Question

4. a) Briefly describe advantages that state space techniques have over classical control techniques. [4 marks] b) A missile in flight, as shown in Figure Q4, is subject to several forces: thrust, lift, and drag. The missile flies at an angle of attack, $\alpha$, from its longitudinal axis, creating lift. For steering, the body angle from vertical, $\phi$, is controlled by rotating the engine at the tail. The transfer function relating the body angle, $\phi$, to the angular displacement, $\delta$, of the engine is of the form $\frac{\phi(s)}{\delta(s)} = \frac{20(s + 5)}{(s + 1)(s + 4)}$ Vertical Velocity $\alpha$ Lift Drag Thrust Figure Q4: A missile in flight. Determine the following i) Draw the state space controller block diagram in phase variable form write down the state and output equation for the missile steering control. [5 marks] ii) Calculate the controllability matrix M and the observability matrix N and demonstrate that the system is fully controllable and fully observable control. [4 marks] iii) Determine the controller feedback gains to yield 2% overshoot and a settling time of one second. [7 marks] (Total Q4: 20 marks)

          4.
a) Briefly describe advantages that state space techniques have over classical control
techniques.
[4 marks]
b) A missile in flight, as shown in Figure Q4, is subject to several forces: thrust, lift, and
drag. The missile flies at an angle of attack, $\alpha$, from its longitudinal axis, creating lift.
For steering, the body angle from vertical, $\phi$, is controlled by rotating the engine at the
tail. The transfer function relating the body angle, $\phi$, to the angular displacement, $\delta$, of
the engine is of the form
$\frac{\phi(s)}{\delta(s)} = \frac{20(s + 5)}{(s + 1)(s + 4)}$
Vertical
Velocity
$\alpha$
Lift
Drag
Thrust
Figure Q4: A missile in flight.
Determine the following
i) Draw the state space controller block diagram in phase variable form write down the
state and output equation for the missile steering control.
[5 marks]
ii) Calculate the controllability matrix M and the observability matrix N and demonstrate
that the system is fully controllable and fully observable control.
[4 marks]
iii) Determine the controller feedback gains to yield 2% overshoot and a settling time of
one second.
[7 marks]
(Total Q4: 20 marks)

4.
a) Briefly describe advantages that state space techniques have over classical control
techniques.
[4 marks]
b) A missile in flight, as shown in Figure Q4, is subject to several forces: thrust, lift, and
drag. The missile flies at an angle of attack, α, from its longitudinal axis, creating lift.
For steering, the body angle from vertical, ϕ, is controlled by rotating the engine at the
tail. The transfer function relating the body angle, ϕ, to the angular displacement, δ, of
the engine is of the form
(ϕ(s))/(δ(s)) = (20(s + 5))/((s + 1)(s + 4))
Vertical
Velocity
α
Lift
Drag
Thrust
Figure Q4: A missile in flight.
Determine the following
i) Draw the state space controller block diagram in phase variable form write down the
state and output equation for the missile steering control.
[5 marks]
ii) Calculate the controllability matrix M and the observability matrix N and demonstrate
that the system is fully controllable and fully observable control.
[4 marks]
iii) Determine the controller feedback gains to yield 2% overshoot and a settling time of
one second.
[7 marks]
(Total Q4: 20 marks)

Added by Margarita E.

Question

Please give Ace some feedback