Question

Controller Design Using Root Locus: Example 10.12 Consider again the closed-loop position-control system presented below. Use the root locus to design a controller $G_c(s)$ that provides a fast, well-damped closed- loop transient response to a reference step position command $x_{ref}(t) = 0.1 m$. The actuator gain is $K_A = 2 N/V$. We worked on this system back in Example 10.6, where the closed-loop responses were obtained with P-and PD-controllers. This example will illustrate how the root-locus plot allows the control engineer to visualize the effect of changing the controller dynamics without deriving the closed-loop characteristic equation. Reference position, $x_{ref}(t)$ + Position error, $x_e(t)$ Actuator voltage, $e_{in}(t)$ Force, $f(t)$ $G_c(s)$ $K_A$ Controller Actuator gain (N/V) $\frac{1}{s^2 + 0.3s}$ Mechanical system dynamics Position, $x(t)$

          Controller Design Using Root Locus:
Example 10.12
Consider again the closed-loop position-control system presented below. Use the
root locus to design a controller $G_c(s)$ that provides a fast, well-damped closed-
loop transient response to a reference step position command $x_{ref}(t) = 0.1 m$.
The actuator gain is $K_A = 2 N/V$.
We worked on this system back in Example 10.6, where the closed-loop responses
were obtained with P-and PD-controllers. This example will illustrate how the
root-locus plot allows the control engineer to visualize the effect of changing the
controller dynamics without deriving the closed-loop characteristic equation.
Reference
position,
$x_{ref}(t)$ +
Position
error,
$x_e(t)$
Actuator
voltage,
$e_{in}(t)$
Force,
$f(t)$
$G_c(s)$
$K_A$
Controller
Actuator
gain (N/V)
$\frac{1}{s^2 + 0.3s}$
Mechanical
system dynamics
Position,
$x(t)$

Controller Design Using Root Locus:
Example 10.12
Consider again the closed-loop position-control system presented below. Use the
root locus to design a controller Gc(s) that provides a fast, well-damped closed-
loop transient response to a reference step position command xref(t) = 0.1 m.
The actuator gain is KA = 2 N/V.
We worked on this system back in Example 10.6, where the closed-loop responses
were obtained with P-and PD-controllers. This example will illustrate how the
root-locus plot allows the control engineer to visualize the effect of changing the
controller dynamics without deriving the closed-loop characteristic equation.
Reference
position,
xref(t) +
Position
error,
xe(t)
Actuator
voltage,
ein(t)
Force,
f(t)
Gc(s)
KA
Controller
Actuator
gain (N/V)
(1)/(s^2 + 0.3s)
Mechanical
system dynamics
Position,
x(t)

Added by Sarah T.

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