This module discusses state space analysis of control systems over 9 hours. It covers properties of state transition matrices and their computation using Laplace transforms and Cayley Hamilton methods. It also covers deriving transfer functions from state equations and solving time-invariant systems by finding the time response of autonomous and forced systems. Finally, it addresses state space analysis of discrete time control systems using phase variable and diagonal canonical forms and computing state transition matrices for second order systems.

1. ACS MODULE 2

2. Module 2
State Space Analysis (9 hours)
State transition matrix- Properties of state transition matrix-
Computation of state transition matrix using Laplace transform and
Cayley Hamilton method. Derivation of transfer functions from state
equations.
Solution of time invariant systems: Solution of time response of
autonomous systems and forced systems.
State space analysis of Discrete Time control systems: Phase variable
form and Diagonal canonical form representations- Pulse transfer
function from state matrix- Computation of State Transition Matrix
(problems from 2nd order systems only).

33. Solution of state equation of forced system

41. 𝒆𝑨𝒕 =∝𝟎 𝑰+∝𝟏 𝑨+∝𝟐 𝑨𝟐 +−−−+∝𝒏−𝟏 𝑨𝒏−𝟏

42. FIND STM USING CH THEOREM