Controlling current through a RL load using Triac firing angle

I want to control the amount of current going through a Triac by adjusting the firing angle accordingly. The Circuit is shown below:

Let's say i want I_RMS to be 0.28A then the controller need to change α to be 90° according the formula:

My problem is I can't derive the Transfer function in order to calculate the needed parameters.Here is what i got so far:$$u(t)in = Vmax.sin(ωt)$$can also be described as:$$u(t)in = i(t)R + L\frac{di}{dt}$$Laplace Transformation gives:$$Vmax \frac{ω}{s²+ω²} = iR + L s i$$Then the Transfer function of the RL load is:$$G(s) = \frac{i}{Vmax} = \frac{\frac{ω}{s²+ω²}}{R+Ls}$$I am stuck here. There is no Correlation with α and the function is too complicated. The controller i am planning to use is a PT1 Controller with the following transfer function:$$G(s) = \frac{K}{1+Ts}$$At the end this will be programmed inside a Raspi Pico W.Can anyone shed some light on this?