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I am a novice in control systems and just learned about PID controller.

So after watching tons of youtube videos I realized that the input of my plant is actually defined by the error. For the case of PID, when a gain multiplies to the error plus the integral of past errors plus the rate of change of error is the new input of my plant.

But what if my error is zero and plant works ideally? meaning there is no history of error being anything other than zero. So three terms have been and will be zero. Does that mean the input of my plant is zero? That means that the desired output of each plant always should have an input equal to zero so that it would be equal to the setpoint?

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But what if my error is zero and plant works ideally? meaning there is no history of error being anything other than zero. So three terms have been and will be zero. Does that mean the input of my plant is zero?

Yes.

That means that the desired output of each plant always should have an input equal to zero so that it would be equal to the setpoint?

No, at least not if I understand what you're saying. If the plant is "perfect" and linear, then for a setpoint that's not equal to zero, the error will start out high. The controller will try to push the plant to the setpoint. Eventually it'll get there, the error will asymptotically settle to zero, and the integrator term will asymptotically settle to whatever it needs to be to hold the plant output at the setpoint.

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