Arm Angle Tracking Control with Pole Balancing Using Equivalent Input Disturbance Rejection for a Rotational Inverted Pendulum

This paper proposes a robust tracking control method for swing-up and stabilization of a rotational inverted pendulum system by applying equivalent input disturbance (EID) rejection. The mathematical model of the system was developed by using a Lagrangian equation. Then, the EID, including external disturbances and parameter uncertainties, was defined; and the EID observer was designed to estimate EID using the state observer dynamics and a low-pass filter. For robustness, the linear-quadratic regulator method is used with EID rejection. The closed-loop stability is proven herein using the Lyapunov theory and input-to-state stability. The performance of the proposed method is validated and verified via experimental results

Performance Comparisons Of Hybrid Fuzzy-LQR And Hybrid PID-LQR Controllers On Stabilizing Double Rotary Inverted Pendulum

Double Rotary Inverted Pendulum (DRIP) is a member of the mechanical under-actuated system which is unstable and nonlinear. The DRIP has been widely used for testing different control algorithms in both simulation and experiments. The DRIP control objectives include Stabilization control, Swing-up control and trajectory tracking control. In this research, we present the design of an intelligent controller called “hybrid Fuzzy-LQR controller” for the DRIP system. Fuzzy logic controller (FLC) is combined with a Linear Quadratic Regulator (LQR). The LQR is included to improve the performance based on full state feedback control. The FLC is used to accommodate nonlinearity based on its IF-THEN rules. The proposed controller was compared with the Hybrid PID-LQR controller. Simulation results indicate that the proposed hybrid Fuzzy-LQR controllers demonstrate a better performance compared with the hybrid PID-LQR controller especially in the presence of disturbances. &nbsp

Adaptive Augmentation of Non-Minimum Phase Flexible Aerospace Systems

This work demonstrates the efficacy of direct adaptive augmentation on a robotic flexible system as an analogue of a large flexible aerospace structure such as a launch vehicle or aircraft. To that end, a robot was constructed as a control system testbed. This robot, named “Penny,” contains the command and data acquisition capabilities necessary to influence and record system state data, including the flex states of its flexible structures. This robot was tested in two configurations, one with a vertically cantilevered flexible beam, and one with a flexible inverted pendulum (a flexible cart-pole system). The physical system was then characterized so that linear analysis and control design could be performed. These characterizations resulted in linear and nonlinear models developed for each testing configuration. The linear models were used to design linear controllers to regulate the nominal plant’s dynamical states. These controllers were then augmented with direct adaptive output regulation and disturbance accommodation. To accomplish this, sensor blending was used to shape the output such that the nonminimum phase open loop plant appears to be minimum phase to the controller. It was subsequently shown that augmenting linear controllers with direct adaptive output regulation and disturbance accommodation was effective in enhancing system performance and mitigating oscillation in the flexible structures through the system’s own actuation effort

Intelligent model-based control of complex three-link mechanisms

The aim of this study is to understand the complexity and control challenges of the locomotion of a three-link mechanism of a robot system. In order to do this a three-link robot gymnast (Robogymnast) has been built in Cardiff University. The Robogymnast is composed of three links (one arm, one torso, one leg) and is powered by two geared DC motors. Currently the robot has three potentiometers to measure the relative angles between adjacent links and only one tachometer to measure the relative angular position of the first link. A mathematical model for the robot is derived using Lagrange equations. Since the model is inherently nonlinear and multivariate, it presents more challenges when modelling the Robogymnast and dealing with control motion problems. The proposed approach for dealing with the design of the control system is based on a discrete-time linear model around the upright position of the Robogymnast. To study the swinging motion of the Robogymnast, a new technique is proposed to manipulate the frequency and the amplitude of the sinusoidal signals as a means of controlling the motors. Due to the many combinations of the frequency and amplitude, an optimisation method is required to find the optimal set. The Bees Algorithm (BA), a novel swarm-based optimisation technique, is used to enhance the performance of the swinging motion through optimisation of the manipulated parameters of the control actions. The time taken to reach the upright position at its best is 128 seconds. Two different control methods are adopted to study the balancing/stablising of the Robogymnast in both the downward and upright configurations. The first is the optimal control algorithm using the Linear Quadratic Regulator (LQR) technique with integrators to help achieve and maintain the set of reference trajectories. The second is a combination of Local Control (LC) and LQR. Each controller is implemented via reduced order state observer to estimate the unmeasured states in terms of their relative angular velocities. From the identified data in the relative angular positions of the upright balancing control, it is reported that the maximum amplitude of the deviation in the relative angles on average are approximately 7.5° for the first link and 18° for the second link. It is noted that the third link deviated approximately by 2.5° using only the LQR controller, and no significant deviation when using the LQR with LC. To explore the combination between swinging and balancing motions, a switching mechanism between swinging and balancing algorithm is proposed. This is achieved by dividing the controller into three stages. The first stage is the swinging control, the next stage is the transition control which is accomplished using the Independent Joint Control (IJC) technique and finally balancing control is achieved by the LQR. The duration time of the transition controller to track the reference trajectory of the Robogymnast at its best is found to be within 0.4 seconds. An external disturbance is applied to each link of the Robogymnast separately in order to study the controller's ability to overcome the disturbance and to study the controller response. The simulation of the Robogymnast and experimental realization of the controllers are implemented using MATLAB® software and the C++ program environment respectively

Proportional Derivative Control with Inverse Dead-Zone for Pendulum Systems

A proportional derivative controller with inverse dead-zone is proposed for the control of pendulum systems. The proposed method has the characteristic that the inverse dead-zone is cancelled with the pendulum dead-zone. Asymptotic stability of the proposed technique is guaranteed by the Lyapunov analysis. Simulations of two pendulum systems show the effectiveness of the proposed technique

Energy-Based Control for the Cart-Pole System in Implicit Port-Hamiltonian Representation

This master thesis is devoted to the design, analysis, and experimental validation of an energy-based control strategy for the well-known benchmark cart-pole system in implicit Port-Hamiltonian (PH) representation. The control scheme performs two tasks: swingup and (local) stabilization. The swing-up controller is carried out on the basis of a generalized energy function and consists of bringing the pendulum trajectories from the lower (stable) position to a limit cycle (homoclinic orbit), which passes by the upright (unstable) position, as well as the cart trajectories to the desired point. The (local) stabilizing controller is designed under a novel algebraic Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) technique and ensures the upright (asymptotic) stabilization of the pendulum as well as the cart at a desired position. To illustrate the effectiveness of the proposed control scheme, this work presents simulations and real-time experiments considering physical damping, i.e., viscous friction. The results are additionally contrasted with another energy-based control strategy for the cart-pole system in explicit Euler-Lagrange (EL) representation.Diese Masterarbeit widmet sich dem Entwurf, der Analyse und der experimentellen Validierung einer energiebasierten Regelstrategie für das bekannte Benchmarksystem des inversen Pendels auf einem Wagen in impliziter Port-Hamiltonscher (PH) Darstellung. Das Regelungssystem erfüllt zwei Aufgaben: das Aufschwingen und (lokale) Stabilisierung. Das Aufschwingen erfolgt auf Grundlage der generalisierten Energiefunktion und besteht darin, sowohl die Trajektorien des Pendels von der unteren (stabilen) Position in einen Grenzzyklus (homokliner Orbit) zu bringen, wobei die (instabile) aufrechte Lage passiert wird, als auch den Wagen in einer gewünschten Position einzustellen. Die (lokale) Regelung zur Stabilisierung ist nach einer neuartigen algebraischen Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) Methode konzipiert und gewährleistet die aufrechte (asymptotische) Stabilisierung des Pendels sowie die Positionierung des Wagens an einem gewünschten Referenzpunkt. Um die Funktionalität des entworfenen Regelungssystems zu veranschaulichen, werden in dieser Masterarbeit Simulationen und Echtzeit-Experimente unter Berücksichtigung der physikalischen Dämpfung, d.h. der viskosen Reibung, vorgestellt. Die Ergebnisse werden zusätzlich mit einem weiteren energiebasierten Regelungsansatz für das System des inversen Pendels auf einem Wagen in expliziter Euler-Lagrange (EL) Darstellung verglichen.Tesi

Stability analysis of non-holonomic inverted pendulum system

The inverted pendulum is doubtlessly one of the most famous control problems found in most control text books and laboratories worldwide. This popularity comes from the fact that the inverted pendulum exhibits nonlinear, unstable and non-minimum phase dynamics. The basic control objective of the study is to design a controller in order to maintain the upright position of the pendulum while also controlling the position of the cart. In our study we explored the relationship that the tuning parameters (weight on the position of the car and the angle that the pendulum makes with the vertical) of a classical inverted pendulum on a cart has on the pole placement and hence on the stability of the system. We then present a family of curves showing the local root-locus and develop relationships between the weight changes and the system performance. We describe how these locus trends provide insight that is useful to the control designer during the effort to optimize the system performance. Finally, we use our general results to design an effective feedback controller for a new system with a longer pendulum, and present experiment results that demonstrate the effectiveness of our analysis. We then designed a simulation-based study to determine the stability characteristics of a holonomic inverted pendulum system. Here we decoupled the system using geometry as two independent one dimensional inverted pendulum and observed that the system can be stabilized using this method successfully with and without noise added to the system. Next, we designed a linear system for the highly complex inverted pendulum on a non-holonomic cart system. Overall, the findings will provide valuable input to the controller designers for a wide range of applications including tuning of the controller parameters to design of a linear controller for nonlinear systems