Article Preview
TopIntroduction
Control and modeling of an inverted pendulum system (IPS) are essential for the autonomous movement of many robotic based applications. The IPS consists of a cart connected to a pendulum via a pivot point. The system is a single input and multi-outputs (SIMO) system. The force on the cart represents the system input while the cart position and the pendulum angle represent the outputs of the systems. It will be complicated to use conventional control techniques in stabilizing cart position or swinging up the pendulum of IPS due to the inherent instability and the uncertainty of the system (El-Bardini & El-Nagar, 2014). IPS is used in various fields such as artificial intelligence, launching of the rockets, nuclear facilities, self- balancing robots, space satellites, intelligent transport systems like segways and jetpacks, heavy cranes in shipyards and earthquake-resistant building design (Papadopoulos & Alexandridis, 2016). The dynamics of the IPS is similar to the dynamics of rocket launcher as the gravity center is behind the drag center, which leads to aerodynamics instability (Krishna, Bindhu, & Vinod, 2016). However, the construction of the IPS is simple; many control challenges exist due to its extremely characteristics such as instability, non-linearity, non-minimum phase and under-actuated system, uncertainty and limitations (Salleh & Shamsudin, 2017). In this research work, the system is considered as SIMO system equipped with new variant of Variable Structure Adaptive Fuzzy (VSAF) based controllers in addition to new Reduced Order Linear Quadratic Regulator (RLQR). One of the main problems of using conventional fuzzy logic control is the fixed rules property, which makes Fuzzy Logic Controller (FLC) may fail in achieving the balancing of nonlinear systems during continuous variation in the operating conditions (Roose, Yahya, & Al-Rizzo, 2017). Linear Quadratic Regulator (LQR) is based on two fundamental weighting matrices Q and R. Q matrix defines the weights of the state variables while R matrix defines the weight of control signal. Some research works selected these two matrices based on trial and error (Marada, Matousek, & Zuth, 2017). In this research work, the two matrices are optimized using a modified Grey Wolf Optimizer (GWO) with Adaptive Constants (AC) property via Particle Swarm Optimization technique (GWO/PSO-AC), which makes the gain more accurate to balance the IPS. The parameters required to generate Q and R matrices are reduced from seventeen parameters to nine parameters (47% reduction level) according to a specific criterion, ensuring positive semi-definite and positive definite for two matrices, respectively. GWO/PSO-AC is used to optimize the VSAF controller with feed forward gain and RLQR gain. One of the main problems in GWO algorithm is the slow convergence speed and low precision. The motion of wolves is based on random values without any velocity vector update (ERKOL, 2018). However, some researches show modification to GWO by hybrid GWO with the PSO technique to enhance its performance as presented in (Singh & Singh, 2017). In this research work, GWO/PSO-AC is proposed based on using adaptive constants in the optimization process.
The organization of this article is as follows: Section 2 introduces the related work. Section 3 shows the mathematical modeling of the IPS. Section 4 displays the employed control techniques that are used in controlling the IPS. Section 5 presents the control strategy containing the design procedures of the proposed new VSAF and RLQR gains with feed forward gain (Kf) that is applied to the IPS. Section 6 provides simulation results of an IPS and tests it in different control conditions. Section 7 finalizes the research work with the conclusion and the perspectives.