state space analysis shortcut rules, control systems,

Unit 5State Space analysis

Prajakta .J. PardeshiAssist. Professor

MITCOE

Types1. Physical Variable form2. Phase Variable Forma) Canonical Form Ib) Canonical Form IIc) Parallel Realization3. State Model To Transfer function4. State Transition Matrix (Theory+Problem)5. Observability & Controllability(Theory+Problem)

Physical Variable Form• Problem: Obtain state model of the given

electrical system1. Write the standard state equations2. Obtain Required state variables from the

circuit & predict the order of the system3. Solve the Network using KVL, KCL4. Equate the equation in differential form5. Form the state model matrices from

equations

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 form3. From B.D; find out equations for state variables4. From the equations form the matrices of the

state equations & output equations

State equation of phase variable(Canonical form I)

Output equation of phase variable(Canonical form I)

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

• If controllable canonical form is determined, the

observable canonical form can be determined

directly without block diagram realization

• 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 diagram4. Form matrices from the equations

Parallel Realization

State Model to Transfer FunctionState Model

Transfer Function

• 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

Observability & Controllability

Controllability Matrix

Observability Matrix

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)