This document discusses different types of state space analysis including physical variable form, phase variable form using canonical forms I and II, parallel realization, converting between state models and transfer functions, state transition matrices, and observability and controllability. It provides examples of obtaining state space models from electrical circuits using different approaches like writing standard state equations, using canonical forms, and parallel realization from transfer functions. It also outlines how to check for observability and controllability of state space models.

1. Unit 5
State Space analysis
Prajakta .J. Pardeshi
Assist. Professor
MITCOE

2. Types
1. Physical Variable form
2. Phase Variable Form
a) Canonical Form I
b) Canonical Form II
c) Parallel Realization
3. State Model To Transfer function
4. State Transition Matrix (Theory+Problem)
5. Observability & Controllability(Theory+Problem)

3. Physical Variable Form
• Problem: Obtain state model of the given
electrical system
1. Write the standard state equations
2. Obtain Required state variables from the
circuit & predict the order of the system
3. Solve the Network using KVL, KCL
4. Equate the equation in differential form
5. Form the state model matrices from
equations

4. Phase Variable Form- Canonical Form I
• Problem: Obtain state model of the given using
canonical form I & II
1. Equation can be in differential/ Transfer function
form
2. Represent the equation in block diagram form
3. From B.D; find out equations for state variables
4. From the equations form the matrices of the
state equations & output equations

6. State equation of phase variable
(Canonical form I)

7. Output equation of phase variable
(Canonical form I)

8. 1. The matrix A in observable form is A
transpose in controllable form
2. The matrix B in observable form is C
transpose in controllable form
3. The matrix C in observable form is B
transpose in controllable form
4. D is same in both forms
Phase Variable Form- Canonical Form II

9. • If controllable canonical form is determined,
the observable canonical form can be
determined directly without block diagram
realization

10. • Problem: Obtain state model of the given
using parallel realization
1. Deduce the transfer function in Partial
Fraction form
2. Represent this forms in block diagram
realization (Each individual partial fraction in
parallel form)
3. Form equations from block diagram
4. Form matrices from the equations
Parallel Realization

11. State Model to Transfer Function
State Model
Transfer Function

12. • Problem Type: A matrix is given, Find x(t)
• Use standard formula;
State Transition Matrix
Imp : 1. Problem can be asked
2. Theory Question- Properties of STM
3. Problems on STM Properties

13. Observability & Controllability
Controllability Matrix
Observability Matrix

14. Problem statement:- Investigate for complete
state controllability and complete state
Observability for the system,
Imp : 1. Problem Can be asked
2. Theory Question- Explain Observability & Controllability
(Explain in brief with all its conditions)