Assignment

The combination of all these elements produces a mathematical model for the Elbow Control System for the Robot Arm, which you will use as the basis of your assignment. Using this model as a basis, perform your assignment by following steps of an investigation:

Mathematical Modelling & Continuous Time Simulation

1. Use the description given above to derive the state space model for the Robot Arm System.

2. Use this model and the parameter values given in the Appendix A to produce an equation or script based simulation of the Robot Arm System in Matlab.

3. Employ a suitable numerical integration solver with a suitable step-size in the simulation of your system. Justify your choice of both solver and step-size. Do not use the in-built Matlab integration functions.

4. Analyse the dynamic response of the system. Do you think this a good design for the Elbow Control System? Explain your answer.
Block Diagram & Validation

5. Using basic, commonly used blocks in Simulink, construct a block diagram simulation of the Robot Arm System.

6. Use the responses from this block diagram simulation to validate your Matlab model from parts
(1) & (2) and simulation responses from part (3).
Control System Design & Implementation

7. Using your Matlab script based simulation, investigate the effect of varying the coupler gain
Gc on the performance of the Robot Arm System.

8. In order to improve the performance of the Elbow Control System further it is normal practice to include an integral term within the controller for such a Robot Arm System. Use your Matlab simulation to investigate the effect of introducing the integral term into your control system and varying the associated gain KI. Is the performance of this system improved?
Interpolation

9. So far the motion of the Upper Arm has been considered to be constant. One way to incorporate these dynamics is to vary the Upper Arm deflection, U. Within your Matlab simulation use the data presented in Table 1 (Appendix B) to represent the change in the deflection of the Upper Arm as time progresses. Calculate by hand the Quadratic Splines that interpolate the deflection values between the data points.

10. Implement the resulting spline interpolant within your Matlab simulation code and analyse the effect of changing Upper Arm deflection values on the Robot Arm System. Do not use the in- built Matlab interpolation functions i.e. write your own code.

Attachment:- Asignment Simulation.rar