPSO, and MOEA/D-DE, by using nonparametric statistical tests, e.g., Kruskal-Wallis test, Mann-Whitney U test, Friedman and Quade tests, in terms of some commonly-used quantitative performance metrics, e.g., convergence, diversity (spread), hypervolume, generational distance, inverted generational distance.

Binary-coded extremal optimization for the design of PID controllers

Abstract Design of an effective and efficient PID controller to obtain high-quality performances such as high stability and satisfied transient response is of great theoretical and practical significance. This paper presents a novel design method for PID controllers based on the binary-coded extremal optimization algorithm (BCEO). The basic idea behind the proposed method is encoding the PID parameters into a binary string, evaluating the control performance by a more reasonable index than the integral of absolute error (IAE) and the integral of time weighted absolute error (ITAE), updating the solution by the selection based on power-law probability distribution and binary mutation for the selected bad elements. The experimental results on some benchmark instances have shown that the proposed BCEO-based PID design method is simpler, more efficient and effective than the existing popular evolutionary algorithms, such as the adaptive genetic algorithm (AGA), the self-organizing genetic algorithm (SOGA) and probability based binary particle swarm optimization (PBPSO) for single-variable plants. Moreover, the superiority of the BCEO method to AGA and PBPSO is demonstrated by the experimental results on the multivariable benchmark plant.

A novel real-coded population-based extremal optimization algorithm with polynomial mutation

As a recently developed optimization method inspired by far-from-equilibrium dynamics of self-organized criticality, extremal optimization (EO) has been successfully applied to a variety of combinatorial optimization problems while its applications in continuous optimization problems are relatively rare. Additionally, there are only few studies concerning the effects of mutation operation on EO algorithms although mutation operation plays a crucial role in controlling the optimization dynamics and consequently affecting the performance of EO-based algorithms. This paper proposes a novel real-coded population-based EO algorithm with polynomial mutation (RPEO-PLM) for continuous optimization problems. The basic idea behind RPEO-PLM is the population-based iterated optimization consisting of generation of a real-coded random initial population, evaluation of individual and population fitness, generation of a new population based on polynomial mutation, and updating the population by accepting the new population unconditionally. One of the most attractive advantages is its relative simplicity compared with other popular evolutionary algorithms due to its fewer adjustable parameters needing to be tuned and only selection and mutation operations. Furthermore, the experimental results on a large number of benchmark functions with the different dimensions by using non-parametric statistical tests including Friedman and Quade tests have shown that the proposed RPEO-PLM algorithm outperforms other popular population-based evolutionary algorithms, e.g., real-coded genetic algorithm (RCGA) with adaptive directed mutation (RCGA-ADM), RCGA with polynomial mutation (RCGA-PLM), intelligent evolutionary algorithm (IEA), a hybrid particle swarm optimization and EO algorithm (PSOEO), the original population-based EO (PEO), and an improved RPEO algorithm with random mutation (IRPEO-RM) in terms of accuracy.

A Real-coded Extremal Optimization Method with Multi-non-uniform Mutation for the Design of Fractional Order PID Controllers

Design of an effective and efficient fractional order PID (FOPID) controller for an industrial control system to obtain high-quality performances is of great theoretical and practical significance. This paper presents a novel real-coded extremal optimization algorithm with multi-non-uniform mutation called RCEO-FOPID to design FOPID controllers. The key idea behind the proposed algorithm is the population-based iterated optimization, which consists of generation of a real-coded random initial population by encoding the parameters of a FOPID controller into a set of real values, evaluation of the individual fitness by using a novel and reasonable control performance index, generation of a new population based on multi-non-uniform mutation and updating the population by accepting the new population unconditionally. The proposed RCEO algorithm for the design of FOPID controller is relatively simpler than these reported popular evolutionary algorithms, e.g., genetic algorithm (GA), particle swarm optimization (PSO), chaotic anti swarm (CAS) due to its fewer adjustable parameters and only with selection and mutation operators. Furthermore, extensive simulation results on automatic voltage regulator system and multivariable control system have shown that the proposed RCEO-based FOPID controller is superior to other reported evolutionary algorithms-based FOPID and PID controllers in terms of accuracy and robustness. DOI: http://dx.doi.org/10.5755/j01.itc.45.4.13310

An Improved Real-Coded Population-Based Extremal Optimization Method for Continuous Unconstrained Optimization Problems

As a novel evolutionary optimization method, extremal optimization (EO) has been successfully applied to a variety of combinatorial optimization problems. However, the applications of EO in continuous optimization problems are relatively rare. This paper proposes an improved real-coded population-based EO method (IRPEO) for continuous unconstrained optimization problems. The key operations of IRPEO include generation of real-coded random initial population, evaluation of individual and population fitness, selection of bad elements according to power-law probability distribution, generation of new population based on uniform random mutation, and updating the population by accepting the new population unconditionally. The experimental results on 10 benchmark test functions with the dimension have shown that IRPEO is competitive or even better than the recently reported various genetic algorithm (GA) versions with different mutation operations in terms of simplicity, effectiveness, and efficiency. Furthermore, the superiority of IRPEO to other evolutionary algorithms such as original population-based EO, particle swarm optimization (PSO), and the hybrid PSO-EO is also demonstrated by the experimental results on some benchmark functions.

Adaptive population extremal optimization-based PID neural network for multivariable nonlinear control systems

Abstract The connection weights parameters play important roles in adjusting the performance of PID neural network (PIDNN) for complex control systems. However, how to obtain an optimal set of initial values of these connection weight parameters in a multivariable PIDNN called MPIDNN is still an open issue for system designers and engineers. This paper formulates this issue as a typical constrained optimization problem firstly by minimizing the cumulative sum of the product of exponential time and the system errors, and a real-time penalty function for overshoots of the system outputs, and then proposes an adaptive population extremal optimization-based MPIDNN method called PEO-MPIDNN for the optimal control issue of multivariable nonlinear control systems. The simulation results for two typical multivariable nonlinear control systems have demonstrated the superiority of the proposed PEO-MPIDNN to real-coded genetic algorithm (RCGA) and particle swarm optimization (PSO)-based MPIDNN, traditional MPIDNN with back propagation algorithm, and population extremal optimization-based multivariable PID control algorithm in terms of transient-state, steady-state, and robust control performance.

Population extremal optimization-based extended distributed model predictive load frequency control of multi-area interconnected power systems

Abstract How to design a set of optimal distributed load frequency controllers for a multi-area interconnected power system is an important but still challenging issue in the field of modern electric power systems. This paper presents an adaptive population extremal optimization-based extended distributed model predictive load frequency control method called PEO-EDMPC for a multi-area interconnected power system. The key idea behind the proposed method is formulating the dynamic load frequency control issue of each area power system as an extended distributed discrete-time state-space model based on an extended state vector, obtaining a distributed dynamic extended predictive model, and rolling optimization of real-time control output signal by adopting an adaptive population extremal optimization algorithm, where the fitness is evaluated by the weighted sum of square predicted errors and square future control values. The superiority of the proposed PEO-EDMPC method to a traditional distributed model predictive control method, a population extremal optimization-based distributed proportional-integral control algorithm and a traditional distributed integral control method is demonstrated by the simulation studies on two-area and three-area interconnected power systems in cases of normal, perturbed system parameters and dynamical load disturbances.

Optimal design of H 2 /H ∞ based robust PID controller by constrained extremal optimization and differential evolution

How to design an optimal mixed H2/H∞ robust FID controller for a complex control system is of great practical importance, but it is still an open issue. From the perspective of evolutionary algorithm, this paper formulates this issue firstly as a typical constrained optimization problem by minimizing a weighted objective function consisting of the robust stability performance, disturbance attenuation performance and tracking error, and then presents a novel a novel optimal design method of mixed H2/H∞ robust FID controllers based on a constrained evolutionary algorithm called CEO-DE by combining constrained extremal optimization and differential evolution. The simulation results on two typical multi-variable control systems have demonstrated the proposed CEO-DE based design method performs better than some reported popular methods such as intelligent genetic algorithm and multi-objective particle swarm optimization.