1. What is the primary purpose of state-space representation in control systems?
A) To represent systems in a form suitable for analysis and design using matrices
B) To provide a graphical representation of the system’s response
C) To simplify the system’s frequency response analysis
D) To visualize the system’s steady-state error
Answer: A) To represent systems in a form suitable for analysis and design using matrices
2. In state-space representation, what does the state vector represent?
A) The current state of the system at a given time
B) The control input to the system
C) The output of the system
D) The system’s transfer function
Answer: A) The current state of the system at a given time
3. What are the main components of a state-space model?
A) State vector, input vector, output vector, and system matrices
B) Transfer function, poles, and zeros
C) Frequency response, gain, and phase shift
D) Proportional, integral, and derivative gains
Answer: A) State vector, input vector, output vector, and system matrices
4. Which matrix in state-space representation describes the relationship between state variables and inputs?
A) The input matrix (B)
B) The state matrix (A)
C) The output matrix (C)
D) The feedthrough matrix (D)
Answer: A) The input matrix (B)
5. What does the state matrix (A) represent in a state-space model?
A) The dynamics of the system and the relationship between state variables
B) The influence of input variables on the state variables
C) The direct relationship between the input and output
D) The noise characteristics of the system
Answer: A) The dynamics of the system and the relationship between state variables
6. In state-space representation, what does the output matrix (C) relate?
A) The state variables to the system output
B) The control input to the system output
C) The system output to the state variables
D) The state variables to the system input
Answer: A) The state variables to the system output
7. What is the role of the feedthrough matrix (D) in a state-space model?
A) It describes the direct influence of the input on the output without involving state variables
B) It represents the dynamics of the system
C) It relates the state variables to the inputs
D) It describes the system’s noise characteristics
Answer: A) It describes the direct influence of the input on the output without involving state variables
8. What is the standard form of a state-space representation?
A)
x˙=Ax+Bu,y=Cx+Du\dot{x} = Ax + Bu, \quad y = Cx + Du
B)
x=Ax+Bu,y˙=Cx+Dux = Ax + Bu, \quad \dot{y} = Cx + Du
C)
x˙=Bx+Cu,y=Ax+Du\dot{x} = Bx + Cu, \quad y = Ax + Du
D)
x˙=Ax+Cu,y=Bx+Du\dot{x} = Ax + Cu, \quad y = Bx + Du
Answer: A) x˙=Ax+Bu,y=Cx+Du\dot{x} = Ax + Bu, \quad y = Cx + Du
9. What is meant by the “controllability” of a state-space system?
A) The ability to drive the system from any initial state to any desired final state using the control inputs
B) The ability to measure the system’s output accurately
C) The ability to observe the system’s behavior over time
D) The system’s response to external disturbances
Answer: A) The ability to drive the system from any initial state to any desired final state using the control inputs
10. What is “observability” in state-space systems?
A) The ability to reconstruct the system’s internal states from its outputs
B) The ability to control the system’s behavior through inputs
C) The system’s response to external disturbances
D) The ability to drive the system to a desired state
Answer: A) The ability to reconstruct the system’s internal states from its outputs