EPE3200: State Space Analysis and Controller Design Home Work, NU, Singapore: Analyze and design a controller for the inverted pendulum shown in the figure
University | Newcastle University (NU) |
In this assignment, you will model, analyze and design a controller for the inverted pendulum shown in the figure. You will apply the principles learned in the model to accomplish the tasks and prepare a report that you will be submitting at the end of the trimester. The parameters of the inverted pendulum system are as follows:
Mass of the cart (M): 0.5 kg
Mass of the pendulum (m): 0.2 kg
Coefficient of friction for cart (b): 0.1 N/m/sec
Length to pendulum center of mass (l): 0.3 m
Mass moment of inertia of the pendulum (I): 0.006 kg.m^2
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Tasks
- Obtain the model of the system in State Space form.
- Obtain the equilibrium point and linearize the model around the equilibrium point.
- Design a pole placement controller that can drive the cart to follow a step reference input while keeping the pendulum upright.
- Design an LQR controller for the task in (c) and compare both approaches.
- Assuming that the speed of the cart and angular speed of the pendulum is not measured, derive a state observer that can estimate those signals and use the observer in parts (c) and (d).
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