###### Abstract  
This paper proposes a new switching adaptive fuzzy controller and applies it to vibration control of a vehicle seat suspension equipped with a semi-active magnetorheological (MR) damper. The proposed control system consists of three functioned filters: (1) Filter 1: a model of interval type 2 fuzzy to compensate disturbances; (2) Filter 2: a'switching term' to evaluate the magnitude of disturbance; and (3) Filter 3: a group of adaptation laws to enhance the robustness of control input. These filters play a role of powerful shields to improve control performance and guarantee the stability of the applied system subjected to external disturbances. After embedding a PID (proportional-integral-derivative) model into Riccati-like equation, main control parameters are updated based on the adaptation laws. The proposed controller  
filter. To enhance the robustness of the controller, a fuzzy system is frequently employed to approximate the unknown linear function. The prescribed performance was embedded into an adaptive fuzzy control in [4] presenting a new transformed error function-based arc-tanh-type function. This function was an inverse hyperbolic tangent function and set following the arc-tanh function to improve its performance. An application of the sliding mode control for the design of adaptive control was presented in [5] where an integral sliding mode controller coupled with a dual-layer adaptive scheme was utilized. A decoupling control using adaptive fuzzy model was developed in [6] in which the main function related to the main control input was analyzed to the second element. Another control methodology used in the design of adaptive model is PID (proportional-integral-derivative) controller. A hybrid PID control integrating with the genetic algorithm and particle swarm optimization was presented in [7]. However, because of large number of iterations, the proposed control proposed in [7] has large time delay in practice. A combination between interval type 2 fuzzy (IT2F in short) model and PID control was described in [8] where the role of IT2F was a feedforward term to compensate the uncertainties and nonlinearities of the system in the design of PID controller. In this work, grey wolf (GW) optimizer and artificial bee colony algorithm were used for automatically turning the parameters of PID. The neural PID control was presented in [9] for minimizing the steady-state error in which the traditional neural PD control was transformed into a new model of neural PID control to compensate the uncertainties. A new adaptive law was developed to adapt the three main parameters of the PID controller considering the signal of dynamic variables of the system [10], and a neural model associated PID controller was also investigated for designing adaptive control laws [11]. It is well known that the classical type of PID model is still an important tool in the design of modern controllers [12]. However, the use of PID-based controller only may cause the lack of robustness against system uncertainties and disturbances. A new form of combination among fuzzy model, adaptive control, sliding mode control and PID model was presented in [13] in which a new form of PID-terminal sliding surface was proposed using the adaptive fuzzy logic to tune the parameters of the PID gains. An adaptive PID controller where the adaptation laws include both the hybrid function error and the gains of the PID controller was also presented in [14]. A composite controller including adaptive control, sliding mode control, PID and fuzzy model was studied in [15] in which a new modified Riccati-like equation and PID model were adopted to control severe disturbances. A new model of adaptive control with prescribed performance of the sliding surface was presented in [16] so that system state variables are to be stayed within the defined boundaries. A new form of adaptive control with optimal control was also investigated in [17] to improve time convergence of the prescribed performance.