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.
Table of Contents
1. Introduction
2. The Proposed Controllers Design
2.1 H∞ Mixed-Sensitivity Synthesis Method for Robust Control Loop Shaping Design of Inverted Pendulum
2.2. H∞ Loop Shaping Design Using Glover McFarlane Method Control of Inverted Pendulum
3. Result and Discussion
3.1 Simulation of the inverted pendulum without Controller
3.2 Simulation of the inverted pendulum with H∞ mixed sensitivity and H ∞ Loop shaping design using Glover McFarlane controllers using step input error voltage signal
3.3. Simulation of the inverted pendulum with H∞ mixed sensitivity and H ∞ Loop shaping design using Glover McFarlane controllers using Impulse input error voltage signal
3.4 Numerical Values of the Simulation Output
4. Conclusion
5. REFERENCES
Research Objectives and Topics
This paper aims to investigate and compare the performance of robust control theories applied to an inverted pendulum system. The primary research objective is to determine which control strategy—H∞ Mixed-Sensitivity or H∞ Loop Shaping using the Glover-McFarlane method—provides superior stabilization for the pendulum's angle when subjected to step and impulse input error voltage signals.
- Mathematical modeling of the inverted pendulum, DC motor, and cart mechanism.
- Application of H∞ Mixed-Sensitivity synthesis for robust control.
- Implementation of H∞ Loop Shaping using the Glover-McFarlane design method.
- Comparative analysis of transient response characteristics (rise time, settling time, and overshoot).
- Simulation and validation of system performance using MATLAB/Simulink.
Excerpt from the Book
1. Introduction
The inverted pendulum is the classical control device problem. It has a few idea like a hand as a cart and stick as a pendulum that's hand strive stability the stick. In addition, the inverted pendulum have confined movement that best can move proper and left meanwhile the hand which attempt to balance the stick has benefit can shifting upward and downward. An inverted pendulum does basically the identical issue. Just like the broom-stick, an inverted pendulum is an inherently unstable system. Force must be well implemented to hold the system intact. To achieve this, right control concept is needed.
The inverted pendulum is crucial in the evaluating and comparing of numerous control theories. The inverted pendulum (IP) is a number of the hardest systems to govern in the discipline of control engineering. Due to its significance within the area of Industrial control engineering, it's been select for very last year challenge to investigate its model and advocate a linear compensator consistent with the robust control system.
The hassle related to stabilization of Inverted Pendulum is a completely basic and benchmark problem of Control System. The design of Inverted Pendulum consists of a DC motor, Cart, Pendulum and Cart using mechanism. The nature of this machine is single input and multi output system in which Control voltage act as input and the output of the system are cart role and angle. Here we must stabilize the pendulum angle to Inverted role that is a challenging paintings to do as the Inverted position is an enormously unstable equilibrium.
Summary of Chapters
1. Introduction: Outlines the fundamental challenge of stabilizing an inverted pendulum and defines the scope of the study regarding robust control systems.
2. The Proposed Controllers Design: Details the mathematical and theoretical framework for the H∞ Mixed-Sensitivity and the H∞ Loop Shaping controllers.
3. Result and Discussion: Presents the comparative simulation outcomes for the uncontrolled system versus the two robustly controlled systems under various input signals.
4. Conclusion: Summarizes the study's findings, affirming the effectiveness of the H∞ Mixed-Sensitivity controller in optimizing performance metrics.
5. REFERENCES: Lists the academic literature and previous studies consulted during the research.
Keywords
Inverted pendulum, H∞ Loop Shaping Design Using Glover McFarlane, mixed H∞ Loop Shaping, robust control theory, Simulink, DC motor, cart-pendulum system, control engineering, system stabilization, sensitivity function, complementary sensitivity, mathematical modeling, transient response, rise time, settling time.
Frequently Asked Questions
What is the primary subject of this research?
This research focuses on the performance investigation and control stabilization of an inverted pendulum system using robust control theory.
What are the main control strategies evaluated in this paper?
The paper evaluates and compares the H∞ Mixed-Sensitivity Synthesis Method and the H∞ Loop Shaping Design using the Glover-McFarlane Method.
What is the ultimate goal of the proposed control systems?
The goal is to stabilize the pendulum angle at an inverted vertical position by minimizing rise time, settling time, and percentage overshoot when the system faces external disturbances.
Which scientific software is used for the simulation?
The study utilizes MATLAB/Simulink to model the system dynamics and verify the performance of the controllers.
What specific components are included in the mathematical model?
The model encompasses the inverted pendulum itself, a DC motor, the cart, and the mechanical cart-driving assembly.
How are the controllers characterized by keywords?
Key terms include inverted pendulum, robust control theory, H∞ Loop Shaping, Glover-McFarlane method, and mixed H∞ Loop Shaping.
Why is the inverted pendulum considered a benchmark problem?
It is highly unstable, non-linear, and under-actuated, making it a rigorous test case for evaluating the effectiveness of control algorithms in engineering.
Which controller yielded better simulation results?
The simulation results indicate that the H∞ Mixed-Sensitivity controller outperformed the H∞ Loop Shaping (Glover-McFarlane) design regarding response speed and overshoot.
What role do weighting functions W1, W2, and W3 play?
These functions are used to shape the sensitivity and complementary sensitivity transfer functions to ensure both good disturbance attenuation and stability margins.
What happens to the pendulum during the simulation of the "without controller" scenario?
Without a controller, the system demonstrates an inherently unstable response, as it lacks the active force required to maintain the upright equilibrium.
- Arbeit zitieren
- Mustefa Jibril (Autor:in), 2020, Robust Control Theory Based Performance Investigation Of An Inverted Pendulum System Using Simulink, München, GRIN Verlag, https://www.grin.com/document/542102
