How to estimate the frequency at certain time of linear sine sweep?
Frequency is the first derivative of the phase so in this case that's f0+(f0-f1)*t/T. If you plug in the numbers you get 110Hz, which is what your measurement shows. Not sure how you got 65Hz for that ??

It's intuitively clear as well. The sweep starts at 20 Hz and ends at 200 Hz after 60s. After 30s you should be at the half way point between 20 and 200, which is 110 Hz.

$$\varphi (t) = 2 \pi \cdot (f_{0}+\frac{f_{1}-f_{0}}{2T}\cdot t)\cdot t = 2 \pi \cdot (f_{0}\cdot t+\frac{f_{1} -f_{0}}{2T}\cdot t^{2})$$

$$f(t)=\frac{1}{2 \pi}\cdot \frac{\partial \phi}{\partial t}=f_{0}+\frac{f_{1}-f_{0}}{T}t$$