Feedback Linearization Control

This example shows the simulation of a non-linear control system from [1] with feedback linearization control technique using

QFIRE Studio

.

Introduction

The non-linear plant is described by:

x1˙=x1sinx1+x2x˙2=u\begin{align*}\dot{x_{1}}& = x_{1}\sin x_{1}+x_{2} \\ \dot{x}_{2}& = u\end{align*}

The dynamic system equations are written in a block diagram as shown in Figure 1.

Figure 1 - Non-linear plant block diagram

Simulation

A feedback linearization control law with non-linear terms can be used to stabilize the plant. Figure 2 shows the block diagram with the implementation.

Figure 2 - Non-linear controller diagram

Figure 3 - Non-linear control system

Figure 4 shows the closed-loop system with the non-linear plant and corresponding control law, starting from the initial state

x1=20x_{1}=20
and
x2=0x_{2}=0
.

Figure 4 - State 1 (blue) and state 2 (orange)

The (unconstrained) control signal amplitude prior to conversion to analog can be observed in Figure 5.

Figure 5 - Control signal

Bibliographic References

[1] Härkegårds O., 2003.

BACKSTEPPING AND CONTROL ALLOCATION WITH APPLICATIONS TO FLIGHT CONTROL

.

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