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- ii) Calculate Vị and V2 (Give the answer in 2 decimal points). V = V2 :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) toThe 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 1 Consider a 2 DOF system shown below. X1 k₁ m1 F₁ k₂ X2 k3 m₂ F2 The modeshape can be written as (1))] What is x for the second modeshape? Use scientific notation with 3 significant digits and omit units. (eg. -0.123) Let m1 = 2, m2 = 2, k1 = 9, k2 = 8, and k3 = 8.A X₁ RA P₁ X₂ P₂ 2 X3 X L 10 C ХА B RB 22 Z P₁ = 30kN; P₂ = 50kN; w= 10kN/m; L = 6m x₁ = 1m; x₂ = 2m; x3 = 3m; x = 5m Find RA and Rg, and draw SFD and BMDYou are tasked to enhance the performance of an analog plant using a digital controller PID. The controller is in connected in series with the plant in a closed-loop configuration. The pulse transfer K(z+a) function is given as GzohGp(s) =- Use sampling time Ts=0.6 second, K=8, a=0.78, b=-0.602 (0+z)(q+z) and c=-0.705. Do the following: i. Obtain the design point in z-coordinates to achieve the requirement of having a system settling time of 3 second, and damping ratio of zeta (z=0.705).
- Define the following terms: Inverse kinematics Serial manipulator What is the difference between Euler angles and fixed axes rotations? What is the difference between Euler angles representation and direction cosine representation? In DH convention the transformation between frames can be represented using four parameters only. How is this possible?- Consider the positions servomechanism is shown in figure below. Assume the following numerical values for the system constant are. Kp = gain of potentiometer detector = 7.64 v/ rad, Kb = back e. m. f. constant -5.5*10-2 V/rad/sec K₁ = motor torque constant = 6*10-5 Nm/A C₁ = 4*10-2 Nm/ (rad /sec). Determine the natural frequency and damping ratio of the system. Amp. % Ra= armature winding resistant =20, Ka=Gain of amplifier =10 Jm= 1*10-5 Kg.m². J₁=4.4*10-³ Kg.m² n = gear ratio=1/10, Neglect Cm and la constant 0050 N₁ DIIf f(x) = x² + cos(x) is a periodic function with period 2W, then a. It is an odd function which gives a value of a = 0 b. Its Fourier series is classified as a Fourier cosine series where a = 0 c. it is neither odd nor even function, thus no classification can be deduced. d. it is an even function which gives a value of b₁ = 0
- 2. Figure 1 shows a sensor consists of a core, an armature and a variable air gap. The core with 3.0 cm depth and 10000 relative permeability has 200 coil turns. On the other hand, the armature is a steel plate of thickness 0.2 cm and has similar relative permeability with the core. Assuming the relative permeability of air is unity and the permeability of free space is equal to 4x x 10-7 H.m, calculate the inductance of the sensor for air gaps of 0 mm and 2 mm. Please write the answers in 3 decimal places. 2.0 cm 1.0 cm 6.0 cm 3.0 cm 1.5 cm Figure IQ2. The application glven as In figure A &B can be realized by using an ultra-sonic sensor. Also explain how triangulation method can be used for the same. Using sultable diagrams, explain the process of operation elaborately. Hll semor Oututpu tan s be courted tita) Figure A Soo: SENSOR OUT Figure BThe armature current of a de machine is controlled with a feedback loop. The following is known about the machine: KPWM = 12 (PWM converter gain) Te = 16 ms (electrical time constant) R = 2.0 2 (Armature resistance) %3D Assuming a PI controller that cancels the electrical time constant is used, what is the proportional time constant in terms of the integral time constant (Kp)? KI 16m K (16m K + 1) 1 16m 1) KI \1500