In PID controller design, an optimization algorithm is commonly employed to search for the optimal controller parameters. The optimization algorithm is based on a specific performance criterion which is defined by an objective or cost function. To this end, different objective functions have been proposed in the literature to optimize the response of the controlled system. These functions include numerous weighted time and frequency domain variables. However, for an optimum desired response it is difficult to select the appropriate objective function or identify the best weight values required to optimize the PID controller design. This paper presents a new time domain performance criterion based on the multiobjective Pareto front solutions. The proposed objective function is tested in the PID controller design for an automatic voltage regulator system (AVR) application using particle swarm optimization algorithm. Simulation results show that the proposed performance criterion can highly improve the PID tuning optimization in comparison with traditional objective functions.

This paper proposes a novel controller for automatic voltage regulator (AVR) system. The controller is a four term control type consisting of proportional, integral, derivative, and second order derivative terms (PIDD2). The four parameters of the proposed controller are optimized using particle swarm optimization (PSO) algorithm. The performance of the proposed PIDD2 is compared with various PID controllers tuned by modern heuristic optimization algorithms. In addition, a comparison with the fractional order PID (FOPID) controller tuned by Chaotic Ant Swarm (CAS) algorithm is also performed. Furthermore, a frequency response, zero-pole map, and robustness analysis of the AVR system with PIDD2 is performed. Practical implementation issues of the proposed controller are also addressed. Simulation results showed a superior response performance of the PIDD2 controller in comparison to PID and FOPID controllers. Moreover, the proposed PIDD2 can highly improve the system robustness with respect to model uncertainties

Combinatorial optimization has been used in different research areas. It has been employed successfully in software testing fields to construct minimum set of combinations (i.e., in terms of size) which in turn represents the minimum number of test cases. It was also found to be a successful approach that can be applied to solve other similar problems in different fields of research. In line with this approach, this paper presents a new application of the combinational optimization in the design of PID controller for DC servomotor. The design of PID controller involves the determination of three parameters. To find optimal initial PID parameters, different tuning methods have been proposed and designed in the literature. The combinatorial design is concerned with the arrangement of finite set of elements into combinatorial set that satisfies some given constraints. Consequently, the proposed method takes the interaction of the input parameters as a constraint for constructing this combinatorial set. The generated sets are then used in the proposed tuning method. The method proved its effectiveness within a set of experiments in a simulated environment.