Design a PD controller to meet the performance requirements.

Consider the rotational mass–spring–damper system. A PD controller, τ = −kpθ − kD, is designed to adjust the input torque τ so that the rotational disk can quickly return to the equilibrium position regardless of disturbances applied to the system. The performance requirements of the closed-loop system are overshoot Mp <>5% and rise time tr <>0.004 s.

a. Design a PD controller to meet the performance requirements.

b. Build a block diagram of the feedback control system, in which the plant is constructed using Simscape blocks and the controller is constructed using Simulink blocks. Find the closed-loop response if the disk is initially 0.1 rad away from the equilibrium position.

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erive the differential equations in terms of the liquid heights h1 and h2.

  Figure 7.18 shows a liquid-level system in which two tanks have cross-sectional areas A1 and A2, respectively. The volume flow rate into tank 1 is qi. A pump is connected to the bottom….

Derive the differential equation relating the liquid height h and the volume flow rate qi at the inlet.

  Consider the single-tank liquid-level system shown in Figure 7.19, where the volume flow rate into the tank through a pipe is qi. The liquid leaves the tank through an orifice….

Derive the differential equations in terms of the liquid heights h1 and h2.

Figure 7.20 shows a hydraulic system of two interconnected tanks that have the same cross-sectional area of A. A pump is connected to tank 1. Assume that the relationship between the….