Why do I receive a warning when analyzing transfer functions which have zeros/poles that do not exist as complex-conjugate pairs using the Control System Toolbox?

I get the following warning when I analyze my transfer function that has complex roots with zeros/poles that do not exist as complex-conjugate pairs:

>> zpk([1+1i],[1i],1,1)

Warning: Not all complex roots come in conjugate pairs (transfer function has complex coefficients).

> In zpk.zpk at 246

Zero/pole/gain:

(z-(1+1i))

----------

    (z-i)

Sampling time: 1

I get similar warnings when using the following functions:

 BODE, STEP, IMPULSE, LSIM, DLSIM

Answer 1

[MathWorks Support Team]

The Control System Toolbox has limited support for such systems. However, you can determine the frequency response of the system using the FREQRESP command. The following code illustrates how you can plot the output of FREQRESP for both the positive and negative frequencies:

wc = 2*pi*500;

wf = 2*pi*100;

wbw = 2*pi*100;

num = conv([1 j*(wc-2*wf)],[1-j*wc]);

den = conv([1 (wbw+j*wc-j*2*wf)],[1 (wbw-j*wc)]);

sys = tf(num,den);

% specify frequency grid w or can generate it using bode

[m,p,w] = bode(sys); % generate freqeuncy grid

sysfrdpos = frd(freqresp(sys,w),w); % positive freqeuncy response

sysfrdneg = frd(freqresp(sys,-w),w); % negative frequency response

bode(sysfrdpos,sysfrdneg) % plot both positive and negative frequencies

Please note that the frequency vector for “sysfrdneg” is actually abs(w) because the bode plot usually has a log scale frequency axes for which negative values are not defined.