Computer-Aided Process Engineering Assignment Help

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ENIN 833 Computer-Aided Process Engineering Assignment

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Task - Figure shows a schematic of an inverted pendulum on a cart. The cart is driven by a DC motor, attached to the wheels, whose specs are provided as an attachment.

Question 1 - Derive the state-space model of the system, including motor's dynamics.

Answer:
To derive the state-space model of a system, including motor dynamics, you'll need to consider the following:

Motor Equations: Use the motor's back-EMF equation and torque-current equation to represent its dynamics.
Mechanical Dynamics: Incorporate the mechanical components (e.g., gears, load) into the model using Newton's laws of motion.
State Variables: Define the state variables, which typically include the motor's angular position, angular velocity, and current.
Input and Output: Identify the input (e.g., voltage applied to the motor) and output (e.g., motor's angular position or velocity).
Matrix Representation: Express the system's dynamics in matrix form, where the state vector, input vector, and output vector are related by the state matrix, input matrix, output matrix, and direct feedthrough matrix.

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Question 2 - Design an MPC controller for keeping the pendulum in an upward configuration, and tracking a position setpoint on the cart, simultaneously (i.e., an inverted pendulum control problem). Set constraints on the pendulum angle and cart position as: |θ| «30 degrees,and |X| «0.5 meters

Question 3 - Repeat (2) when adding a full-state observer. Design proper observer gains and explain your design process.

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Physical parameters of the system -

1. Mass of the cart (M) = 0.5 kg

2. Mass of the pendulum (m) = 0.2 kg

3. Coefficient of friction for cart (b) = 0.1 N/m/sec

4. Length of pendulum center of mass (l) = 0.3 m

5. Mass Moment of inertia of the pendulum (I) = 0.006 kg.m²

6. Radius of the wheels (r) = 0.10 m.

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