Question

Note that $K_d$ is the derivative gain and $K_o$ is the proportional gain for the PD control system shown below. 1. Replace the controller with a proportional control. Determine the characteristic equation of the system in the format of $1+K_pP(s)$ for this system. 2. Add a zero at -4 to the controller (and therefore to $P(s)$) and generate a new root locus for the proportional control. 3. Assuming that $K_o$ is to be varied and $K_d = 1$, determine the characteristic equation of the system in the format of $1+K_pP(s) = 0$. 4. Assuming that $K_d$ is to be varied and $K_o = 4$, determine the characteristic equation of the system in the format of $1+K_pP(s) = 0$. Vr E (+ Kp 10s Vf s+10 Kd Vin 75 X $s^2+29s$ Figure: Practical PD controller for Positioning system

          Note that $K_d$ is the derivative gain and $K_o$ is the proportional gain for the PD control system shown below.
1. Replace the controller with a proportional control. Determine the characteristic equation of the system in the format of $1+K_pP(s)$ for this system.
2. Add a zero at -4 to the controller (and therefore to $P(s)$) and generate a new root locus for the proportional control.
3. Assuming that $K_o$ is to be varied and $K_d = 1$, determine the characteristic equation of the system in the format of $1+K_pP(s) = 0$.
4. Assuming that $K_d$ is to be varied and $K_o = 4$, determine the characteristic equation of the system in the format of $1+K_pP(s) = 0$.
Vr
E
(+ 
Kp
10s
Vf
s+10
Kd
Vin
75
X
$s^2+29s$
Figure: Practical PD controller for Positioning system

Note that Kd is the derivative gain and Ko is the proportional gain for the PD control system shown below.
1. Replace the controller with a proportional control. Determine the characteristic equation of the system in the format of 1+KpP(s) for this system.
2. Add a zero at -4 to the controller (and therefore to P(s)) and generate a new root locus for the proportional control.
3. Assuming that Ko is to be varied and Kd = 1, determine the characteristic equation of the system in the format of 1+KpP(s) = 0.
4. Assuming that Kd is to be varied and Ko = 4, determine the characteristic equation of the system in the format of 1+KpP(s) = 0.
Vr
E
(+
Kp
10s
Vf
s+10
Kd
Vin
75
X
s^2+29s
Figure: Practical PD controller for Positioning system

Added by Samuel D.

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