Consider a DC motor system as illustrated in Figure 2a, which is subjected to a unit-step input. The corresponding system output response is presented in Figure 2b. Determine the values of the gain K, and the velocity feedback constant K, using the data from the output response curve. Find the numeric expression of the closed-loop transfer function C(s) for the system. Ensure that the transfer function does not contain any unknown values. Assume J = 4 kg-m², K₁ = 6, and B=3 N-m/rad/sec. R(s) R(s) Κα K₁ 1 C(s) JS + B S Figure 2a Kh

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P4. The open loop transfer function of a unity feedback system is given by G(s)= K s(as+1)(Bs+1) Determine the range of K for stability in terms of a and ß.

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Consider the system whose transfer function is given by G(s) = 24/(s² + 4s + 20.3). At which input frequency (in rad/s), is the steady-state response amplitude maximum? Assume the input amplitude of 1. Do not include units. Use scientific notation with 3 significant figures (1.23e-1).

An underdamped second order system forward transfer function is given as: 3a + b + 2d +e G(s) = s2 + as + (3a + b + 2d + e) Answer the following questions: Manual Calculation Find the poles of the system and sketch it in an s-plane. Determine the natural frequency and damping ratio of G(s). Find the peak time, Tp, percent overshoot, %OS, settling time, Ts, and rise time, T, under unit step input.

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A common actuator in control systems is the DC motor. It directly provides rotary motion and, coupled with wheels or drums and cables, can provide transitional motion. The electric circuit of the armature and the free body diagram of the rotor are shown in figure 3. Determine the following. i. The differential equations from the electrical circuit and the mechanical part. ii. Convert the differential equations to state space representation. The output is the speed of the de motor dt ii. Given component values R=5 Ohms, L= 6H, J= 8 kg-m?, b=4 N-m s/rad, assuming back Emf constant and motor torque constant are equal Kb=Kt=K=10, determine its controllability of the DC motor. iv. Based on the performance of the DC motor, recommend at least 3 ways on how to increase it angular velocity, and justify your answer. Fixed field R L Armature circuit indows bui انتقل إلى الإعدادت Rotor Figure 3

Q.4- A model for feedback control system employing both angular position and velocity feedback is shown in figure bellow .The equation describing d²0 do di the system is J di² - = • K.[V₁-K₁0. K₂0-Ka ((1) Summing V,(r) Motor 白口食 amplifier Velocity sensor K₂8 Position sensor Where J is the rotary inertia KandK are the position and velocity feedback gains, and K, is the gain between the input voltages to the motor torque produced. Derive expression for the closed loop system undamped natural frequency and damping ratio.