Infusion-pump Model- PID-controller- running very slow

I'm trying to implement a PID-controller for the attached system, where I have a transfer function that gives me the concentration of neuromuscular drug's concentration and then through Hill's eqaution, I obtain the neuromuscular blockade percentage given that I'm aiming for a NMB of 10% as the desired output. But it's running very slowly with $T \approx e^{-107}$. How should I tackle this issue or restructure this model?

P.S After using either 'ode15s' or 'ode23s', it showed a message as the following :"Derivative of state '1' in block 'Transfer Fcn' at time 2.6309053879766232E-108 is not finite. The simulation will be stopped. There may be a singularity in the solution. If not, try reducing the step size (either by reducing the fixed step size or by tightening the error tolerances)" I'm using \alpha as 0.0307, is this value concerning, what is this 'state 1' in this case, more precisely?

The first thing I would recommend exploring when you have a simulation nearly grinding to a halt with extremely small step size is trying a stiff solver.

https://www.mathworks.com/help/matlab/math/solve-stiff-odes.html https://www.mathworks.com/help/simulink/slref/exploring-variable-step-solvers-using-a-stiff-model.html

If that doesn't help, look into zero crossings or other problems using the Solver Profiler like @wolfie suggested. https://www.mathworks.com/help/simulink/slref/solverprofiler.html