手把手建立Simulink四分之一车辆模型/Building a quarter car model step by step!

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This article is originally created by Dr. Goddard. And re-edited by the author

It is greatly appreciated for Dr. Goddard's outstanding work! see the following

http://www.modeling-simulation-visualization.com/simulink-quarter-car-model.html#actuatormodel

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In this section, a quarter car model built in simulink is introduced for future research on vehicle dynamics.

Topic 1: tyre model

    Standard Pacejk magic formula is used here; where λ is the wheel slip, and the coefficientsa,b andc change depending on the current road surface. This example assumes that the vehicle is being driven on dry asphalt and hence the coefficients area = 1.28,b = 23.99 andc = 0.52.

 

The implmentation for the tire model equations is shown in Figure 2.

Figure 2: Tire Model Subsystem.

 

Topic 2: quarter car model

It contains two continuous time states, and is described by the set of non-linear equations inEquation 2.  

Name	Description	Value
ω	Angular Speed	Output Signal
ν	Longitudinal Speed	Output Signal
J	Inertia	1 Kg m2
R	Wheel Radius	0.32 m
Tb	Brake Torque	Input Signal
Fx	Longitudinal Force	Calculated
λ	Longitudinal Wheel Slip	Calculated
Fz	Vertical Force	Calculated
μx	Road Friction Coefficient	Calculated
m	Quarter Vehicle Mass	450 Kg
g	Gravitational Force	9.81 ms-2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The implementation of quarter car equations is shown in Figure 3.

Figure 3: Quarter Car Model Subsystem.

TOPIC 3: The Actuator Model

Actuator dynamics, and particular time delays, are often critical to the design of a sufficiently accurate control algorithm. This example uses a simple first order lag in series with a time delay to model the actuator. (In practice a second order model is almost always required, and often actuators have different responses when they are opening and closing, and hence need to be modeled in considerable more detail than is done here.)

The model for the actuator are given by Equation 3,

 

 

Equation 3: Actuator Equation.

subject to the constraint that 0 < T_b < T_{b_sat}.

The following table lists the definition of the notation used in Equation 3.

Name	Description	Value
τ	Time Delay	0.05 s
a	Filter Pole Location	70
Tb_sat	Saturation	4000

             

Table 2: Notation for the Actuator Model.

The implementation of actuator equations is shown in Figure 4.

Figure 4: Actuator Model Subsystem.

Note that the first order lag (transfer function) has been implemented using an integrator, gain and summation/negation block rather than aTransfer Funtion Block (from theContinuous library).This has been done as the Transfer Function block does not allow vector signals as an input, but the current implementation does. Hence the model being developed can more easily be expanded to allow for 4-channels, i.e. one for each wheel on a four wheeled vehicle. A Transfer Function Block would preclude that from happening (without replacing the block).

TOPIC 5: The Controller Model

There are many different potential implementations for the controller. Here a simple PI (proportional–integral) controller has been shown to be adequate.

The implementation of controller is shown in Figure 5.

Figure 5: The Controller Subsystem.

Note that the subsystem has been made atomic, and given a discrete sample rate ofT_s = 5ms.

Controller gains that have been determined to work reasonably well for the configuration chosen here areK_p = 1200 andK_i = 100000.