Introduction to Signals and Systems, Laplace Transform, Transfer function, Mathematical Modeling from first principles for DC motor and 1D-Quadrotor, Transfer functions from experimental measurements in time-domain.
Transfer functions and Bode-plot
Response of a system, Bode plots, Finding transfer function using Bode plot, Transfer functions from experimental measurements in frequency-domain.
Poles, zeros, and time-domain analysis
Effect of poles and zeros on response, Time domain analysis for first order, second order systems and higher order systems, Steady state error, Experimental demonstration of steady state error.
Root locus and System Stability
Introduction to root locus, Root locus of a linearized quadrotor 1D-model, BIBO Stability, PID controller, Effect of PID on a 1D-quadrotor model
PID Controller Design
Design of PID controller., MATLAB based design of controllers, Design of speed controller and position controller of DC motor experimentally, Importance of speed control in quadrotors
State-space analysis
State-space modeling of system, Solution of state equations, State-space equations of a quadrotor
Controllability
Solution of state equations continued, Introduction to controllability, Linearization of the quadrotor model and discussion on controllability
Pole placement
Concept of state feedback and pole-placement, Ackermann’s formula, Simulation with the quadrotor example
Observers and Observability
State observer (or estimator) design, Separation principle, Observer-based state feedback controller design, Discussions on need of an observer in a quadrotor
Introduction to optimal control
Optimal control problem, LQR problem and its Solution, MATLAB Simulation with the quadrotor example