# What does Ki*Ts mean in Discrete PI controller ?

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jefazo jefazo on 15 Apr 2020
Hi everyone,
I am using a Discrete PI controller for an FOC algorithm I am developing in Simulink using the Motor Control Blockset. I would like to use a Ki gain if 2. At the input of the block, I have an input labelled Ki*Ts. If I use my gain with a sampling period of, let's say, 1ms, should Ki*Ts = 2e-3 ? What would be an appropiate sampling period (Ts) and what would be the reason for it ? Please any help would be really appreciated.

Sharat Yadav on 2 Dec 2020
I think the answer by Jesus clears the question, I am adding few points which one might find helpful.
• For the Ki gain of value 2, The value of Ki*Ts = 2*Ts, where Ts is the sample time of the block, which in many cases is the sample time of the algorithm where the block is used.
• One can refer any of the shipping demo of MCB (Motor Control Blockset) for clear understanding on how to decide the value of Ts. for eg: mcb_pmsm_foc_qep_f28379d, https://www.mathworks.com/help/mcb/gs/foc-pmsm-using-quadrature-encoder.html

Jesús Zambrano on 18 Apr 2020
From the documentation about the meaning of Ki*Ts, it indicates that: "You must premultiply the integral gain value by the integrator sample time (Ts) for the block to execute within asynchronous interrupts."
About: What would be an appropiate sampling period (Ts) and what would be the reason for it ?
This depends on your specific application. The sample time of the signal you want to implement the PI controller will give you this answer.

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