Tuning Of PID Parameters Based On Chaotic Optimization Algorithm

During the past decades, process control techniques in the industry have made great advances. In despite of many efforts, the PID (proportional-integral-derivative) controller continues to be the main component in industrial control systems, and the reason is that it has a simple structure which is easy to be understood by the engineers and it presents robust performance within a wide range of operating conditions, especially with a reduced number of parameters to be selected and a good performance to be achieved when dealing with complex processes.However, since it is fairly difficult to determine the PID parameters suitably, lots of researches have been reported with respect to PID parameter tuning schemes. Over the years, many techniques have been suggested for tuning of the PID parameters. In this context there are classical Ziegler-Nichols, Cohen-Coon, pole placement and advanced techniques (minimum variance, gain scheduling and predictive). Some disadvantages of these control techniques for tuning PID controllers are:(ⅰ) excessive number of rules to set the gains, (ⅱ) inadequate dynamics of closed loop responses, and (ⅲ) mathematical complexity of the control design.Recently, as an alternative to the classical mathematical approaches, modern heuristic optimization techniques have been given much attention by many researchers due to their ability to find an almost global optimal solution in PID tuning. In this paper, a tuning method for determining the parameters of PID control system using a chaotic optimization approach based on logistic map is proposed. One of them is the Chaotic optimization algorithms(COA) based on chaotic theory which is a bounded unstable dynamic behavior and exhibits sensitive dependence on initial conditions and includes infinite unstable periodic motions. The calculation methods of Lyapunov exponent on continuous nonlinear dynamic systems are discussed. The Lyapunov exponent of logistic map and its doubling period bifurcation to chaos are quantitatively analyzed. Ergodicity probability are especially studied when logistic map is in chaos state. COA as an emergent method of global optimization have attracted much attention in engineering applications and differ from any of the existing traditional stochastic optimization techniques. Due to the non-repetition of chaos, it can carry out overall searches at higher speeds than stochastic ergodic searches that depend on probabilities. COA, which has the features of easy implementation, short execution time and robust mechanisms of escaping from local optimum, is a promising tool for engineering applications. Since chaotic mapping enjoys certainty, ergodicity and the stochastic property, the proposed COA introduces logistic chaotic sequences. Numerical simulations was based on MATLAB and the results are promising and show the effectiveness of the proposed approach on tuning the PID parameters and step response output demonstrate the good performance of chaotic optimization.