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State space analysis shortcut rules, control systems,
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.
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Introduction to State Space Analysis in the context of electrical systems.
Exploration of various state space representations, including physical variable form, phase variable forms, and topics like observability and controllability.
Steps to obtain the state model of an electrical system using physical variable form.
Obtaining state models using canonical form I & II, incorporating equations in block diagram representation.
Focus on the state equation representation for phase variable form in canonical form I.
Output equation derivation based on canonical form I state variable definition.
Relationship between observable and controllable forms of matrices in state space.
The method to derive observable canonical form from controllable canonical form without block diagrams.
Steps to form state models using parallel realization, emphasizing block diagram representation.
Conversion from state model representation to transfer function.
Handling of state transition matrix, including problems and associated properties.
Discussing matrices for observability and controllability in states.
Focus on probing for complete state controllability and observability with theoretical explanations.
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Similar to State space analysis shortcut rules, control systems,
State space analysis shortcut rules, control systems,
- 1. Unit 5 State Spaceanalysis Prajakta .J. Pardeshi Assist. Professor MITCOE
- 2. Types 1. Physical Variableform 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 ofphase variable (Canonical form I)
- 7. Output equation ofphase variable (Canonical form I)
- 8. 1. The matrixA 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 controllablecanonical form is determined, the observable canonical form can be determined directly without block diagram realization
- 10. • Problem: Obtainstate 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 toTransfer 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 ControllabilityMatrix Observability Matrix
- 14. Problem statement:- Investigatefor 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)