Comparison of Neural Network NARMA-L2 Model Reference and Predictive Controllers for Nonlinear Quarter Car Active Suspension System

Recently, active suspension system will become important to the vehicle industries because of its advantages in improving road managing and ride comfort. This paper offers the development of mathematical modelling and design of a neural network control approach. The paper will begin with a mathematical model designing primarily based at the parameters of the active suspension system. A nonlinear three by four-way valve-piston hydraulic actuator became advanced which will make the suspension system under the active condition. Then, the model can be analyzed thru MATLAB/Simulink software program. Finally, the NARMA-L2, model reference and predictive controllers are designed for the active suspension system. The results are acquired after designing the simulation of the quarter-car nonlinear active suspension system. From the simulation end result using MATLAB/Simulink, the response of the system might be as compared between the nonlinear active suspension system with NARMA-L2, model reference and predictive controllers. Besides that, the evaluation has been made between the proposed controllers thru the characteristics of the manage objectives suspension deflection, body acceleration and body travel of the active suspension system. . As a conclusion, designing a nonlinear active suspension system with a nonlinear hydraulic actuator for quarter car model has improved the car performance by using a NARMA-L2 controller. The improvements in performance will improve road handling and ride comfort performance of the active suspension system.


Introduction
The suspension system of a vehicle has two main operations. The primary one is to isolate the vehicle body from external road input profiles which occurs due to road disturbances. The secondary is to provide a balanced contact between the road and the tires. In a classical suspension system which it's parameter only contains passive elements, the feats of rendering both ride comfort and road handling makes the system with low performance. To sustain the vehicle mass and to perfectly track the road, a stiffened suspension system is needed, but, to isolate the road disturbance a soft suspension is needed.
In general, all suspension system must provide the best ride comfort and road handling within a reasonable range of suspension deflection. Moreover, these criteria always depends on the parameters of the automobile. Race vehicles usually have high stiffness value, strong suspension with low performance ride quality while passengers vehicle have loosely suspensions with low performance road handling ability. From a system design idea, there are two main area of distraction on a vehicle, namely road and load disturbances. Road disturbances have the qualities of large magnitude in low frequency and small magnitude in high frequency. Load disturbances include the deviation of loads induced by accelerating, decelerating and cornering. Therefore, for the best suspension system design, care must be given to reduce the road disturbance to the outputs.
2 Mathematical Models 2.1 Mathematical modelling of nonlinear active suspension system The quarter car model of nonlinear active suspension system is shown in Figure 1. The nonlinear active suspension system has the extra advantages which a terrible damping can be produced and producing the huge variety of force into the system at low velocities. Besides, this condition potentially will increase the overall performance of the suspension system. The derivations of mathematical equation of nonlinear active suspension system of quarter vehicle system are given through Eqs.

Hydraulic Actuator Design
The three by four-way valve-piston system is shown in Figure 2 is used for the hydraulic controller design. The pressure Hh from the actuator is given by Eqn.
Where Rd is the release coefficient, is the spool valve vicinity gradient, y5 is the pressure inside the chamber of hydraulic piston and y6 = ysp is the valve displacement from its closed position,  is the hydraulic fluid density and Ps is the supply pressure, since, the term   The bump road profile input has a maximum peak of 10 cm as shown in Figure 3.

NARMA-L2 Controller Design
NARMA-L2 controller is used to become aware of the system to be controlled. Here in this system, we must train a neural network to represent the forward dynamics of the system.

Model-Reference Controller Design
The designing of neural model reference control uses two neural networks: 1. A Neural network controller and 2. A Neural network controller for the plant model As shown in Figure 6 bellow.

Result and Discussion
The nonlinear quarter car active suspension system parameter values are shown in Table 2.

Control Targets Output Specifications
The control targets output specifications of the nonlinear quarter car active suspension system is shown in Table  3 below. Suspension deflection Same as Road Profile

Simulation of a Bump Road Disturbance
The Simulink model for a bump input road disturbance including the nonlinear active suspension system with NARMA-L2, model reference and predictive controllers is shown in Figure 7 below.

Simulation of a Sine Pavement Road Disturbance
The Simulink model for a sine pavement input road disturbance including the nonlinear active suspension system with NARMA-L2, model reference and predictive controllers is shown in Figure 11 below.

Numerical Values of the Simulation Outputs
The numerical values of the simulation output for the control targets body travel, body acceleration and suspension deflection is shown in Table 3, Table 4 and Table 5 bellow.   Table 4 shows us the active suspension system with NARMA-L2 controller have the minimum body acceleration amplitude in the bump & sine pavement road profile.  Table 5 shows us the active suspension system with NARMA-L2 controller have the suspension deflection amplitude the same as the road profile input in the bump & sine pavement road profiles.

Conclusion
In this paper, the mathematical model of the nonlinear active suspension system and the nonlinear hydraulic actuator was developed successfully. Matlab/Simulink model was designed for the NARMA-L2 , model reference and predictive controllers and comparisons of this proposed controllers have been done for the control targets (suspension deflection, body acceleration and body travel) using bump and sine pavement road profiles. The simulation results prove that the nonlinear active suspension system with NARMA-L2 controller shows a good response in minimizing the body acceleration and adjusting the suspension deflection and body travel vertical amplitude in both the road disturbances input. Finally, that the nonlinear active suspension system with NARMA-L2 controller shows a good improvement in ride comfort and road handling.