Using the same technique as before, the
nonlinear system (52) can be exactly converted into the following two-rule polynomial fuzzy system:
The previous assumptions are not very restrictive and they can be verified for a large class of MIMO
nonlinear systems. The appropriate state observer can be rewritten in the following form:
However, when the analytical equations of the
nonlinear system is available, a TS model can be obtained by linearizing around different selected operation points [25].
The control law of the
nonlinear system in the performance index is
Since the 1990s, the research of output regulation of
nonlinear systems has been concentrated on.
PID controller demonstrates weak tracking performance since classical linear control methods do not work well on controlling
nonlinear systems. This situation can be seen in Figure 6 b clearly.
A general
nonlinear system can be described by the following equation:
Wang, "Dropping damage evaluation for a tangent
nonlinear system with a critical component," Computers & Mathematics with Applications, vol.
Modelling of many
nonlinear systems is based on Hammerstein and Wiener models, as can be also proven by many publications during last years.
Problem statement: Consider a
nonlinear system P and a model G, described by the transfer functions