# Power Systems State Transition

AbundantIsland
·
·

Start Quiz

Study Flashcards

## 15 Questions

### What is the purpose of the matrix $A$ in the equation $dx = A(t)x(t) + B(t)u(t)dt$?

To model the system dynamics

### In the context of a linear system, what does $\Phi(t)$ represent?

Transition matrix

Output vector

### What is the role of matrix $B$ in the state-space model equation $dx = A(t)x(t) + B(t)u(t)dt$?

To describe the input vector

### What does the term 'Zero-state response' refer to in the context of a linear system?

The response of a system with zero initial conditions

Observability

### How is the observability of an input-free system studied?

By obtaining derivatives of continuous-time measurements

### What criterion ensures a unique solution for a system of linear algebraic equations with n unknowns?

The system matrix has rank n

### How is the completeness of the rank of square matrices tested?

By finding their determinants

### Under what condition is a linear continuous-time system considered controllable?

The controllability matrix C has full rank

Observability

### How is the observability of an input-free system studied?

By taking derivatives of the continuous-time measurements

### Under what condition is a linear continuous-time system considered controllable?

If the controllability matrix has full rank

### What criterion ensures a unique solution for a system of linear algebraic equations with n unknowns?

Full rank of the system matrix

### What is the role of matrix $B$ in the state-space model equation $dx = A(t)x(t) + B(t)u(t)dt$?

Representing an input in the state-space model

## Study Notes

### Controllability and Observability

• Controllability and observability are two major concepts of modern control system theory
• Controllability: the system must be controllable to do whatever we want with the given dynamic system under control input
• Observability: the system must be observable to see what is going on inside the system under observation

### Controllability

• Definition: the process G is said to be controllable if every state variable x of G can be affected or controlled in finite time by some unconstrained control signal u(t)

### Observability

• Definition: the process G is said to be observable if every state variable x of G eventually affects some of the outputs y of the process

### State Transition Matrix

• The state transition matrix is denoted by Φ(t) = e^(At)
• It satisfies the following properties:
• Φ(0) = I
• Φ(t1 + t2) = Φ(t1) Φ(t2)
• Φ(t) = Φ^(-1)(-t)
• Φ(t) is non-singular for all t
• Φ(t) is continuous for all t

Test your understanding of state transition matrix and the behavior of x(t) and y(t) in power systems. Explore concepts such as homogeneous and non-homogeneous solutions as well as the principle of homogeneity.

## Make Your Own Quizzes and Flashcards

Convert your notes into interactive study material.

## More Quizzes Like This

Use Quizgecko on...
Browser
Information:
Success:
Error: