Majalah Ilmiah UNIKOM
Vol.9, No. 2
210
H a l a m a n
DESIGNING THE CONTROL SYSTEM
In this section a linear Proportional-
Integral-Derivative (PID) controller is
designed to regulate the elevation and
travel angles of the 3-DOF Helicopter to
desired positions. The PID control gains
are computed using the Linear-Quadratic
Regular algorithm.
Using the weighting matrices
and
and the state-space matrices (A,B) found
previously, the control gain
is calculated by minimizing the cost
function
with the Matlab LQR command. Examining
the feedback gains obtained from LQR
design, we note the following feature : the
second row gains have the exact same
magnitudes as the first row.
Further examination reveals that the sum
of the rows results in :
which can be re-written as
which is the Proportional+Integral+
Derivative (PID) controller about the
elevation axis.
Examining the difference between the
gains, the feedback loop can be
decomposed into two loops : one for pitch
and one for travel.
The above equation can be re-written as.
which is a PD loop to command the pitch
to track the desired pitch. The desired
pitch is defined as.
which is another PID loop that controls the
travel position. We now have the following
control equations.
Muhammad Aria
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