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Electrohydraulic servomechanisms are used in control systems requiring a rapid response for a large mass. An electrohydraulic servomechanism can provide an output of $100 \mathrm{~kW}$ or greater [17]. A photo of a servovalve and actuator is shown in Figure P9.8(a). The output sensor yields a measurement of actuator position, which is compared with $V_{\text {in }}$. The error is amplified and controls the hydraulic valve position, thus controlling the hydraulic fluid flow to the actuator. The block diagram of a closed-loop electrohydraulic servomechanism using pressure feedback to obtain damping is shown in Figure P9.8(b) $[17,18]$. Typical values for this system are $\tau=0.02 \mathrm{~s}$; for the hydraulic system they are $\omega_2=7(2 \pi)$ and $\zeta_2=0.05$. The structural resonance $\omega_1$ is equal to $10(2 \pi)$, and the damping is $\zeta_1=0.05$. The loop gain is $K_A K_1 K_2=1.0$. (a) Sketch the Bode diagram and determine the phase margin of the system. (b) The damping of the system can be increased by drilling a small hole in the piston so that $\zeta_2=0.25$. Sketch the Bode diagram and determine the phase margin of this system.

    Electrohydraulic servomechanisms are used in control systems requiring a rapid response for a large mass. An electrohydraulic servomechanism can provide an output of $100 \mathrm{~kW}$ or greater [17]. A photo of a servovalve and actuator is shown in Figure P9.8(a). The output sensor yields a measurement of actuator position, which is compared with $V_{\text {in }}$. The error is amplified and controls the hydraulic valve position, thus controlling the hydraulic fluid flow to the actuator. The block diagram of a closed-loop electrohydraulic servomechanism using pressure feedback to obtain damping is shown in Figure P9.8(b) $[17,18]$. Typical values for this system are $\tau=0.02 \mathrm{~s}$; for the hydraulic system they are $\omega_2=7(2 \pi)$ and $\zeta_2=0.05$. The structural resonance $\omega_1$ is equal to $10(2 \pi)$, and the damping is $\zeta_1=0.05$. The loop gain is $K_A K_1 K_2=1.0$. (a) Sketch the Bode diagram and determine the phase margin of the system. (b) The damping of the system can be increased by drilling a small hole in the piston so that $\zeta_2=0.25$. Sketch the Bode diagram and determine the phase margin of this system.

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Modern Control Systems

Modern Control Systems

Dorf 11th Edition

Chapter 9, Problem 8

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Step 1

02 \, \text{s}\) - Hydraulic system natural frequency, \(\omega_2 = 7(2\pi) \, \text{rad/s}\) - Hydraulic system damping ratio, \(\zeta_2 = 0.05\) - Structural resonance frequency, \(\omega_1 = 10(2\pi) \, \text{rad/s}\) - Structural damping ratio, \(\zeta_1 = Show more…

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Electrohydraulic servomechanisms are used in control systems requiring a rapid response for a large mass. An electrohydraulic servomechanism can provide an output of $100 \mathrm{~kW}$ or greater [17]. A photo of a servovalve and actuator is shown in Figure P9.8(a). The output sensor yields a measurement of actuator position, which is compared with $V_{\text {in }}$. The error is amplified and controls the hydraulic valve position, thus controlling the hydraulic fluid flow to the actuator. The block diagram of a closed-loop electrohydraulic servomechanism using pressure feedback to obtain damping is shown in Figure P9.8(b) $[17,18]$. Typical values for this system are $\tau=0.02 \mathrm{~s}$; for the hydraulic system they are $\omega_2=7(2 \pi)$ and $\zeta_2=0.05$. The structural resonance $\omega_1$ is equal to $10(2 \pi)$, and the damping is $\zeta_1=0.05$. The loop gain is $K_A K_1 K_2=1.0$. (a) Sketch the Bode diagram and determine the phase margin of the system. (b) The damping of the system can be increased by drilling a small hole in the piston so that $\zeta_2=0.25$. Sketch the Bode diagram and determine the phase margin of this system.

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