Azar Ahmad Taher - Fractional Order Control and Synchronization of Chaotic Systems

Department of Instrumentation and Control Engineering, Netaji Subhas Institute of Technology, Sector-3, Dwarka, New Delhi, 110078, India

Noise is generally an inherent part of every measurement and control system. Noise affects the decision-making capability of the controller in the plant as it introduces uncertainty in the process variable and control action. There are several causes of measurement noise in the process industry such as loose wiring, improper soldering, thermal noise, electromagnetic interference, etc. Furthermore, the execution of control action in a closed-loop control system may be seriously affected due to the improper connection of signal line from the controller to the final control element particularly in a vibrating environment. This action may add considerable noise in the control action and may even try to destabilize the process being controlled. Most general nature of sensor and controller noise is likely to be random. Robotic manipulator being a highly non-linear, time-varying and uncertain system noise has adverse effect on the positioning and accuracy of the end-effectors of robotic manipulator. Therefore, it is a challenging task to design such a robust controller which can effectively deal with external noises and uncertainties [].

Conventional PID controller has been the most popular controller in the industries for last sixty years due to its simple structure, low cost, easy design and robust performance. For its implementation it is available in many forms in industry, like pneumatic, hydraulic and electronic etc. Due to these features, it is one of the popular choices of control engineers in robotics as well [].

The fractional order calculus has a very long mathematical history, but its applications to science and engineering are just recent. One of its popular applications is in fractional order chaotic system []. Due to advancements in the electronics now it has become possible to design and realize the FO-PID controllers. It offers additional design Degree of Freedom (DOF) to the control engineers. Advancements also have been observed in the controller tuning methods for customized performance indices. Now-a-days the trend has been the usage of optimization methods such as Genetic Algorithm (GA) and other bio-inspired techniques for tuning the controllers. Therefore, the main goal of this chapter is to demonstrate the capabilities of FO-PID controller to cater the effect of noise in closed loop. In this regard, an intensive simulation studies were performed in closed loop by controlling a complex coupled system i.e. 2-link rigid planar robotic manipulator in presence of sensor and controller noise and using fractional and integer order PID controllers. Uniform White Noise (UWN) and Gaussian White Noise (GWN) were considered for this study. Both the controllers were tuned using GA for minimum Integral of Absolute Error (IAE). The performed comparative study reveals that FO-PID controller with low fractional order derivative term effectively suppress the noise in closed loop. The main contributions of this chapter can be summarized as follows:

The rest of the chapter is organized as follows: A brief literature review of the related works have been presented in Sect..

Noise in any form may degrade the performance of any controller in closed loop. Therefore, it has drawn attention of various researchers and scientists over the time especially in the field of control system. Many research works have been reported in this regard and presented as follows.

Tsai et al. presented the robustness testing for sensor noise for the fuzzy model-following control applied to a 2-link robotic manipulator [].

Bingul and Karahan presented a comparative study of fractional PID controllers tuned by Particle Swarm Optimization (PSO) and GA for a 2-link robotic manipulator. The robustness testing included parameter change, trajectory change and addition of white noise. Simulation results, for the robot trajectory experiment, showed that the FO-PID controller tuned by PSO has better performance than the FO-PID controller tuned by the GA [].

Lin and Huang presented a hierarchical supervisory fuzzy controller for the robot manipulators with oscillatory base. The proposed method had various benefits such as reduced chattering effect, lesser overshoot, faster convergence and lesser online computation time [].

Petras presented the hardware implementation of digital FO-PID control for permanent magnet DC motor. The digital and analog realization of proposed controller was done with microprocessor and fractance circuits, respectively [].

Pan and Das proposed a FO-PID controller for automatic voltage regulator (AVR) with chaotic multi-objective optimization. In this work, FO-PID controller was not completely superior to PID controller as the simulations results were better for FO-PID for some cases and for conventional PID in other cases [] have also been reported in the literature for making use of fractional order control system.

The literature survey conducted above clearly indicates that several authors have investigated effects of the model uncertainties and external disturbances for the robotic manipulators but the effects of sensor as well as controller noise has not been well explored by the researchers and therefore needs attention.