I have a system whose the plant transfer function is continuous and the compensation is discrete. I have an ADC which allows to measure the output of the system and a DAC which allows to control the plant transfer function. The compensation is very slow with respect to the plant transfer function and it slows down the dynamics of the whole system.
I want to improve the discrete compensation by modelling the whole system and then build a compensation for achieve the performances whished. For this, firstly I would build a compensation into the s domain and then I will discretize it by the tustin method. Nevertheless, I want to have the effect of the discretization into the s domain otherwise my system could be stable in the s domain but it would be unstable into the z domain. So I need to place a ZoH for the DAC and use the padé approximation to get the ZoH transfer function into the s domain. But How can I do for having the effect of the sampler which is as slow as the DAC. I need to place a ZoH, ie to place a second padé approximation ?
Have a nice day,