DP5_1.m

syms s;
syms K;
para_k = [0.7 3 6];

Ga = K / (s + 7);
Gd = 12.2 / (s * (s + 2.2));

Gc = Ga * Gd;
T = Gc / (1 + Gc);
T = simplify(expand(T))

for i = 1:3
    figure(i);
    k = para_k(i);
    T_origin = tf([61 * k], [5, 46, 77, 61*k]);
    step(T_origin);
    info = stepinfo(T_origin);
    disp('before:');
    fprintf('overshoot = %f,\n peaktime = %f\n', info.Peak, info.PeakTime);
    hold;
    
    poles = roots([5  46  77  61*k])
    %挑出最左邊的pole，也就是實部最小的pole
    ignore = 1;
    for j = 1:3
        if real(poles(j)) < real(poles(ignore))
            ignore = j;
        end
    end
    compensate = poles(ignore);
    %把那個pole省略掉
    poles(ignore) = [];
    T_ignored = zpk([], poles, -61*k/compensate/5);
    step(T_ignored);
    info = stepinfo(T_ignored)
    disp('after:');
    fprintf('Overshoot = %f, \n Peak Time = %f\n', info.Peak, info.PeakTime)
    legend('before', 'after');
    fprintf('------------------------------');
    
    
end

k0 = 7;
T_origin = tf([61 * k0], [5, 46, 77, 61*k0]);
info = stepinfo(T_origin);

iter = 200;
L = 0;
R = 7;
M = 0;
while iter > 0
    M = (L + R) / 2;
    
    T_origin = tf([61 * M], [5, 46, 77, 61*M]);
    info = stepinfo(T_origin); 
    if(info.Overshoot < 16) L = M;
    else R = M;
    end
    iter = iter - 1;
end
M
figure(4);
step(T_origin);
stepinfo(T_origin)