ILO1: Understand the derivation of state equations. Apply basic matrix operations. Identify which state variables to choose based on energy storage or other considerations.
ILO1: the state-space approach, state equations, ordinary differential equations, choice of state variables, canonical form, energy storage
ILO1: state space, matrices, linear systems, state variables
ILO1: Selection of state variables for a particular engineering model represented as a system of ordinary differential equations
ILO1: state variables electrical circuits, Kirchhoff’s law, electro-mechanical systems, DC motor
ILO1: Level 2 - understand, describe, identify; Level 3 - apply, demonstrate, solve.
ILO2: Solve the linear canonical state equation using the matrix exponent. Explain matrix eigenvalues and eigenvectors. Create time dependency plots for each vector component.
ILO2: Matrix exponent computation, state equation solution, state vector components
ILO2: matrix exponent, eigenvalues, eigenvectors
ILO2: Explicitly solve for each state variable using one of the selected formulas for computing the matrix exponent.
ILO2: matrix determinant, eigenvector space, Vandermonde matrix
ILO2: Level 2 - understand, describe, explain, classify; Level 3 - apply, solve, execute
ILO3: Apply second-order approximation. Interpret controllability. Use pole placement for a linear feedback controller. Compare the Bass-Gura and the Ackermann’s formulas.
ILO3: Second-order approximation, pole placement technique, step response characteristics, linear feedback controller, controller canonical form.
ILO3: step response, overshoot, settling time, feedback controller, controllability, Bass-Gura formula
ILO3: Approximate a state equation as a second order system to explicitly set the needed step response characteristics, choose the correct poles and find the linear feedback vector using one
ILO3: peak time, pole placement, Ackermann’s formula, linear state feedback
ILO3: Level 3 - apply, implement, use, operate, interpret; Level 4 - analyse, compare, test
linear state feedback controller
