{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Sol_HW5

# Sol_HW5 - 3.32 In aircraft control systems an ideal pitch...

This preview shows pages 1–3. Sign up to view the full content.

1 2 0 2 2 3.32 In aircraft control systems, an ideal pitch response ( ) versus a pitch command ( ) is described by the transfer function ( ) ( 1/ ) ( ) 2 The o c n c n n q q Q s s Q s s s τω τ ζω ω + = + + actual aircraft response is more complicated than this ideal transfer function; nevertheless, the ideal model is used as a guide for autopilot design. Assume that is the desired rise time, r t and that 1.789 1 1.6 0.89 Show that this ideal response possesses a fast settling time and minimal overshoot by plotting n r r t t ω τ ζ = = = the step response for 0.8, 1.0, 1.2, and 1.5 sec. r t = Solution: The following program statements in MATLAB produce the following plots: % Problem 3.32 tr = [0.8 1.0 1.2 1.5]; t=[1:240]/30; tback=fliplr(t); clf; for I=1:4, wn=(1.789)/tr(I); %Rads/second tau=tr(I)/(1.6); %tau zeta=0.89; % b=tau*(wn^2)*[1 1/tau]; a=[1 2*zeta*wn (wn^2)]; y=step(b,a,t); subplot(2,2,I); plot(t,y); titletext=sprintf('tr=%3.1f seconds',tr(I)); title(titletext); xlabel('t (seconds)'); ylabel('Qo/Qc'); ymax=(max(y)-1)*100; msg=sprintf('Max overshoot=%3.1f%%',ymax); text(.50,.30,msg); yback=flipud(y); yind=find(abs(yback-1)>0.01); ts=tback(min(yind)); msg=sprintf('Settling time =%3.1f sec',ts); text(.50,.10,msg); grid; end

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document