Real Time Optimal Implementation Of Stabilizing Controller For Inverted Pendulum

This paper present real time control of an inverted pendulum. The system is inherently unstable, nonlinear and under-actuated system. The dynamic model of the system was derived based on Lagrange approach and it was linearized about an appropriate operating point by the use of Taylor’s series approximation. Linear Quadratic Regulator (LQR) controller was designed to stabilize the system in an upright position. The robustness of the control algorithm was tested based on disturbance rejection. Simulation and Experimental results show a good performance was achieved and the controller is robust to external disturbances

Control of a modified double inverted pendulum using machine learning based model predictive control

Abstract: A machine learning-based controller (MLC) has been developed for a modified double inverted pendulum on a cart (MDIPC). First, the governing differential equations of the system are derived using the Lagrangian method. Then, a dataset is generated to train and test the machine learning-based models of the plant. Different types of machine learning models such as artificial neural networks (ANN), deep neural networks (DNN), long-short-term memory neural networks (LSTM), gated recurrent unit (GRU), and recurrent neural networks (RNN) are employed to capture the system’s dynamics. DNN and LSTM are selected due to their superior performance compared to other models. Finally, different variations of the Model Predictive Controller (MPC) are designed, and their performance is evaluated in terms of running time and tracking error. The proposed control methods are shown to have an advantage over the conventional nonlinear and linear model predictive control methods in simulation.Communication présentée lors du congrès international tenu conjointement par Canadian Society for Mechanical Engineering (CSME) et Computational Fluid Dynamics Society of Canada (CFD Canada), à l’Université de Sherbrooke (Québec), du 28 au 31 mai 2023

Using real interpolation method for adaptive identification of nonlinear inverted pendulum system

In this paper, we investigate the inverted pendulum system by using real interpolation method (RIM) algorithm. In the first stage, the mathematical model of the inverted pendulum system and the RIM algorithm are presented. After that, the identification of the inverted pendulum system by using the RIM algorithm is proposed. Finally, the comparison of the linear analytical model, RIM model, and nonlinear model is carried out. From the results, it is found that the inverted pendulum system by using RIM algorithm has simplicity, low computer source requirement, high accuracy and adaptiveness in the advantages

Regional Pole Placement Design Based Stabilization for Cart Inverted Pendulum System

The inverted pendulum has been considered as a benchmark control problem due to its nonlinearity and stabilization around the unstable equilibrium point. To achieve stabilization, it is well known that all the closed loop system poles should lie in left half of s-plane. In present work, different approaches have taken to shift the system poles to left half of the plane. At first Linear Quadratic Regulator (LQR) is used, where the desired pole locations can be achieved by suitably selecting weight matrix of cost function. With this guaranteed cost control scheme, one does not have to bother about specifying closed-loop poles. Next, a two loop PID is designed based on pole matching conditions. Where the closed loop with unknown controller coefficient characteristic equation is compared with desired characteristics, to find out the controller gains. In both the methods, one has to deal with point wise pole placing, which can be tricky sometimes. With the recent development of LMIs tool, regional pole placement is well suited to achieve the goal. At last, a regional pole placement controller is synthesized, where desired specifications are transformed into LMI regions. In present case, a conical sector of left half plane is taken so that stabilisation with better transient performance can be achieve

Development of U-model enhansed nonlinear systems

Nonlinear control system design has been widely recognised as a challenging issue where the key objective is to develop a general model prototype with conciseness, flexibility and manipulability, so that the designed control system can best match the required performance or specifications. As a generic systematic approach, U-model concept appeared in Prof. Quanmin Zhu’s Doctoral thesis, and U-model approach was firstly published in the journal paper titled with ‘U-model based pole placement for nonlinear plants’ in 2002.The U-model polynomial prototype precisely describes a wide range of smooth nonlinear polynomial models, defined as a controller output u(t-1) based time-varying polynomial models converted from the original nonlinear model. Within this equivalent U-model expression, the first study of U-model based pole placement controller design for nonlinear plants is a simple mapping exercise from ordinary linear and nonlinear difference equations to time-varying polynomials in terms of the plant input u(t-1). The U-model framework realised the concise and applicable design for nonlinear control system by using such linear polynomial control system design approaches.Since the first publication, the U-model methodology has progressed and evolved over the course of a decade. By using the U-model technique, researchers have proposed many different linear algorithms for the design of control systems for the nonlinear polynomial model including; adaptive control, internal control, sliding mode control, predictive control and neural network control. However, limited research has been concerned with the design and analysis of robust stability and performance of U-model based control systems.This project firstly proposes a suitable method to analyse the robust stability of the developed U-model based pole placement control systems against uncertainty. The parameter variation is bounded, thus the robust stability margin of the closed loop system can be determined by using LMI (Linear Matrix Inequality) based robust stability analysis procedure. U-block model is defined as an input output linear closed loop model with pole assignor converted from the U-model based control system. With the bridge of U-model approach, it connects the linear state space design approach with the nonlinear polynomial model. Therefore, LMI based linear robust controller design approaches are able to design enhanced robust control system within the U-block model structure.With such development, the first stage U-model methodology provides concise and flexible solutions for complex problems, where linear controller design methodologies are directly applied to nonlinear polynomial plant-based control system design. The next milestone work expands the U-model technique into state space control systems to establish the new framework, defined as the U-state space model, providing a generic prototype for the simplification of nonlinear state space design approaches.The U-state space model is first described as a controller output u(t-1) based time-varying state equations, which is equivalent to the original linear/nonlinear state space models after conversion. Then, a basic idea of corresponding U-state feedback control system design method is proposed based on the U-model principle. The linear state space feedback control design approach is employed to nonlinear plants described in state space realisation under U-state space structure. The desired state vectors defined as xd(t), are determined by closed loop performance (such as pole placement) or designer specifications (such as LQR). Then the desired state vectors substitute the desired state vectors into original state space equations (regarded as next time state variable xd(t) = x(t) ). Therefore, the controller output u(t-1) can be obtained from one of the roots of a root-solving iterative algorithm.A quad-rotor rotorcraft dynamic model and inverted pendulum system are introduced to verify the U-state space control system design approach for MIMO/SIMO system. The linear design approach is used to determine the closed loop state equation, then the controller output can be obtained from root solver. Numerical examples and case studies are employed in this study to demonstrate the effectiveness of the proposed methods

Design and implementation of control concepts for image-guided object movement

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Fuzzy adaptive control of a two-wheeled inverted pendulum

Recently, the two-wheeled inverted pendulum has drawn the attention of robotic community in view of a plethora of applications, such as transport vehicles: Segway, teleconferencing robots, and electronic network-vehicle. As a widely-used personal transportation vehicle, a two-wheeled inverted pendulum robot has the advantages of small size and simple structure. Moreover, with the advent of modern control technology, these kinds of platforms with safety features and sophisticated control functions can be cost down, so that they have high potential to satisfy stringent requirements of various autonomous service robots with high speed. At the same time, it is of great interest from control point of view as the inverted pendulum is a complicated, strongly coupled, unstable and nonlinear system. Therefore, it is an ideal experimental platform for various control theories and experiments. To understand such a complex system, the Lagrangian equation has been introduced to develop a dynamic model. And following the mathematical model, linear quadratic regulator control and fuzzy adaptive method are proposed for upright stabilization, velocity control and position control of the system. However, sometimes these kinds of robots need to move on a slope, so an advanced linear quadratic regulator controller and a modified fuzzy adaptive controller have been proposed to achieve position control on a slope for the robot while stabilizing its body in balance. In addition, trajectory tracking control using proportional integral derivative control and sliding mode control with fuzzy adaptive backstepping method is also designed to make the robot autonomously navigate in two dimensional plane. Simulation results indicate that the proposed controllers are capable of providing appropriate control actions to steer the vehicle in desired manners. Then, a couple of real time experiments have been conducted to verify the the effectiveness of the developed control strategies

Control of a Two-wheeled Machine with Two-directions Handling Mechanism Using PID and PD-FLC Algorithms

This paper presents a novel five degrees of freedom (DOF) two-wheeled robotic machine (TWRM) that delivers solutions for both industrial and service robotic applications by enlarging the vehicle′s workspace and increasing its flexibility. Designing a two-wheeled robot with five degrees of freedom creates a high challenge for the control, therefore the modelling and design of such robot should be precise with a uniform distribution of mass over the robot and the actuators. By employing the Lagrangian modelling approach, the TWRM′s mathematical model is derived and simulated in Matlab/Simulink®. For stabilizing the system′s highly nonlinear model, two control approaches were developed and implemented: proportional-integral-derivative (PID) and fuzzy logic control (FLC) strategies. Considering multiple scenarios with different initial conditions, the proposed control strategies′ performance has been assessed