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Ejemplos de controles analógicos: control de velocidad, control de posicionamiento, control de par, control de tensión, etc. ¿Qué tienen todos estos controles en común? Controlan processos rápidos. Sistema de controle em malha fechada com controle PID step response controller

Analyze the control behavior

Principle: A voltage jump of ideally 1V is applied to the input of the controller. The parameters of the controller are determined by means of the step response. We regard the P, I and D shares on their own:

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P-controller or proportional controller
A P-controller has an output signal u(t), that is proportional to the control error (u ~ e) without delay. As soon as the control error returns to the value 0, this controller does not have an output signal u any more. step response P-controller

Determine the parameter proportional gain factor Kp:  Kp  =   Δ u / Δe

Although a P-controller reacts immediately, a pure P-control has a permanent control deviation!

I-Controller or Integral-controller

The integral part is used for optimization because it can reduce a control deviation to zero. As you can see, the Integral force increases steadily as long as there is still a control deviation. When the control deviation is zero, the I-force remains at its constant value and reduces again only by a control deviation with opposite sign. step response Integral-controller

Determine of the parameters for the I-force:

Since the output signal of the I-force constantly changes during a control deviation, you would relate the slope of the I-force to the input quantity e:

Integral gain K :     K=   (Δ u / Δt) / Δ e  =    (u – u0) / (Δt  * Δe)

The unit of this integral gain KI is 1/s. Because this parameter is hard to understand for the user you would use the so-called Integral time, which represents the reciprocal: Integral-time I-controller

Integral time TI  =    1 /  K    =    (Δ t * Δe ) / Δu           (without regarding the sign)

To tell it in a few words: TI is the time until the output equals the level of the input signal.

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D-controller or Differential controller

The differential-part also serves for optimization. With its force, the controller reacts to a change of a control deviation very quickly. It also dampens the oscillation of the control. step response D-controller

The D controller reacts to a change in the control deviation! Problem: No parameters can be derived from the step response of a D controller. Trick: As input signal we use a ramp: Determine parameter of a D-controller

Derivative gain KD

K    Δ u _ _     =   Δ u *  Δt
.          Δ e /  Δt                Δe

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Exercise: Step response of a PI-Controller

Empirically, you have set the PID controller as best as possible with the following parameters:  KP = 1.5, Ti = 0.002 s

A voltage jump of 1 volt is applied to the input of the controller. Complete the step response of the P- and I-force as well as the combined PI controller on the solution sheet. Exercise Step-response PI-controller