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- Response using matlab.4G I. 3:22 A moodle1.du.edu.om Consider the 3 degree of freedom robot manipulator as shown in the figure Link 3 Länk 2 Trint 1 The objective is to find the kinematics inverse of the robot Px=0.9 m, Py=0.6, L1=1.5m, L2=1.5m and qz= 2 rad The value of cos(q2) is equal to Choose... + The positive value of sin(q2) is equal to Choose... + The value of q2 in rad is Choose... + The value of qı in rad is Choose... + The value of q3 in rad is Choose... +2- Using Matlab, what are the step response curves of the closed-loop system, as shown in fig.1. the feedback represents the second-order dynamic system. (fill in the following table) For=0.4 Wn 1 3 6 9 10 R(S) 0.1 0.3 0.6 0.9 1 For w 5 rad/sec 3 Settling time Peak response 2 Wn s(s+23wn) Settling time Peak response C(s) Discuss the follow Which parameters or w occur on the rise time of the response? Which parameter increases the speed of response? Which parameters can be decreases the response amplitude? Which parameter decreases the steady error state? fig.2
- A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.Statics ( Please show step by step solution, Thank you!)A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?
- For the system shown in the figure: b V f(t) a) Find the mathematical model of the system b) Consider null initial conditions, f(t)=1 N₁ m=1 Kg and find values of k and b for the position x(t) to show the following responses: Sustained oscillations • Attenuated oscillations No oscillations c) Obtain an analog simulation diagram and use Simulink to solve the system c) Plot the position x(t) for the 3 cases in point (b)The transfer function of a system is shown below. G (s) = S-a (8+b)(8-c) Where: a = 6, b = 5 and c = 9 %3D When you solve the step response in which R(s) = 1/s, you will get the form of c(t) as shown below: c (t) = X+Y e-bt + Z ect %3D X, Y and Z are constant values which you will obtain when you solve the response c(t). For the blank below, enter the sum of Y and Z (if negative, place a "-" sign before the value). Use FOUR decimal places. Y+Z = %3DA simple mechanical system with T(t) input, and w(t) output is given below, a) Find transfer function of the system parametrically and determine the order of system. b) If J=1 kg-m2, B = 0.5 N-m-s/rad, then find time constant, rise time and settling time of the system. @(t) T(t) J inertia B Viscous friction
- 4. Solve T(s)=C(s)/R(s). R(S) T(s) 3 T(s) 2/s -5/s 5. What is the natural response c(t) of the following transfer functions if the input R(s) = 1/s. 625 s² +625 1/s 225 s² + 30s + 225 -4 C(s)Convert the Transfer Function into Differential Equation. (s – 1)'s (s2 + 1)2s2 R(s) C(s) Convert the Differential Equation into Transfer Function. d³b 5d²b 4b 2df -8f dt dt3 dt2Mechanics of machines QUESTION 4 Consider two degree of freedom of coupled pendulum with horizontal rod vibration system are shown in figure 4. MA KG. oooo MB BAW a Figure 4 k d L 4.1- Determine differential equations of motion in matrix form using The equation of equation with, and ß as generalized coordinates; 4.2- Develop state-space model.