Question

The block diagram of a unity feedback control system shown below with the following transfer functions: Controller Process E(s) R(s)+ G$_c$(s) G(s) Y(s) G$_c$(s) = K, G(s) = \frac{(s+5)}{s(s+2)(s+7)} 1) Determine the closed-loop transfer function of this system. 2) Write the characteristic equation in the form $\Delta(s) = 1 + KP(s)$ where $P(s) = \frac{\prod_{i=1}^{m}(s+z_i)}{\prod_{j=1}^{n}(s+p_j)}$ and locate all open-loop poles and zeros in the s-plane.

          The block diagram of a unity feedback control system shown below with the
following transfer functions:
Controller
Process
E(s)
R(s)+
G$_c$(s)
G(s)
Y(s)
G$_c$(s) = K, G(s) = \frac{(s+5)}{s(s+2)(s+7)}
1) Determine the closed-loop transfer function of this system.
2) Write the characteristic equation in the form
$\Delta(s) = 1 + KP(s)$ where $P(s) = \frac{\prod_{i=1}^{m}(s+z_i)}{\prod_{j=1}^{n}(s+p_j)}$
and locate all open-loop poles and zeros in the s-plane.

The block diagram of a unity feedback control system shown below with the
following transfer functions:
Controller
Process
E(s)
R(s)+
Gc(s)
G(s)
Y(s)
Gc(s) = K, G(s) = ((s+5))/(s(s+2)(s+7))
1) Determine the closed-loop transfer function of this system.
2) Write the characteristic equation in the form
Δ(s) = 1 + KP(s) where P(s) = (∏i=1^m(s+zi))/(∏j=1^n(s+pj))
and locate all open-loop poles and zeros in the s-plane.

Added by Scott E.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Dominique Jan Tan

Step 1

The closed-loop transfer function is given by T(s) = G(s)Gc(s)/[1 + G(s)Gc(s)]. From the given information: Gc(s) = K and G(s) = (s+5)/[s(s+2)(s+7)]. Substituting these values: T(s) = [K(s+5)/s(s+2)(s+7)]/[1 + K(s+5)/s(s+2)(s+7)] Show more…

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The block diagram of a unity feedback control system shown below with the following transfer functions: Controller Ea(s) G(s) Process G(s) Yx (s+5) G(s)=K,G(s)= s(s+2)(s+7) 1) Determine the closed-loop transfer function of this system 2) Write the characteristic equation in the form I(s+2) (s)=1+KP(s)where Ps=-i I1(s+ p) j=1 and locate all open-loop poles and zeros in the s-plane