Abstract
In this study, a general type-2 fractional order fuzzy PID (GT2FO-FPID) controller is proposed to fulfil the balance adjustment of the Power-line Inspection (PLI) robot system. It is a combination of Mamdani general type-2 fuzzy logic controller (GT2-FLC) and fractional PID controller. Since the PLI robot system is an under-actuated system, it’s necessary to get complete information of the system. However, when all state variables are treated as input to the controller, there is a problem with the rule explosion. Because of this, the information fusion method is adopt to solve the problem and simplify the controller design. At the same time, fractional-order integral-differential operators and input-output scaling factors, which are taken as design variables and optimized by genetic algorithm (GA). To assess the performance of proposed controller based on symmetry criterion, we compared it against existing controllers, i.e., interval type-2 fractional order fuzzy PID (IT2FO-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), and conventional fractional order (FOPID) controllers. Furthermore, to show the anti-inference ability of the proposed controller, three common perturbed process are tested. Finally, simulation results show that the GT2FO-FPID controller outperforms other controllers in the presence of external perturbations on the PLI robot system.
Highlights
Fractional calculus has been around for over 300 years
The combination of fuzzy logic controller (FLC) and PIλ Dμ controller has a great improvement in system performance, it is uncertain whether the effectiveness of the controller can be maintained when faced with more uncertainty
The type-1 fuzzy logic controller (T1-FLC) is usually not effective when the controlled object is full of uncertainty, because it has limited capability to handle uncertainties [2]
Summary
Fractional calculus has been around for over 300 years. It is a generalization of the integrals of ordinary differentials and non-integer (arbitrary) orders [1]. The first research on fractional order PIλ Dμ controllers was proposed by Podlubny in 1999. The combination of fuzzy logic controller (FLC) and PIλ Dμ controller has a great improvement in system performance, it is uncertain whether the effectiveness of the controller can be maintained when faced with more uncertainty. The type-1 fuzzy logic controller (T1-FLC) is usually not effective when the controlled object is full of uncertainty, because it has limited capability to handle uncertainties [2]. From the application mentioned above, we can see the superiority of the general type-2 fuzzy logic controller (GT2-FLC) in the presence of uncertainties compared with the traditional counterparts. Whether it is an extension from interval to general or an extension of integer order PID to fractional order PID, it means that the degree of freedom of the controller is increased and the control performance is improved.
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