CONTROL INTRO & OVERVIEW What really is Control Systems System Modelling and Model Verification System Analysis Techniques Controllers for Performance Improvement Feedback based Classical control Stability, disturbances, noise,

State Space Techniques Key Points Concept of state State equation from differential equations State equations from transfer functions

CONTROL SYSTEMS II Classic Control Limitations Generally SISO Systems Generally Linear Generally Time Invariant Systems State-Space Techniques Advantages MIMO systems Non-linear and time-invariant systems A variety of alternative controller designs e.g state-feedback, LQR, LQG, H2, H∞, μ-synthesis

Terms and Definitions State x set of variables for which x(t0) and u(t) fully define system for t>t0 State-space is the n dimensional space for n states State trajectory is the state path within the state space Phase plane special state space when one state is a derivative of the other

State Vectors & Differential equations

State equations from Transfer Functions U(s) Y(s)

Controllable Canonical State Equation

State Solutions I

State Solutions II

State Solution III

State Space Techniques Key Points Concept of state State equation from differential equations State equations from transfer functions State equation solutions D.E model equations to state equations Ex 8.1-3 State transformations A look into the future Control of multivariable systems