Robust Control Theory Based Performance Investigation of an Inverted Pendulum System using Simulink

In this paper, the performance of inverted pendulum have been Investigated using robust control theory. The robust controllers used in this paper are H∞ Loop Shaping Design Using Glover McFarlane Method and mixed H∞ Loop Shaping Controllers. The mathematical model of Inverted Pendulum, a DC motor, Cart and Cart driving mechanism have been done successfully. Comparison of an inverted pendulum with H∞ Loop Shaping Design Using Glover McFarlane Method and H∞ Loop Shaping Controllers for a control target deviation of an angle from vertical of the inverted pendulum using two input signals (step and impulse). The simulation result shows that the inverted pendulum with mixed H∞ Loop Shaping Controller to have a small rise time, settling time and percentage overshoot in the step response and having a good response in the impulse response too. Finally the inverted pendulum with mixed H∞ Loop Shaping Controller shows the best performance in the overall simulation result

Regression between headmaster leadership, task load and job satisfaction of special education integration program teacher

Managing school is a daunting task for a headmaster. This responsibility is exacerbated when it involves the Special Education Integration Program (SEIP). This situation requires appropriate and effective leadership in addressing some of the issues that are currently taking place at SEIP such as task load and job satisfaction. This study aimed to identify the influence of headmaster leadership on task load and teacher job satisfaction at SEIP. This quantitative study was conducted by distributing 400 sets of randomized questionnaires to SEIP teachers across Malaysia through google form. The data obtained were then analyzed using Structural Equation Modeling (SEM) and AMOS software. The results show that there is a significant positive effect on the leadership of the headmaster and the task load of the teacher. Likewise, the construct of task load and teacher job satisfaction has a significant positive effect. However, for the construct of headmaster leadership and teacher job satisfaction, there was no significant positive relationship. This finding is very important as a reference to the school administration re-evaluating their leadership so as not to burden SEIP teachers and to give them job satisfaction. In addition, the findings of this study can also serve as a guide for SEIP teachers to increase awareness of the importance of managing their tasks. This study also focused on education leadership in general and more specifically on special education leadership

Backstepping Sliding Mode Control for Inverted Pendulum System with Disturbance and Parameter Uncertainty

The inverted pendulum system is highly popular in control system applications and has the characteristics of unstable, nonlinear, and fast dynamics. A nonlinear controller is needed to control a system with these characteristics. In addition, there are disturbances and parameter uncertainty issues to be solved in the inverted pendulum system. Therefore, this study uses a nonlinear controller, which is the backstepping sliding mode control. The controller is robust to parameter uncertainty and disturbances so that it is suitable for controlling an inverted pendulum system. Based on testing with step and sine reference signals without interference, the controller can stabilize the system well and has a fast response. In testing with disturbances and mass uncertainty, the backstepping sliding mode controller is robust against these changes and able to make the system reach the reference value. Compared with sliding mode control, backstepping sliding mode control has a better and more robust response to disturbances and parameter uncertainty

Synthesis of LQR Controller Based on BAT Algorithm for Furuta Pendulum Stabilization

In this study, a controller design method based on the LQR method and BAT algorithm is presented for the Furuta pendulum stabilization system. Determine the LQR controller, it is often based on the designer's experience or using trial and error to find the Q, R matrices. The BAT search algorithm is based on the characteristics of the bat population in the wild. However, there are advantages to finding multivariate objective functions. The BAT algorithm has an improvement for the LQR controller to optimize the linear square function with fast response time, low energy consumption, overshoot, and a small number of oscillations. Swarm optimization algorithms have advantages in finding global extrema of multivariate functions. Therefore, with a large number of elements of the Q and R matrices, they can also be quickly found and these matrices still satisfy the Riccati equation. The controller with optimal parameters is verified through simulation results with different scenarios. The performance of the proposed controller is compared with a conventional LQR controller and implemented on a real system

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Finite-Time State Estimation for an Inverted Pendulum under Input-Multiplicative Uncertainty

A sliding mode observer is presented, which is rigorously proven to achieve finite-time state estimation of a dual-parallel underactuated (i.e., single-input multi-output) cart inverted pendulum system in the presence of parametric uncertainty. A salient feature of the proposed sliding mode observer design is that a rigorous analysis is provided, which proves finite-time estimation of the complete system state in the presence of input-multiplicative parametric uncertainty. The performance of the proposed observer design is demonstrated through numerical case studies using both sliding mode control (SMC)- and linear quadratic regulator (LQR)-based closed-loop control systems. The main contribution presented here is the rigorous analysis of the finite-time state estimator under input-multiplicative parametric uncertainty in addition to a comparative numerical study that quantifies the performance improvement that is achieved by formally incorporating the proposed compensator for input-multiplicative parametric uncertainty in the observer. In summary, our results show performance improvements when applied to both SMC- and LQR-based control systems, with results that include a reduction in the root-mean square error of up to 39% in translational regulation control and a reduction of up to 29% in pendulum angular control

Design Of Linear Quadratic Regulator Controller With Adjustable Gain Function For Rotary Inverted Pendulum System

Design of controllers for non-linear systems has long drawn the attention of researchers especially in the fields of robotics, aerospace engineering and marine engineering. A classic example of a non-linear under-actuated control system is the balance control for a rotary inverted pendulum. Basically, the control approach for such system focusses on torque control of the servo-motor for the purpose of rotating the arm and stabilising the pendulum in its upright position at the shortest possible time. The aim of this research is to supplement and further enhance the control performance of a linear quadratic regulator (LQR) controller with focus on reduced response time and degree of oscillation of the pendulum with added robustness against input disturbance applied to the pendulum position and voltage to the motor. Initially, this thesis comprehensively analysed the LQR controller parameters based on minimal balance time of the pendulum. The LQR controller by itself produced high degree of oscillations, long balance time and poor robustness against input disturbance. As an enhancement over this approach, an adjustable gain was added to the existing LQR control structure. The results showed that for a 30° balancing control, the LQR controller with adjustable gain managed to reduce as much as 70% in the balance time and 98% in the degree of oscillation, while improved its robustness by producing faster balance time and lower oscillation upon excitation by input disturbance forces. In conclusion, the LQR controller with adjustable gain has significantly improved the control performance of the rotary inverted pendulum system