P9.5 A speed control for a gasoline engine is shown in Figure P9.5. Because of the restriction at the carburetor intake and the capacitance of the reduction manifold, the lag tt occurs and is equal to 1 second.

The engine time constant te is equal to J>b = 3 s.

The speed measurement time constant is tm = 0.4 s.

(a) Determine the necessary gain K if the steadystate speed error is required to be less than 10% of the speed reference setting.

(b) With the gain determined from part (a), apply the Nyquist criterion to investigate the stability of the system.

(c) Determine the phase and gain margins of the system.

FIGURE P9.5 Engine speed control. Throttle 1 Torque K Y(s) R(s) 7,5+1 Tes+1 Speed 7ms +1