Earticle

The appropriate choice of crossover and mutation rates is critical to the success of genetic algorithms. Earlier researches focused on finding optimal non-dynamic crossover or mutation rates, which vary for different problems, and different stages of the genetic process in a problem. This paper proposed an ameliorate adaptive genetic algorithm where the mutation and crossover rates are adapted dynamically based on the evaluation results of the respective offspring in the next generation. Simultaneously, we combined this new algorithm with PD controllers to improve the stability of control systems. The experimental results are compared with other researchers’ approaches in this field. The PD-GA method can also significantly accelerate the system response and induce lower overshoot as well.

The PI-PD controller structure provides an excellent four-parameter controller for control of integrating, unstable and resonant processes to set point changes while the conventional PID controller has limitations in controlling such systems. In this paper, a graphical method for the computation of all stabilizing PI-PD controllers is given. The proposed method is based on plotting the stability boundary locus, which is a locus dependent on the parameters of the controller and frequency, in the parameter plane. The stability boundary loci are first obtained in the ($K_d$, $K_f$) and ($K_p$, $K_i$) planes and then it is shown that all the stabilizing values of the parameters of a PI-PD controller can be found. Computation of stabilizing PI-PD controllers which achieve user specified gain and phase margins is also studied. The method is used to design robust PI-PD controllers for control systems with parametric uncertainties. A design procedure for interval control systems is proposed. Examples are given to show the benefit of the method presented.

Fuzzy controller's design depends mainly on the rule base and membership functions over the controller's input and output ranges. This paper presents two different approaches to deal with these design issues. A simple and efficient approach; namely, Fuzzy Subtractive Clustering is used to identify the rule base needed to realize Fuzzy PI and PD type controllers. This technique provides a mechanism to obtain the reduced rule set covering the whole input/output space as well as membership functions for each input variable. But it is found that some membership functions projected from different clusters have high degree of similarity. The number of membership functions of each input variable is then reduced using a similarity measure. In this paper, the fuzzy subtractive clustering approach is shown to reduce 49 rules to 8 rules and number of membership functions to 4 and 6 for input variables (error and change in error) maintaining almost the same level of performance. Simulation on a wide range of linear and nonlinear processes is carried out and results are compared with fuzzy PI and PD type controllers without clustering in terms of several performance measures such as peak overshoot, settling time, rise time, integral absolute error (IAE) and integral-of-time multiplied absolute error (ITAE) and in each case the proposed schemes shows an identical performance.

Recently, Datta at al. [1] have developed a metDattad of obtaining the complete set of stabilizing PI, PID controllers for a given LTI system, in which tDattase are determined by solving a set of linear inequalities parameterized by the proportional(P) gain. In this paper, we provide a note about Dattaw Datta's idea can be extended to the problem of finding all stabilizing PD controllers and about an improved metDattad that allows us to calculate the admissible range of P gain more rigorously. An illustrative example is given.