School of Electrical Engineering and Telecommunications
ELEC4632 Computer Control Systems
Final Examination, Term 3, 2023
Question 1 (10 marks)
Sample the continuous-time system
y(t) =( -3 4 -2 )x(t) using the sampling interval h = 0.25.
Question 2 (10 marks)
A discrete-time control system is described by
where the parameter a varies from -∞ to +∞ . Determine for which values of the parameter a this system is
(a) reachable; (b) controllable.
Question 3 (10 marks)
Given the system
y(k) =( 1 0 )x(k). Design deadbeat output feedback control law.
Question 4 (10 marks)
The characteristic equation of a discrete-time control system is given by z3 - 0.25z2 + Kz - 0.25K = 0
where the parameter K varies from -∞ to +∞ . Determine the range of the parameter K for stability.
Question 5 (10 marks)
Consider the following nonlinear discrete-time system
x(k + 1) = -x(k)3 - y(k) - y(k)3 , y(k + 1) = -x(k) - x(k)3 - y(k)3 .
(a) Is this system globally asymptotically stable?
(b) Is the singular point (0, 0) of this system asymptotically stable?
(c) Is the singular point (0, 0) of this system stable in the sense of Lyapunov?
Question 6 (10 marks)
Consider the optimal control problem for the system x(k + 1) = 3x(k) + u(k)
with initial condition x(0) = 1. Determine the optimal control strategy and the optimal value of the cost function for the cost function
(a) → min;
20
(b) → min;
(c) → min .
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