الفهرس 
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Abstract
The inherited instability of the inverted pendulum system (IPS) makes it one of
the most difficult nonlinear problems in the control theory. This system is nonlinear,
unstable, non-minimum phase and under-actuated. The problem of finding a control
law such that a certain optimality criterion is a highly demand for stabilizing IPS.
Selecting optimal values for Linear Quadratic (LQ) control to reach a desired
degree of stability when stabilizing IPS is done usually via trial and error process,
which is time-consuming, cumbersome and results are in a non-optimized
performance. A proposed control algorithm ”Modified Linear Quadratic Gaussian
(LQG) based on prescribed degree of stability (PDOS)” (MLQG) is presented.
MLQG control algorithm is a hybrid of the LQG controller and the PDOS
technique. The proposed MLQG controller is capable of solving the problem related
to the time wasted in selecting the optimal values for LQ control with a guaranteed
desired degree of stability.
However, when IPS swings over a wide range, its nonlinear dynamics becomes
significant and the stabilization of IPS becomes challenging task due to the
inconsistency between its nonlinear dynamics and the controllers designed based on
linearized models. Hence, to address this problem, an improvement of MLQG
controller has been added, and a proposed ”Nonlinear Sigma Point Kalman Filter
(SPKF) based Time-varying LQG” (TV-LQG) is presented.
This thesis also introduced a proposed algorithm to identify a model for the IPS
in a fractional nature. The proposed algorithm finds a fractional order model (FOM)
of the IPS based on simulated and experimental data. To solve the identification and
optimization problem, sine-cosine algorithm (SCA) is adopted.
All the proposed methods are benchmarked against previously recent techniques
and implemented using the MATLAB® environment for simulation purposes and
with Arduino Mega 2560 microcontroller board for practical implementation.
Algorithms described in this thesis were successful and consistently produced the
satisfactory results.