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The following EOMs describe the behavior of an electric motor attached to a torsional spring and damper: [Lz + Rz + vb = Vin(t) IÖ = -ko-b0 + T Importantly, the equations are coupled by the fact that 7 = k₁z and v=k₂0. Here, L, R, kv, I, k, b, and ke 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 = k₁² and 2 = k,0) into the EOMs, write the state space form of the System x - Ax + Bu, assuming your states are r₁=2,3₂ = 0, and 3 = 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

The following EOMs describe the behavior of an electric motor attached to a torsional spring and damper: [Lz + Rz + vb = Vin(t) IÖ = -ko-b0 + T Importantly, the equations are coupled by the fact that 7 = k₁z and v=k₂0. Here, L, R, kv, I, k, b, and ke 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 = k₁² and 2 = k,0) into the EOMs, write the state space form of the System x - Ax + Bu, assuming your states are r₁=2,3₂ = 0, and 3 = 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

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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 = k₁² and v = k„0) into the EOMs, write the state space form of the system x = Ax + Bu, assuming your states are 2₁=2, 22 = 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 Assume represen angular velocity and 9(s) to
Transcribed Image Text: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 = k₁² and v = k„0) into the EOMs, write the state space form of the system x = Ax + Bu, assuming your states are 2₁=2, 22 = 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 Assume represen angular velocity and 9(s) to
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