Hi Jack,
You can do the list of actions you mentioned by using the pid, pidtuneOptions, pidtune functions. As an example, using a similar third order system you have shown, you can do something like this:
sys = tf(1,[1 3 3 1]);
C_0 = pid(1,1,1); % Parallel form PID controller object with initial gains
gm = 0.80 % Gain margin
pm = 45 % Phase margin
opts = pidtuneOptions('PhaseMargin',pm,'DesignFocus','disturbance-rejection');% Set your tuning options
[C,info] = pidtune(sys,C_0, gm,opts);
>> C
C =
1
Kp + Ki * --- + Kd * s
s
with Kp = 1.99, Ki = 1.11, Kd = 0.885
Continuous-time PID controller in parallel form.
>> info
info =
struct with fields:
Stable: 1
CrossoverFrequency: 0.8000
PhaseMargin: 45
