How to deal with "weird" phase plots in bode diagram when designing a controller I am trying to design a balance controller for a robot. With MATLAB simulink I arrived at the transfer function between the input and the pitch angle for the robot. I have plotted the bode and Nyquist plot below.

As you can see, the Nyquist plot looks very weird, and in the bode diagram the signals at low frequencies are attenuated. To fix this, I added a zero at the peak of the magnitude plot, so
$$\omega_i=10 \text{rad}/s \Rightarrow \tau_i = \frac{1}{\omega_i}=0.1\text{s}$$
This results in an I-term which looks like this: $C_i(s)= \frac{\tau_is+1}{\tau_is}=\frac{0.1s+1}{0.1s}$
When I add this to the controller the bode plot now becomes.

Now I also want to add a lead-term to prevent overshoots but the way I usually do that is to change the crossover frequency $\omega_c$ such that there is good phase margin, define some constant $\alpha$, and then find the lead term with the formula $\tau_d = \frac{1}{\omega_c \sqrt{\alpha}}$. Then I can make my lead-term with
$$C_d = \frac{\tau_d s + 1}{\alpha \tau_d s + 1} $$
But when I look at the current phase plot, it all around looks like there is no trouble regarding the phase margin. The phase is never close to $-180^{\circ}$ so I am not sure how to proceed with such a weird looking phase plot.
So my question is, how do I find my lead-term when the phase plot looks like this? Is there another way to do than I have proposed?
Edit
The open loop transfer function between the input and pitch angle is $G(s) = \frac{ 5.893e05 s^4 + 7.71e08 s^3 + 1.435e11 s^2 + 2.566e12 s + 7.683e09}{s^7 + 2418 s^6 + 1.317e06 s^5 + 1.977e08 s^4 + 1.312e10 s^3 + 1.796e11 s^2 - 9.658e11 s - 1.525e13}$
Using the &quot;pole&quot; command in MATLAB I noticed that there was a pole in the RHP which should cause some instability.
I'm a bit puzzled with your Bode plot, here's what I get with your transfer function and Matlab 2019b. My phase starts at almost -180 degrees while yours start at 0 degree. Is it possible that you've made a mistake somewhere in your analysis?

Your transfer function is a bit complex, you could simplify it by removing the fast poles and zeroes. For example, you have 2 fast poles at -1714 and -516 and a fast zero at -1088. You can remove the 2 fast poles and the fast zero to simplify your transfer function. This will make your analysis easier.
Secondly, I think the rule-of-thumb formulae you use for the cross-over frequency is only valid when your open loop system has a low-pass characteristic. Your system has a band-pass characteristic.