KOKKRATHOKE, Surapong (2021). Nonlinear optimal control and its application to a two-wheeled robot. Doctoral, Sheffield Hallam University.
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Kokkrathoke_2021_PhD_NonlinearOptimalControl.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.
Kokkrathoke_2021_PhD_NonlinearOptimalControl.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.
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Abstract
This research studies two advanced nonlinear optimal control techniques, i.e.,
the freezing control and the iteration scheme, and their associated applications,
such as a single inverted pendulum (IP) on a cart system and a two-wheeled
robot (TWR) system. These techniques are applied to stabilise the highly
unstable nonlinear systems in the vertical upright position when facing different
initial pitch angles. Different linear optimal controllers (linear quadratic regulator
and linear quadratic Gaussian) and nonlinear optimal controllers are designed
and applied to the models for concurrent control of all state variables. The
controlled systems are tested in simulation and the best performing control design
is eventually implemented on a robot prototype built with an educational kit – the
LEGO EV3, after practical factors such as motor voltage limitation, gyro sensor
drift and model uncertainties have been considered, analysed and dealt with.
Simulations and experiments on the TWR robot prototype demonstrate the
superiority of the nonlinear freezing optimal control technique, showing larger
operation ranges of the robot pitch angle and better response performances (i.e.,
shorter rise time, less overshoot and reduced settling time) than the linear optimal
control methods. In particular, a novel mixing method to create a new nonlinear
model (Model AB) from two different models on the same physical prototype with
an increased controllable region of the TWR system is introduced, for the first
time, for the calculations of optimal feedback gains for the system. Significantly,
the utilisation of this mixed model, combined with the nonlinear freezing
controller, achieves true global control of the TWR, even from an initial pitch angle
of 90° (i.e., the horizontal position), when a motor with a saturated voltage of 48V
and nominal torque of 298 mNm is adopted in simulation tests. This is wider than
the angle achievable from the primary model (Model A) and any other single
feedback control method on TWR reported in the literature. Robustness tests
when introducing model uncertainties by adding mass and height on the TWR
also illustrate excellent control performances from the nonlinear optimal control
in both simulations and hardware implementations.
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