A highperformance aircraft uses ailerons rudder and elevator

A high-performance aircraft uses ailerons, rudder. and elevator to steer through a three-dimensional flight path. The pitch rate control system for a fighter aircraft at 10.000 m and Mach 0.9 can be represented by the system in the figure below. The transfer function for the aircraft is G(s) = -18(s+0.015)(s+0.45)/(s^2+1.2s+12)(s^2+0.01s + 0.0025) Plot the squareroot locus when D is a proportional controller, so that D(s) = K. and determine the value of K when for the squareroot s with omega_n > 2 is larger than 0.15. (Seek a maximum). Plot the response q(t) for a step input r(t) with the K value chosen in Part (a). Does the closed loop system behave as if it is larger than 0.15? Explain the behavior. A designed suggests an anticipatory controller with D(s) = K(s+2). Plot the squareroot locus for this system as K varies and determine a K so that the of all the closed-loop poles is > 0.8. Plot the response q(t) for a step input r(t) with K from Part (c). Does the closed loop system behave as if for all poles is larger than 0.8? Explain the behavior. In your write-up. include A summary of what you did in the problem explaining what techniques you used and what skills you learned and or applied. Answers to questions posed in (a) - (d) with explain Commented MATLAB code.

Solution

After using the “rlocus” command, use the “axis equal” command to make the resize the root locus plot appropriately. You may need to zoom in to see what’s happening. The “sgrid” command can help identify the appropriate value of K on the root locus plot. Clicking on the root locus plot will show values of gain (K), damping ( ), and undamped natural frequency (wn).