ECCE323: The Purpose of the Rigid Transform Blocks - The Advantages of using Simscape Multibody Blocks - Engineering Assignment Help

Assignment Task:

It is likely that you came across the Segway Loomo robot somewhere or you might have used it yourself. One of the major design concerns in such robots is the control system. You would like to have a product that meets the common objectives of a control system: 

1- Responds quickly to user commands (moves quickly towards the desired location).

2- Tracks the reference accurately (reaches the desired location).

3- Rejects disturbances (acts against external forces due to wind, nudges, etc).

4- Maintains stability at any cost (you don’t want to harm your customers!).

Part I 

1. Discuss the advantages of using Simscape Multibody blocks instead of integrators, gains, and summing points. You can find these blocks inside the plant subsystem. 

2. Insert the following parameters in their appropriate locations in the Simulink model of the plant. The cart has the dimensions [0.5/6 0.5/6 0.5/3] meters and a mass of 1 kg. The pendulum has the dimensions [0.5 0.5/12 0.5/12] meters and a mass of 1 kg. The prismatic joint has a damping coefficient of 10 N/(m/s). In the revolute joint settings, specify the position target to 0 degrees. 

3. What is the purpose of the rigid transform blocks? What about the prismatic and revolute joints? (hint: you can apply changes to the block parameters and observe the new animation). 

4. Use negative feedback with PID control with gains of 30,30,10 to control the position of the cart. Are you able to control the position? 

5. Remove the previous controller. Measure the angle and use negative feedback with PID control of high gains (e.g. 200,200,10) to regulate the angle with zero references. While the pendulum is subject to an impulsive disturbance, does your controller stabilize the angle? Is your solution physically feasible? 

6. Can you control both the position and angle with only one measurement? Why? 

7. Use the linear analysis tool to find the linearized model of the plant. Did you expect the plant to have this order? What are the states of the model? 

8. Use the same tool to obtain the Bode plots and the pole-zero map. Use any of the obtained information to comment on the stability of the linearized model. 

9. Increase the inertia of the pendulum and obtain the pole-zero map again. How does the inertia relate to the relative stability of the system? Provide an explanation for your observation. Return the inertia of the pendulum to the original value. 

10. You have seen that if a system is not BIBO stable, its output goes unbounded. Apply xref to the plant input F. Does the output of the plant blow up? Explain your answer. 

11. Comment on the equilibrium of the system at t = 0.5 s (when the pendulum is up) versus when the pendulum is down. What is the type of each equilibrium? 

12. Use both the position and angle measurements to design a reasonable controller using any method that you know within 30 minutes. You do not necessarily need to give a working controller, but you should discuss all the observations and the difficulties in this task.

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