Answer: The parameter values for a certain

Chapter , Problem 10.18

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The parameter values for a certain armature-controlled motor, load, and tachometer are

                                \(\begin{array}{rlrlrl}K_T & =K_b=0.2 \mathrm{~N} \cdot \mathrm{m} / \mathrm{A} & & & \\c_m & =5 \times 10^{-4} \mathrm{~N} \cdot \mathrm{m} \cdot \mathrm{s} / \mathrm{rad} & c_L & =2 \times 10^{-3} & & \\R_a & =0.8 \Omega & L_a & =4 \times 10^{-3} \mathrm{H} & & \\I_m & =5 \times 10^{-4} & I_t & =10^{-4} & I_L=5 \times 10^{-3} \mathrm{~kg} \cdot \mathrm{m}^2 \\N & =2 & K_a & =10 \mathrm{~V} / \mathrm{V} & & \\K_{\text {tach }} & =20 \mathrm{~V} \cdot \mathrm{s} / \mathrm{rad} & K_{\text {pot }} & =10 \mathrm{~V} / \mathrm{rad} & K_d=2 \mathrm{rad} /(\mathrm{rad} / \mathrm{s})\end{array}\)

For the control system whose block diagram is given by Figure 10.3.9, determine the value of the proportional gain \(K_P\) required for the load speed to be within 10% of the desired speed of 2000 rpm at steady state, and use the characteristic roots to evaluate the resulting transient response. For this value of \(K_P\), evaluate the resulting steady-state deviation of the load speed caused by a load torque \(T_L = 0.2 \ \mathrm{N} \cdot \ \mathrm{m}\).