ACT3701
EXAM PACK
2025
,ACT3701
Assessment 05
Due October 2025
, Assessment 5
A control system for a solar tracking mechanism is written in state-space form as
0 6 0
ẋ = Ax + Bu, A= , B = ,
−1 −5 1
where x contains the angular displacement θ and angular velocity ω, and u is a step
torque input.
Determine:
(a) The roots of the characteristic equation (the eigenvalues of A).
(b) The state transition matrix Φ(t) = eAt .
1
EXAM PACK
2025
,ACT3701
Assessment 05
Due October 2025
, Assessment 5
A control system for a solar tracking mechanism is written in state-space form as
0 6 0
ẋ = Ax + Bu, A= , B = ,
−1 −5 1
where x contains the angular displacement θ and angular velocity ω, and u is a step
torque input.
Determine:
(a) The roots of the characteristic equation (the eigenvalues of A).
(b) The state transition matrix Φ(t) = eAt .
1
