An automatic speed control system will be necessary for passenger cars traveling on the automatic highways of the future. A model of a feedback speed control system for a standard vehicle is shown in Figure P4.6. The load disturbance due to a percent grade Td1s2 is also shown. The engine gain Ke varies within the range of 10 to 1000 for various models of automobiles. The engine time constant te is 20 seconds.

(a) Determine the sensitivity of the system to changes in the engine gain Ke.

(b) Determine the effect of the load torque on the speed.

(c) Determine the constant percent grade Td1s2 = d>s for which the vehicle stalls (velocity V1s2 = 0) in terms of the gain factors.

Note that since the grade is constant, the steady-state solution is sufficient. Assume that R1s2 = 30>s km>hr and that KeK1 W 1. When Kg>K1 = 2, what percent grade d would cause the automobile to stall?

FIGURE P4.6 Automobile speed control. R(s) + Speed setting Load torque AT (s) K g Throttle controller G(5)= Throttle K 0(s) 75+1 Tachometer K = 1 Engine and vehicle G(s)= Ke V(s) TeS +1 Speed