Dynamics of a current controller DC motor is given as follows:KimJm+bBwhere, ẞ denotes the shaft angle (output), i, is the motor current (input), K, is the torque constant, im is rotor inertia along the rotation axis, b, is the coefficient of viscous friction for the rotor.im= 0.48gm, bm = 0.2Nms/rad, K, = 0.96 Nm/AInitial conditions are zero.Obtain the transfer function of the system, Design a lead controller such that the static velocity error constant is improved by a factor of 13 when compared to the case of unit feedback. Use unit ramp for both cases. Moreover, gain marginshould be at least 10 dB and the phase margin should be at least 40 degrees. Clearly show all the necessary steps. (When computing max. phase lead, consider additional 34.33 degrees for safety)Using MATLAB's margin function, indicate the phase margin and the gain margin of the controlled system. Show this Bode plot, steps used.Using MATLAB/Simulink, simulate the controller. Compare it with respect to unit feedback. Use a 3-input scope to plot the outputs (unit feedback and your controller) and the step input. Show the Simulink model, scope and the parametersused.

% ParametersJm = 0.48; % kg*m^2bm = 0.2; % Nms/radKt = 0.96; % Nm/A% Transfer function of the…

Answered: Dynamics of a current controller DC…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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The following EOMS describe the behavior of an electric motor attached to a torsional spring and damper: [Li + Rz + vb = Vin(t) IÖ= k0b0 + T Importantly, the equations are coupled by the fact that 7 = k₁z and v₂ = k₂0. Here, L, R, kv, I, k, b, and kt are constants. z is the current in the motor, and is the angular displacement of the motor (clearly then, is the motor's angular velocity). Finally, the input to the system is vin (t). Your tasks: A Substituting in the coupling terms (7 = ktz and v k0) into the EOMs, write the state space form of the system x = Ax + Bu, assuming your states are x₁ = z, x₂ = 0, and x3 = 0. Clearly identify your matrices. B Assume that the desired outputs of the system (to be measured) are the current z, the angle and the input Vin all as separate elements in the vector y. Write the output equation y = Cx + Du. Hint: D will NOT be zero in this case. Clearly identify your matrices C Assume there is no stiffness to the spring (k = 0). Using w(t) to represent…
QUESTION 2 a) A single degree of freedom system with viscous damper is shown in Figure 3. The system driven by external forces, F = Fo cos cot. If m= 1 kg, k, = 11 N/m, k₂ = 14 N/m, c = 3 N.s/m, c₂= 2 N.s/m, Fo= 100 and = 7 rad/s. Derive the total response of the system if x(0)=0 and x(0) = Vo. Z m 5 I Figure 3 Fo cos wt
QUESTION 1 Consider the equations of motion of an armature controlled DC motor given by Jw(t)+bw (t) Ki (t) = di (l) L + Ri (t) + Kw (t) = -Tfriction - Tload (t) Vin (t), dt where vin(t) is the input voltage and Tload(t) is the input load torque. The outputs are the armature current i(t) and the motor speed w(t). When the input voltage and torque are constant, the transient response of this system has the form of the homogeneous solution. What is the time constant of the transient response? Find the characteristic roots of this system first. Keep 3 significant figures, and do not include units. Use scientific notation. The constants are given below: Nominal voltage, Vin(t) = 17 V Moment of inertia of the rotor, J = 0.02 kg-m² Motor viscous friction constant, b = 0.009 N-m-s Friction torque, Tfric = 0.003 N-m Armature inductance, L = 0.1 H Armature resistance, R = 0.35 Back emf constant and motor torque constant, K = 0.21 N-m/A. **Recall that the time constant (or relaxation time) is…
T C We consider a rotating shaft. A torque T is applied, resuting in a rotation of the shaft. The bearing system and the output connections yield a viscous damping torque D. T: input torque 2: output angular velocity Dan: viscous damping = J: moment of inertia Governing equation (obtained using Euler equation for rotating solids): JN+an = T αΩ
Given the torsional system shown below actuated by a step input torc T(t): TO) 00) lll fro> K D 1- Write first the equation of motion, and then: 2- for K=2 N.m/rad, find J and D to yield 15% overshoot and a 2% settling time of 5 seconds, and then calculate the resultant natural frequency and damping ratio. 3- for K=2 N.m/rad, find J and D to yield a peak time of 2 seconds and a 2% settling time of 10 seconds, and then calculate the resultant natural frequency and damping ratio. 4- for D=1 N.m.s/rad, find K and J to yield 20% overshoot and a peak time of 2 seconds, and then calculate the resultant natural frequency and damping ratio. 5- for J=0.5 kg.m², find K and D to yield 5% overshoot and a peak time of 1 second, and then calculate the resultant natural frequency and damping ratio.
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Hello Sir.Good Night I have a question related Machine Vibration Lesson. The following below is my question.Please advise, Thank you so much.
ponse Clear selection A block attached to a spring, oscillates on a frictionless horizontal surface with a period of 0.3 s. The time needed by the block to move (for the first time) from position x = A to x = -A/2 is: O 0.2 sec 0.3 sec 0.05 sec 0.1 sec O 0.15 sec
If wo = 106 rad/s, Q, = 5 × 10² and m = 10-1ºkg, calculate the stiffness, and resistive constant (b) of the system. S For a driven damped oscillator, show that the energy dissipated per cycle by a frictional force Fa = bv at an angular frequency (@) is given by: E = nbwA².
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