- 1 In Order To Simplify The Model Neglect The Armature Inductance L And Assume That The Coupling Is Infinitely Stiff 1 (97.59 KiB) Viewed 32 times
- 1 In Order To Simplify The Model Neglect The Armature Inductance L And Assume That The Coupling Is Infinitely Stiff 2 (139.7 KiB) Viewed 32 times
1. In order to simplify the model, neglect the armature inductance L, and assume that the coupling is infinitely stiff (i.e. 01 = 02). Write the continuity equations for the simplified model and show that the simplified transfer function is: = X (s = < < 1 V(s) s? +5.5s 2. Assume you have a perfect sensor ( H(s)=1). Use the simplified transfer function and control the position of the carriage x(t) when f(t) 0 with a proportional (P) controller. Find the value range for the controller gain K, to achieve less than 10% overshoot (Mp < 0.1) within 1 s (tp < 1) of a unit-step input. 3. Simulate Problem 2 in Simulink or Xcos to validate your range of K, values. 4. Test your controller with the original (unsimplified) transfer function of the plant and compare the response with the one for the simplified plant.
x(t) R L ܠܠܠܠܠܠܠ i 0,(t) 02(t) b, + v(t) செய் V M Km, K. m f(t) IIIIIIIIIIIII The physical model of a lathe axis is shown above. The system consists of an electric motor, a flexible coupling, a rigid leadscrew, and a carriage attached to the nut of the leadscrew. The inputs of the system are the motor supply voltage V(t), and the cutting force F(t) applied to the carriage. The electric motor is modeled with armature resistance R, armature inductance L, torque constant Km and back-emf constant Ke. Torsional stiffness of the coupling is kt. Mass of the carriage is m. Pitch of the rigid leadscrew is 1. All the frictional effects are modeled as if they are accumulated at the right-hand-side bearing as a rotational viscous friction (damping) with coefficient bio The model parameters are as follows: R = 0.1 22 = 5000 N.m/rad λ Km = 0.1 N.m/A Ke = 0.1 V.s/rad kt bt = 0.02 m = 50 kg L = 0.01 H = 0.01 N.m.s/rad m