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Electrical EngineeringQ&A LibraryPre-Lab ReadingThe block diagram of the closed-loop system for control of motor position is shown in the figure.Motor1Iy=e1PIDS+DC Motor PID position control closed-loop block diagram with set point weight bsp 1The two-degree of freedom PID compensator with set point weighting isu) ( () y(t)) +r(T)y(T) dtk(t)6.4.1]sd41-...Question

Asked Nov 18, 2019

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- Derive the plant transfer function, , for the DC motor position system in terms of the motor gain constant,
*K*, and the time constant,*τ*. - Consider PD-Control with set-point weighting by setting
*k*= 0 in Equation 6.4.1. Determine the closed-loop transfer function from the position reference,_{i}*r*, to the angular position output,*θ*in radiansi.e.,_{, }*Y*(*s*)/*R*(*s*), in terms of*K,**τ*,*b*,_{sp}*k*and_{p }*k*._{d} - Determine
*k*and_{p }*k*in terms of the closed-loop natural frequency,_{d}*ω*, damping ratio,_{n}*ζ*, motor time constant,*τ*, and motor gain constant,*K.* - Determine the steady-state error to a unit step input. Given
*b*= 1, determine the DC Gain of the closed-loop motor position system._{sp}

Step 1

Write the expression of the PID controller in Laplace transform:-

Step 2

The transfer function of the DC motor from the given block diagram can be expressed as:-

Step 3

The transfer function of the ...

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