Figure 1 shows the simplified model of an electronic throttle body (Bosch DV-E5) that is driven by an electric DC motor. Va(t) is the input voltage to the motor, which drives the throttle through a gear pair. The throttle is connected to a spring that causes the throttle angle to return to zero position when no input is applied. In [1], the Bosch DV-E5 throttle body is mathematically modeled and using system identification methods, its parameters are estimated. The parameter values and variables you are going to use are given below in Table 1, which might be slightly different than the values in [1]. Note that in this model, the torque generated by the motor is proportional to the armature current, and the back emf voltage eb(t) is proportional to the angular velocity of the motor shaft. These proportionality constants are equal. Therefore, the following relations hold: Tm(t)= Kmia(t), es(t) = Km0m(t) Table 1: Parameters and variables of the model. Description Value resistance of the armature circuit 1.5 1.5 inductance of the armature circuit motor torque constant 0.02 back emf constant 0.02 moment of inertia of motor shaft 3.2x 10-6 2.05x10-5 Symbol Ra La Km Km Jm N= TLL 74m JL BL Ks Va(t) ia (t) eb(t) Om (t) motor damping coefficient gear ratio moment of inertia of the throttle plate throttle plate damping coefficient stiffness of the return spring armature voltage armature current emf voltage motor shaft angle kg m Nms/rad Nm/rad V A V rad OL(t) throttle angle rad Tm(t) torque generated by the motor Nm TL (t) torque transmitted through the gears Nm Using hand calculations, show that the transfer function of this system is Gp(s) = 20 OL(S) 78895 Va(s) s +1002s + 34016s+25740 = 2.110-3 2.05x10-5 0.087 Unit S2 mH Nm/A Vs/rad kg m Nms/rad in(t) + V(t) R ni m + est) M em(t) Tm(t) Jm Bm NL> nm nm L nL e(t) TL(1) JL BL Return mm Figure 1: Electronic throttle body schematic [1].