# A Novel Adaptive PID Controller with Application to Vibration Control of a Semi-Active Vehicle  
Seat Suspension  
[PERSON]  
1 MediRobotics Laboratory, Department of Mechatronics and Sensor System Technology,  
Vietnamese-German University, 820000 Binh Duong, Vietnam; [EMAIL_ADDRESS]  
2 Smart Structures and Systems Laboratory, Department of Mechanical Engineering, Inha University,  
Incheon 402-751, Korea; [EMAIL_ADDRESS]  
2  
[PERSON]  
2 [PERSON]  
type 1 fuzzy model and interval type 2 fuzzy model. A hybrid adaptive fuzzy controller based on H-infinity technique was presented in [1]. In this controller, adaptation laws were developed by using parameters of Riccati-like equation and non-derivative functions. To guarantee control robustness, error dynamics were proposed and combined with the laws. The H-infinity technique was also used to design a hybrid adaptive controller in [2]. The H-infinity tracking inequality function was modified following the sum of values of adaptive function at zero. The sum function was less than the prescribed value which was defined in the adaptation law. A similar hybrid controller was also proposed in [3] and the combination of the fuzzy-neural networks model and H-infinity technique was presented in [4]. In this work, the Riccati-like equation was modified, and then the modified parameters were used as a robust control function. On the other hand, a different type of hybrid controller using several control strategies such as H-infinity technique, sliding mode control, and fuzzy model were suggested in [5]. The H-infinity inequality function was modified following the sum and integration of the prescribed attenuation value, and control robustness was derived from the simplified inequality function of the Riccati-like equation. The disadvantage of this hybrid controller is slow response (or heavy calculation) because of the complicated functions. A similar hybrid controller was also presented in [6]. It should be noted here that the hybrid controllers formulated in previous studies mostly featured the type 1 fuzzy model. A hybrid adaptive controller utilizing the interval type 2 fuzzy model was proposed in [7; 8]. In these works, a hybrid controller was formulated by combining several control methodologies such as sliding mode function, H infinity technique, and the type 2 fuzzy model. In this case, adaptation laws and inequality functions should be determined considering the inherent properties of each controller. The design method of this type of hybrid controller was also described in [9; 10; 11; 12; 13]. It is noted that the recursive method for design of an adaptive controller has been introduced in [11] and the direct adaptive control method has been used to formulate a hybrid controller [8]. Another method for the design of adaptive controller is to combine the fuzzy model and H-infinity approach by considering the back-stepping method [14]. In this case, the adaptation law was a sum function of parameters of the fuzzy output and calculated factors of the back-stepping function. The model of interval type 2 fuzzy model was used and combined with a new sigmoid function of the sliding mode control to design a hybrid controller [15]. A similar adaptive fuzzy H-infinity controller was also studied by considering the linear matrix inequality approach [16]. A new hybrid controller with a special exponential function was developed by combining the fuzzy model, the sliding surface, and H-infinity technique [17]. Recently, the development of a new adaptive controller integrated with a PI controller was also undertaken [18]. It is noted here that, in order to develop an effective hybrid controller, the property of uncertain (indefinite) systems should be removed. One of solutions is to use the interval type 2 fuzzy (IT2F in short) model. However, prior to applying the IT2F, the clustering method for finding the feature of the uncertain system needs to be clearly expressed [19; 20; 21].