# A Novel Adaptive PID Controller with Application to Vibration Control of a Semi-Active Vehicle
## 4 Experimental Results and Discussions  
An experimental apparatus for the evaluation of the proposed hybrid controller is established as shown in Figure 6. It is remarked that the equipment used for this experiment is similarly to the devices used in [17]. The signal from the sensors such as linear variable differential transformer (LVDT) transducer, accelerometers at the seat and driver are used as feedback signals to the controller. For the information about sensor characteristics, the production makers and the specific model of each sensor are given as follows: (i) a linear variable differential transformer sensor (Honeywell, type JEC-AG-DC-DC, Honeywell Inc., Morris Plains, NJ, USA) is used to measure the displacement of seat, (ii) an accelerometer (CLX Xbow MEMSIC-IMU440, MEMSIC Inc., San Jose, CA, USA) is used for measurement of the acceleration of the mass (i.e., human) on the seat, (iii) an accelerometer (Crossbow, type CXL04M1Z, Sumitomo Precision Products Co., Ltd., Amagasaki Hyogo, Japan) is used for measurement of the acceleration at the seat. The controller designed in [5] is used in this experimental evaluation as a comparative controller. This comparative controller is a kind of complicated hybrid controller whose adaptation laws are designed from the governing equation and sliding surface. In addition, the robustness function in [5] is built from the sliding mode motion and the Riccati-like equation. In this experiment, two exciting signals of the random step wave and the random regular bump are imposed via the hydraulic shaker system. Figures 7 and 8 present control results obtained from the realization of the controllers using the microprocessor which consists of signal converters and controller chips. Vibration control results under the regular bump excitation are shown in Figure 7. Based on the values of the measured results, the maximum values of dynamic parameters such as displacement, velocity and acceleration can be found. The maximum displacement at the seat shown in Figure 7(a1,a2) is identified by 0.02118 and 0.03503 m for the proposed control and the control of [5], respectively. The maximum velocity at the seat is found from Figure 7(b1,b2) and the values are 0.25930 and 0.61020 m/s for the proposed control and the control of [5], respectively. The maximum acceleration at the seat is identified from Figure 7(c1,c2) and the values are 1.80093 and 2.31462 m/s\({}^{2}\) for the proposed control and the control of [5], respectively. The maximum acceleration at the driver position is evaluated from Figure 7(d1,d2) and the values are 1.03392 and 2.05639 m/s\({}^{2}\) for the proposed control and the control of [5], respectively. It is noted that the maximal values of the sinusoidal bump obtained from the proposed controller are smaller than those achieved form the controller in [5]. This is attributed to the fact that, in the proposed controller, the fuzzy neural network model is applied in which the centroid vectors are properly determined as given in Table 4. Figure 8 presents vibration control performance of MR seat suspension system subjected to the random-step-wave excitation. Similar to the previous case, the maximum values of the displacement, velocity, and acceleration of  
Figure 6: Experiment setup for vibration control of MR seat suspension system. dynamic parameters at the seat and driver position can be identified from the results. The maximum displacement at the seat is found from Figure 8(a1,a2) and the values are 0.02009 and 0.04944 m for the proposed control and the control of [5], respectively. The maximum velocity at the seat is identified from Figure 8(b1,b2) and the values are 0.29681 and 0.71328 m/s for the proposed control and the control of [5], respectively. The maximum acceleration at the seat is evaluated from Figure 8(c1,c2) and the values are 2.16084 and 3.16171 m/s\({}^{2}\) for the proposed control and the control of [5], respectively.