INTERVAL TYPE-2 FUZZY LOGIC CONTROLLERS FOR ROBOT MANIPULATORS

Abstract

Fuzzy logic systems (FLSs) are well known in the literature for their ability to model linguistics and system uncertainties. Due to this ability, FLSs have been successfully applied in almost all areas of science and engineering research. Moreover, the ability of higher order fuzzy systems to handle system uncertainty has become an interesting topic of research in the field. In particular, type-2 fuzzy logic systems (T2FLSs), consisting of fuzzy sets with fuzzy grades of membership, are most well-known for this capability. Due to crisp membership grades, type-1 fuzzy logic systems (T1FLSs) do not offer such a feature. The structure of T2FLSs allows for the incorporation of uncertainty in the input membership grades, a common situation in reasoning with physical systems. The membership function of T2FLSs is itself a fuzzy which is due to the presence of its third dimension called the footprint of uncertainty. General T2FLSs have a complex structure, thus making them difficult to adopt on a large scale. As a result, interval type-2 fuzzy logic systems (IT2FLSs), a special class of T2FLSs, have shown great potential in various applications with input-output system uncertainties. The invention of fractional calculus has given a new face to control engineering in such a way that controllers designed using fractional order integral-differential operators produce better control attributes in comparison to integer order controllers. Because they have extra parameters to make the system more robust and effective for many control applications. The robot manipulators are extremely nonlinear, multi-input multi-output (MIMO), highly coupled, and complex systems wherein the parameter uncertainties, external disturbances, and random noise adversely affect the performances of these systems. In view of the foregoing complexities, it is a challenging task for control engineers to design efficient and robust controllers for these systems. In response to this challenge, this thesis proposes novel design and implementation of fractional calculus based type-1 and interval type-2 fuzzy logic control theories for different robot manipulator systems and some benchmark linear, nonlinear, and fractional order plants with robustness analysis. The main objectives of the research work presented in this thesis are formulated as:  Design and implementation of the fractional order fuzzy pre-compensated fractional order PID controller for the 2-DOF robot manipulator.  Evolving an interval type-2 fuzzy PID controller for the redundant robotic manipulator.  A novel interval type-2 fractional order fuzzy PID controller: design, performance evaluation, and its optimal time domain tuning. ii  Performance analysis of optimal hybrid interval type-2 fractional order fuzzy logic controllers for fractional order systems. One of the main contenders in the control field which has been benefited from the study of the intelligence controllers is robotic control. As a preliminary study, the type-1 fractional order fuzzy pre-compensated fractional order proportional integral derivative (FOFP-FOPID) controller is proposed for 2-degree of freedom (2-DOF) robot manipulator dealing with trajectory tracking problem. The proposed controller comprises the fractional order fuzzy pre-compensator and the conventional fractional order proportional integral derivative (FOPID) controller. The fractional order fuzzy pre-compensator is inserted to modify the control signal for compensating overshoots and undershoots in transient output response and also enhanced the performances in the presence of parameter variations and disturbances. The conventional FOPID controller has an extra parameter to make the controller more robust, effective and improve the performance further. To obtain the optimal controller parameters, a metaheuristic optimization technique, viz., artificial bee colony-genetic algorithm (ABC-GA) is used. In order to demonstrate the efficacy of the proposed controller, it is compared against an integer order fuzzy pre-compensated PID (IOFP-PID), fuzzy PID (FPID), and conventional PID. Further, in this direction, the robustness analysis for proposed controllers is also investigated for parameter variations and external disturbance. Even though, a significant improvement of system performance with type-1 fuzzy logic controllers (T1FLCs) is seen over their conventional counterparts. It is also noticed that they are not able to directly deal uncertainties because their membership functions (MFs) are totally crisp. The type-2 fuzzy logic controllers (T2FLCs) have been recognized as a suitable tool for modeling the uncertainties in system parameters. In order to establish their applicability for redundant robot manipulator, the interval type-2 fuzzy proportional derivative plus integral (IT2FPD+I) controller is designed and implemented for trajectory tracking problem with robustness analysis and comparative performance analysis is done with the type-1 fuzzy PID (T1FPID), conventional PID controllers. Further, selecting a large number of tuning parameters is a challenging task, because all joint controllers' parameters are optimized simultaneously. For this, the genetic algorithm (GA) is applied to optimize the tuning parameters of controllers. Although, GA is a global optimization technique, the selection of initial search range is a complicated process for fuzzy logic controllers (FLCs). Therefore, an efficient procedure for selecting appropriate initial search space is adopted. At last, the robustness of the proposed controllers for model uncertainties, disturbance rejection, and random noise rejection is investigated to witness the effectiveness of the proposed iii controllers. The next part of thesis concentrates on the extensional of fractional order calculus to design interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller with optimal time domain tuning for control of linear and nonlinear plants. Further, the effectiveness of the proposed controller is also investigated on highly nonlinear 2-DOF robot manipulator. Here, the proposed IT2FO-FPID controllers comprised unique features of interval type-2 fuzzy logic controller (IT2FLC) and fractional order, with the aim to provide additional degrees of freedom to overcome the uncertainties problems and extra flexibility for finer tuning as well as more robustness in control design. It is noticed that the main advantage of fractional order controller is that it is less sensitive to the parameters change of both controlled system and the controller itself. A hybridized algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing the fitness function. Furthermore, the proposed controller is successfully implemented with wide diversity of parameter variations for linear and nonlinear plants as well as for robotic system with un-modeled dynamics to demonstrate the effectiveness. Finally, the simulation results explicitly show that the performance of the proposed IT2FO-FPID controller is superior to its existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers in most of the cases. After the successful implementation of the IT2FO-FPID controller, the last part of the thesis focuses to design the family of hybrid IT2FO-FPID controllers, which incorporates fractional order integrator-differentiator, for non-integer order plus time delay plants for unit step response and unit load disturbance with robustness analysis. The proposed hybrid IT2FO-FPID controllers incorporate two controllers: IT2FPID controller and FOPID controller. The combined features of both techniques result in a better control system performance while also enjoying the benefits of both the controllers. Here, fractional order integral-differential operators are adopted as design variables along with input/output scaling factors for designing of effective hybrid controllers. The tuning parameters of the hybrid proposed controllers are also optimized by the ABC-GA algorithm. To witness the effectiveness of the hybrid controllers, robustness performance is also validated for parameters variation and external load disturbance. Finally, the simulation investigations explicitly suggest that proposed different hybrid IT2FO-FPID control structures can be recommended in terms of better step response, better load disturbance rejection, small control signal response, and parameters variation.