Estimate first order transfer function from Phase at Frequency

What command would I use to estimate a first order transfer function (TF), from a known Phase at Frequency?

The TF is known order (first-order), known gain of 1 at DC, and monotically decreasing phase (ie only passes through a phase value once).

Let's say the given data point is a phase P at freq F (say, -45 deg at 100 Hz).

How would I programatically find the TF that includes this datapoint?

The TF should be unique, once the TF order, DC gain, monotically decreasing phase is assumed, and P&F are defined.

I looked at tfest using iddata, and other similar commands, but non are exactly what I'm looking for...

Answer 1

[Paul]

@John

Based on the problem statement can you write the symbolic form of a first order transfer function, H(s)? How many free parameters does H(s) have? Given that angle(H(1j*(2*pi*100)) = -45*pi/180 (example data from the Question), can you solve for the free parameter(s)? Don't make the problem more complicated than it needs to be.

[John]

Apologies, I'll clarify: this is for arbitrary N-order TF, since the 1st-O example is simple (as you pointed out).

I'm looking for a more general programmatic way to find what TF(s) could fit, with a defined phase/freq point.

[Paul]

Oh, well that's a bit different. Specifying the phase at a single frequency is not enough information to uniquely specify the parameters of an arbitrary n-th order TF, even with the stated constraints. The problem will require additional constraints or some cost that to be optimized among all TFs that satisfy the stated constraints. Additionally, I think it could be very tricky to define the constraints on the TF to enforce the monotonically decreasing phase for a general TF.