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Unit 5State Space analysis
Prajakta .J. PardeshiAssist. Professor
MITCOE
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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)
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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
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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
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State equation of phase variable(Canonical form I)
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Output equation of phase variable(Canonical form I)
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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
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• If controllable canonical form is determined, the
observable canonical form can be determined
directly without block diagram realization
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• 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
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State Model to Transfer FunctionState Model
Transfer Function
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• 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
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Observability & Controllability
Controllability Matrix
Observability Matrix
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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)