2-8 (a) (b) Y (s ) 3s + 1 Y (s) 5. = 3 2. = 4 2. R (s ) s + 2 s +5s + 6 R (s ) s + 10 s + s + 5. (c) (d) −s. Y (s ) s ( s + 2) Y ( Automatic Control Systems, 8th ed. (Solutions Manual)
It was one of the first editions to include virtual lab components to replicate physical systems. 2-8 (a) (b) Y (s ) 3s + 1 Y (s) 5
The solution involves an exponential term, likely from a time delay or specific input: R (s ) s + 2 s +5s + 6 R (s ) s + 10 s + s + 5
% 3. Desired poles (example: 2% overshoot, 0.5 s Ts) zeta = 0.78; % approx. for 2% overshoot wn = 4/(zeta*0.5); % natural frequency p1 = -zeta*wn + 1i*wn*sqrt(1-zeta^2); p2 = conj(p1); extraPoles = -10*wn*ones(1,size(A,1)-2); % fast poles desiredPoles = [p1 p2 extraPoles]; (Solutions Manual) It was one of the first
% 2. Check controllability & observability Co = ctrb(A,B); % controllability matrix Ob = obsv(A,C); % observability matrix assert(rank(Co)==size(A,1), 'System not controllable'); assert(rank(Ob)==size(A,1), 'System not observable');