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I use 3 sensors and later with the data I got, I need to perform calculation (in which I also need trigonometric calculation) for my control. After that the result of the control is gonna actuate a actuator.
Given a choice of uc and fpga, which should I use? What critical here is time respond until the system become stable.
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This sounds like a microcontroller task. If sensors are analog voltages, they will need to be analog-to-digital converted; which for an FPGA requires an external component, but exists on a microcontroller.
If you are using actuators, then I would imaging your 'speeds' are quite slow. Well within the capabilities of microcontrollers .
For example, the STM32F4-Discovery kit is available from ST for free. Its got a 168MHz ARM Cortex-M4 core, with floating-point unit, fast I/O, USB, etc. That may even be overkill.
Cheers,
Dave