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 Td (s) is also shown. The engine gain Ke varies within the range of 10 to 1000 for various models of automobiles. The engine time constant e 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 Td (s) = d/s for which the vehicle stalls (velocity V(s) = 0 ) in terms of the gain factors. Note that since the grade is constant, the steady-state solution is sufficient. Assume that R(s) = 30/s km/hr and that KeK1 1. When Kg/K1 = 2, what percent grade d would cause the automobile to stall?

FIGURE P4.6 Automobile speed control. Load torque AT(s) K 8 Throttle controller Throttle R(s) K 0(s) Speed G(s)= T5+1 setting Tachometer K = 1 Engine and vehicle G(s)= Ke V(s) TeS +1 Speed