Fuzzy adaptive optimal backstepping control of the FO MEMS resonator under imprecise target trajectory with disturbance compensation mechanism

With the deep research of the fractional-order (FO) calculus theory, it has been found that the FO model can more realistically depict electromechanical devices with viscoelastic characteristics, such as the micro-electromechanical system (MEMS) resonator. Dynamic analysis is an important link to deeply understanding the dynamic characteristics of the system. Therefore, we established the FO model and FO circuit differential equation of the MEMS resonator and revealed that the chaos oscillation in the MEMS resonator is closely related to order α and parameter V AC through dynamic analysis including numerical simulation and analog circuit. For suppressing the chaos oscillation, we integrate the optimal control into the technical framework of fuzzy adaptive backstepping control, and then design a fuzzy adaptive optimal backstepping controller with a disturbance compensation mechanism. In the design of the controller, firstly, to reduce the damage caused by the matched disturbance for the control effect, a disturbance compensation mechanism based on the FO disturbance observer is proposed. Secondly, to approximate the unknown function in the FO MEMS resonator, the interval type-3 fuzzy logic system (IT3FLS) with adaptive law is constructed. Then, the Fourier series and IT3FLS are introduced to reconstruct the imprecise target trajectory, and the FO hyperbolic tangent tracking differentiator (HTTD) is introduced to deal with the “explosion of complexity” associated with traditional backstepping. Finally, the optimal control input is designed to improve the tracking accuracy of the controller and minimize the cost function, and the effectiveness and robustness of the designed controller are verified by simulation results.