PID Controller using elementary blocks

This example shows the simulation of a PID Controller used to stabilize a second order plant using

QFIRE Studio

.

Introduction

The

QFIRE CTR-101

implements a PID controller to control the plant represented by the transfer function below:

G(s)=1s2+1G(s)=\frac{1}{s^{2}+1}
Simulation

Originally, the PID controller was designed in [1] to be:

C(s)=2.3333(s+1)(s+0.5714)sC(s) = 2.3333 \frac{(s+1)(s+0.5714)}{s}

The corresponding proportional, integral, and derivative gains are respectively:

KP=3.66654762K_P = 3.66654762
,
KI=1.33324762K_I = 1.33324762
and
KD=2.3333K_D = 2.3333
, see Figure 1. As

QFIRE CTR-101

uses fixed-point, the values of the gains are not exactly the same as those designed, see Figure 1.

Figure 1 - PID Controller

The control task was configured to have a sampling period of

T=0.02sT=0.02s
as shown in Figure 2.

Figure 2 - Properties window of the

QFIRE CTR-101

block

In Figure 3, the control system includes:

QFIRE CTR-101

controller, plant, and a feedback loop.

Figure 3 - Control system

The plant is stabilized as in Figure 4.

Figure 4 - Unit-step response of the closed-loop system in Figure 3

Bibliographic References

[1] - Katsuhiko Ogata, Modern Control Engineering, Fourth Edition, Delhi: Pearson, 2003.

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