The block diagram shown in Figure 1 represents an unmanned car's speed function. Accelerator/Braker Speed Dynamics...

Transcribed Image Text:

The block diagram shown in Figure 1 represents an unmanned car's speed function. Accelerator/Braker Speed Dynamics Ge(s) Desired Speed + An unmanned car's speed control system which is operating with a closed loop response has 15% overshoot. K Speed dynamics of the system has the following transfer function: G₁ (S) = Input Step, u(t) Ramp, tu(t) Parabola, fu(t) Figure 1: Unmanned car's speed control system. (a) Sketch the root locus. (b) Compute the steady state error for a unit ramp input. (c) Choose a controller/compensator to improve the steady state error by a factor of 20. (d) Calculate the steady state error for a unit ramp input to your compensated system. (e) Compute how much improvement in S.S.E was realized. Hints: TABLE 7.2 Relationships between input, system type, static error constants, and steady-state errors Type 1 Steady-state error formula 1 1+Kp Ky Ka Type 0 Static error constant Kp = Constant K₁ = 0 K₁=0 Error 1 1+ Kp G₁(s) 8 Static error constant Kp = ∞ K, Constant Ka=0 s(s+2) (s+7)' Error 0 1 Ky Actual Speed ; Now- ∞ Static error constant Kp = ∞ Type 2 K₂ = ∞ Ka Constant Error 0 O 1 Ka The block diagram shown in Figure 1 represents an unmanned car's speed function. Accelerator/Braker Speed Dynamics Ge(s) Desired Speed + An unmanned car's speed control system which is operating with a closed loop response has 15% overshoot. K Speed dynamics of the system has the following transfer function: G₁ (S) = Input Step, u(t) Ramp, tu(t) Parabola, fu(t) Figure 1: Unmanned car's speed control system. (a) Sketch the root locus. (b) Compute the steady state error for a unit ramp input. (c) Choose a controller/compensator to improve the steady state error by a factor of 20. (d) Calculate the steady state error for a unit ramp input to your compensated system. (e) Compute how much improvement in S.S.E was realized. Hints: TABLE 7.2 Relationships between input, system type, static error constants, and steady-state errors Type 1 Steady-state error formula 1 1+Kp Ky Ka Type 0 Static error constant Kp = Constant K₁ = 0 K₁=0 Error 1 1+ Kp G₁(s) 8 Static error constant Kp = ∞ K, Constant Ka=0 s(s+2) (s+7)' Error 0 1 Ky Actual Speed ; Now- ∞ Static error constant Kp = ∞ Type 2 K₂ = ∞ Ka Constant Error 0 O 1 Ka