Essentials of Mechatronics

Chapter 10 - Further Control Theory

So far, we have followed the trend and concentrated on developing linear
theory. But in the world of mechatronics, very few systems are linear. We have
already seen a simulation in Section 6.5 that shows that drive limitation can
totally change the way that a system performs. Nonlinearity should be a prime
consideration in designing the controller. We will also find that nonlinear
elements can be very useful additions to the controller itself.

10.1   CONTROL TOPOLOGY AND NONLINEAR CONTROL

10.1.1   Feedback Topology


We have examined a position control system, a second-order system with a
single input. It has a characteristic equation determined by two coefficients
that are set by the position and velocity terms in the equation that determined
the acceleration. Putting it another way, if we decide on the roots that we want
for that characteristic equation, the feedback coefficients are uniquely
determined.

When there are more inputs than one, if all the state variables can be
measured, we have some freedom of choice in assigning the feedback coeffi-
cients. If the system is fourth-order and has two inputs, for example, there are
eight elements in the 2 × 4 feedback matrix. But these determine just four
coefficients in the characteristic polynomial.

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