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Issue
110, September 1999
Internet
Control
by
Jacob Apkarian
Start
• Model Derivation
• Linearization • Control-System
Design • Simulation
•
Coding •
Configurations•
Implementation •
Tuning and Results •
Ready for Takeoff •
Software
and Sources •
Equations PDF
SIMULATION
Figure 2 shows the Simulink
model used to simulate the system. It consists of the
open-loop model, command generation, and the controller.
Figure
2—The
Simulink diagram consists of three main blocks:
the command generation block, the open-loop
model, and the controller.
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Figure 3 shows the open-loop
model, where system dynamics and measurement are simulated.
The A and B matrices are reduced to a set
of integrators and gains and the elevation integrator
is limited to positive values to simulate the helicopter
landing on the ground.
Figure
3—In
this open-loop model of the helicopter, the
A and B matrices are reduced to a set of integrators.
Quantizers simulate the quantization effect
of the encoders. High-pass filters are used
to obtain the derivative.
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The gravitational bias is
simulated by augmenting the motor voltages by the constants
minus Vq. Encoder measurements are simulated by
multiplying by a calibration constant that converts from
radians to degrees. The quantization effect is simulated
using a quantizer set to the resolution of the encoders.
The three displacement states
are differentiated using high-pass filters, as they would
be in the actual system. Numerical differentiation is
not recommended, and high-pass filters function as differentiators
at a frequency below the passband.
To evaluate the response
of the system, you need to generate the commands to the
elevation and travel axes. The command is for the elevation
to rise to various levels and the travel to go +60° and
return to zero.
Both commands are rate limited,
using rate-limiting blocks. This block can, of course,
be replaced by another input block (e.g., a joystick that
lets the user command the system directly).
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