Question

Choose the correct sequence of steps in state variable method. A. Choose state variables B. Write state equations C. Write matrix model D. Form output equations Choose the correct answer from the options given below :

• A. A, B, D, C
• B. A, B, C, D
• C. A, C, B, D
• D. C, A, B, D

Hint:

Standard state-space modeling sequence: \[ \text{Choose State Variables} \rightarrow \text{Write State Equations} \rightarrow \text{Matrix Representation} \rightarrow \text{Output Equations} \]

Answer 1

The Correct Option is B

Concept: State variable analysis is a systematic method used for representing dynamic systems in first-order differential equation form. The procedure involves:
• Selecting suitable state variables
• Writing state equations
• Expressing equations in matrix form
• Writing output equations This method is widely used in:
• Control systems
• Signal processing
• Modern system analysis

Step 1: Choose the state variables. The first step is to identify independent energy storage variables such as:
• Capacitor voltages
• Inductor currents These are called state variables. Hence: \[ A \] comes first.

Step 2: Write the state equations. After selecting state variables:
• Differential equations governing system behavior are written. General form: \[ \dot{x}=f(x,u,t) \] Thus: \[ B \] comes next.

Step 3: Write matrix model. The state equations are then converted into matrix form: \[ \dot{X}=AX+BU \] This representation simplifies analysis and controller design. Hence: \[ C \] comes after state equations.

Step 4: Form output equations. Finally, output equations are written: \[ Y=CX+DU \] These equations relate outputs to states and inputs. Thus: \[ D \] comes last.

Step 5: Write the correct sequence. Therefore, the correct sequence is: \[ A \rightarrow B \rightarrow C \rightarrow D \] Hence, the correct option is: \[ \boxed{(B)\ A,B,C,D} \]