Adaptive Lqr-based Control of 3 Dof Spherical Articulated Robotic Manipulator

This paper intends to compare controllers used for non-isolated (transformer less) interleaved double dual boost (IDDB) converter which provide high voltage gain and can be used for high-power applications. A control subsystem is required to improve dynamic behaviour of converter and to have a better output response. In most cases small signal model of converter is obtained which are linearized at an operating point to derive a controller which cannot take uncertainties into consideration. Robust control and Nonlinear control methods are probably areas which can handle uncertainties and non-linearities effectively. Conventional linear quadratic regulator (LQR) controller cannot assure stability if system is highly uncertain. A convex model of converter dynamics is obtained taking uncertainties into account. To apply LQR control in uncertain converter case linear matrix inequalities(LMIs) are used to optimize the performance index. A comparative study of LMI-LQR control, LQR Controller and PID controller is done.

Robust Adaptive Control

This paper presents a longitudinal trajectory tracking scheme with [Formula: see text] adaptive control for hypersonic reentry vehicles (HRVs). A linear time-varying (LTV) multiple input multiple output (MIMO) model, in which influences of lateral states, earth rotation, and linearization are considered as model uncertainties, is derived based on state and input errors of longitudinal model. The normalization of error model is used to reduce differences of magnitude orders in state and input matrix elements which may affect the stability of [Formula: see text] adaptive controller. In order to achieve an accurate tracking performance, a linear quadratic regulator (LQR) controller is employed as the baseline controller, augmented with an [Formula: see text] adaptive controller to attenuate the matched and unmatched uncertainties. Based on the augmented controller, the optimization process is executed with the estimate of uncertainties at the same time. The simulation results of LQR controller, [Formula: see text] augmentation controller and robust [Formula: see text] controller show that the [Formula: see text] adaptive control method can reduce the terminal and integral of squared state errors validly. Terminal state errors in all simulation scenarios are less than 2.5m/s, 1e-3 and 10m, respectively, which reflects its effectiveness in increasing robustness of baseline controller.

This work introduces the design of an adaptive tracking control strategy for a 6-DOF Staubli TX2-60L industrial robot manipulator operating under dynamic model uncertainties caused by variable payloads. A complete kinematic and dynamic model of the robot is derived using Denavit–Hartenberg parameters and the Lagrangian formulation, respectively. To address the limitations of conventional control methods under payload variations, an adaptive controller is designed, which continuously updates its parameters based on real-time tracking errors. A Lyapunov stability analysis is conducted to rigorously establish that the closed-loop system guarantees convergent tracking errors and bounded internal states. Simulation studies with different payload scenarios, including no load, step load variation, and continuous load changes, show the performance of the proposed control strategy. The results confirm that the adaptive controller maintains precise trajectory tracking and robust stability despite significant model uncertainties, highlighting its suitability for industrial pick-and-place and high-precision automation tasks. Keywords: Robot manipulator, kinematic model, dynamic model, variable payloads, adaptive control, stability analysis.

This study explores the integration of the adaptive control approach with the Model Reference Adaptive Control (MRAC) method, with a view to examining the impact of this integration on the performance of dynamic systems. Adaptive control is highlighted as a versatile and robust methodology that enables systems to cope with uncertainties and adapt to rapidly changing conditions in their operating environments. As a branch of adaptive control, the MRAC method focuses on efficiently achieving desired performance objectives by adjusting system parameters based on a predefined reference model. The primary focus is on investigating how these methods can be applied to optimize the functionality of systems characterized by dynamic and variable nature, such as unmanned aerial vehicles. By addressing challenges related to uncertainties, disturbances, and adaptability, the integration of adaptive control with the MRAC method demonstrates significant potential in improving the robustness, responsiveness, and reliability of such systems. This research investigates the performance of adaptive techniques in enhancing the capabilities of modern control systems. The objective of the research is to assess the effectiveness of MRAC in terms of reference signal tracking. Simulation results demonstrate the ability of MRAC to maintain accurate tracking of the desired reference for key vehicle dynamics, including roll, pitch and yaw. The results demonstrate the robustness of the MRAC algorithm in attitude control, which may lead to support for sustainability issues such as energy consumption.

Structural control has gained significant attention in recent times. The standalone issue of power requirement during an earthquake has already been solved up to a large extent by designing semi-active control systems using conventional linear quadratic control theory, and many other intelligent control algorithms such as fuzzy controllers, artificial neural networks, etc. In conventional linear–quadratic regulator (LQR) theory, it is customary to note that the values of the design parameters are decided at the time of designing the controller and cannot be subsequently altered. During an earthquake event, the response of the structure may increase or decrease, depending the quasi-resonance occurring between the structure and the earthquake. In this case, it is essential to modify the value of the design parameters of the conventional LQR controller to obtain optimum control force to mitigate the vibrations due to the earthquake. A few studies have been done to sort out this issue but in all these studies it was necessary to maintain a database of the earthquake. To solve this problem and to find the optimized design parameters of the LQR controller in real time, a fast Fourier transform and particle swarm optimization based modified linear quadratic regulator method is presented here. This method comprises four different algorithms: particle swarm optimization (PSO), the fast Fourier transform (FFT), clipped control algorithm and the LQR. The FFT helps to obtain the dominant frequency for every time window. PSO finds the optimum gain matrix through the real-time update of the weighting matrix R, thereby, dispensing with the experimentation. The clipped control law is employed to match the magnetorheological (MR) damper force with the desired force given by the controller. The modified Bouc–Wen phenomenological model is taken to recognize the nonlinearities in the MR damper. The assessment of the advised method is done by simulation of a three-story structure having an MR damper at the ground floor level subjected to three different near-fault historical earthquake time histories, and the outcomes are equated with those of simple conventional LQR. The results establish that the advised methodology is more effective than conventional LQR controllers in reducing inter-storey drift, relative displacement, and acceleration response.

Backstepping based model reference adaptive control for nuclear reactor with matched and unmatched uncertainties

This paper presents an example of the linearization of a robot manipulator's dynamics using Koopman operators (KP), and presents practical issues to be considered when applying the principal of KP theory to robotic systems. Using the KP, this work presents the successful design of a Generalized Predictive Controller (GPC) that is able to handle any posture/velocity/acceleration for a 3-Dof robot arm, and shows that our GPC performance outperforms a traditional PD controller under a very wide range of operating conditions. KP have only recently begun to attract attention in the field of robotics, and only a few application examples are available. Its basic idea is to lift a non-linear function to a higher dimensional space by extending its explanatory variables, and these new variables are often referred to as “observables”. In this higher dimension space, nonlinear functions can be described in a linear form. Here, how the observables should be augmented depends on the dynamical system's property. For the robotic manipulator, it still remains unclear what is the best set of observables to describe its dynamics. In this study, the optimal set of observables was acquired by expanding the robot dynamics equation and using its monomials. The KP was then identified by the least-squares minimization, and an approximate linear state-space model of the robot was identified. Using this model a GPC controller was designed, and it was shown that our observables choice was properly describing the non-linear behavior globally and made the linear state space model accurate as same as previous research.

The linear quadratic regulator (LQR) is a classical optimal control approach that can regulate gait dynamics about target kinematic trajectories. Exoskeletons to restore gait function have conventionally utilized time-varying proportional-derivative (PD) control of leg joints. But, these PD parameters are not uniquely optimized for whole-body (full-state) performance. The objective of this study was to investigate the effectiveness of LQR full-state feedback compared to PD control to maintain bipedal walking of a sagittal-plane computational model against force disturbances. Several LQR controllers were uniquely solved with feedback gains optimized for different levels of tracking capability versus control effort. The main implications to future exoskeleton control systems include (1) which LQR controllers out-perform PD controllers in walking maintenance and effort, (2) verifying that LQR desirably produces joint torques that oppose rapidly growing joint state errors, and (3) potentially equipping accurate sensing systems for nonjoint states such as hip-position and torso orientation. The LQR controllers capable of longer walk times than respective PD controllers also required less control effort. During sudden leg collapse, LQR desirably behaved like PD by generating feedback torques that opposed the direction of leg-joint errors. Feedback from nonjoint states contributed to over 50% of the LQR joint torques and appear critical for whole-body LQR control. While LQR control poses implementation challenges, such as more sensors for full-state feedback and operation near the desired trajectories, it offers significant performance advantages over PD control.

The inverse dynamics of a robotic manipulator is instrumental in precise robot control and manipulation. However, acquiring such a model is challenging, not only due to unmodelled non-linearities such as joint friction, but also from a machine learning perspective (e.g., input space dimension, amount of data needed). The accuracy of such models, regardless of the learning techniques, relies on proper excitation and exploration of the robot’s configuration space, in order to collect a rich dataset. This study aims to provide rich data in learning the inverse dynamics of a serial robotic manipulator using supervised machine learning techniques. We propose a method, called Max-Information Configuration Exploration (MICE), to incrementally explore and generate information-rich data via computing parameters of a trajectory set. We also introduce a new set of excitation trajectories that explores robot’s configuration through imposed stable limit cycles in robot joints’ phase space while satisfying feasibility constraints and physical bounds. We benchmark MICE against state-of-the-art in terms of data quality and learning accuracy. The proposed methodology for data collection, model learning, and evaluation, is validated with a KUKA IIWA14 robotic arm where the results prove significant improvement over traditional approaches.

Model reference adaptive fuzzy control (MRAFC) is proposed to control the active power filter (APF) and model the APF system caused by nonlinear characteristics, variable parameters and external interferences. T-S fuzzy theory is utilized on the approximation of nonlinear model and the current tracking control. APF system based on MRAFC can be guaranteed to be asymptotical stable. Simulation results are included to confirm the effectiveness of the proposed controller and comparisons with APF system based on model reference adaptive control (MRAC) demonstrate that MRAFC method is capable of reducing the modeling error and tracking reference current signal accurately. Moreover, APF based on the proposed method shows the dynamic and static control performance of stronger robustness, better suitability and higher accuracy than the one based on MRAC modus.

Inverted pendulum systems, such as double or single, rotational or translational inverted pendulums are non-linear and unstable, which have been the most dominant approaches for control systems. The double inverted pendulum is one kind of a non-linear, unstable system, multivariable, and strong coupling with a wide range of control methods. To model these types of systems, many techniques have been proposed so that motivating researchers to come up with new innovative solutions. The Linear Quadratic Regulator (LQR) controller has been a common controller used in this field. Meanwhile, the Artificial Bee Colony (ABC) technique has become an alternative solution for employing Bee Swarm Intelligence algorithms. The research solutions of the artificial bee colony algorithm in the literature can be beneficial, however, the utilization of discovered sources of food is ineffective. Thus, in this paper, we aim to provide a double inverted pendulum system for stabilization by selecting linear quadratic regulator parameters using a bio-inspired optimization methodology of artificial bee colony and weight matrices Q and R. The results show that when the artificial bee colony algorithm is applied to a linear quadratic regulator controller, it gains the capacity to autonomously tune itself in an online process. To further demonstrate the efficiency and viability of the suggested methodology, simulations have been performed and compared to conventional linear quadratic regulator controllers. The obtained results demonstrate that employing artificial intelligence (AI) together with the proposed controller outperforms the conventional linear quadratic regulator controllers by more than 50 % in transient response and improved time response and stability performance

This book is the second edition of a textbook published in 1996 by McGraw Hill and originates from a graduate level course given by the authors at the University of Naples. The topics include kinematics, statics and dynamics of robot manipulators together with trajectory planning and active control. There are only minor additions the first edition, which are mainly the use of quaternion to describe the orientation of the end effector and a short description of a closed chain architecture for a manipulator (parallelogram arm). The book is largely devoted to serial manipulators, with special developments about active control including adaptative control, robust controls and stability analysis. Another strength of this book is the great number of problems proposed at the end of each chapter, together with a list of references related to it. The fundamental features covered by the text are illustrated on simple examples of serial manipulators (two-link planar arm, parallelogram arm) including analytical results and numerical tests.The book has nine chapters followed by three appendices. The first appendix is devoted to linear algebra, the second recalls some fundamental aspects of rigid body mechanics and the third gives some basic principles of feedback control of linear systems.Chapter one is an introduction to the study of robot manipulators, giving an interesting classification of their architectures, the corresponding workspace and describes the tasks for which theyare used. After some standard examples of industrial manipulators, bibliographical reference texts are proposed, including textbooks on modelling and control of robots, general books on robotics, specialized texts, scientific robotic reviews and some international conferences on robotics.Chapters two, three and four are devoted to mechanical modelling of robot manipulators. The fundamental basics of kinematics are given in chapter two, including the representation of finite rotations by Euler angles or unit quaternions, homogeneous transformations, Denavit-Hartenberg parameters and workspace. The direct and inverse kinematical problems are solved in analytical form for some typical manipulator structures. The differential kinematics of robots are presented in chapter three, with an introduction to the geometric and analytic Jacobian matrices, kinematic singularities and redundancy. The inverse kinematic problem is presented, with special attention to the case of redundant robots where the solution is obtained by a linear optimization problem leading to the introduction of the pseudo-inverse Jacobian matrix and to the solution of several objectives such as avoidance of collision with an obstacle or moving away from singularities. Several inverse kinematics algorithms are given wih an interesting application to a three-link planar arm. Finally, a property of kineto-statics duality is deduced from the principle of virtual work applied to an equilibrium configuration of the robot. Chapter four is a standard presentation of the derivation of the dynamical model by Lagrange formulation and then by the Newton-Euler method. In the Lagrange formulation method, the linearity with respect to inertial parameters is shown and a detailed formulation of the dynamical model is obtained for a two-link Cartesian arm, a two-link planar arm and a parallelogram arm. The problem of dynamic parameter identification is also briefly presented from a numerical point of view. The recursive algorithm constructed from the Newton-Euler formulation is presented and illustrated by considering a two-link planar arm. Finally, the operational space dynamic model is introduced.In chapter five, paths and trajectory planning in joints and in operational spaces are presented; several classical methods of interpolation are described.Chapter six is an extensive study of active control of manipulators. Several methods are presented, involving classical independent joint control, non-linear centralized control, robust control and adaptative control. Both joint-space control and operational-space control are studied together with stability analysis by using Liapounoff functions. An interesting application to the two-link planar arm already used shows the comparison between various control schemes.Chapter seven deals with interaction control of serial manipulators with the working environment. Several strategies involving compliance control, impedance control, force control and hybrid control are presented.Chapter eight describes the actuators and the sensors used in robotics. Several types of servomotors (electric and hydraulic) are presented, together with the model giving their input/output relationship. Several kinds of sensors are also described including encoders, tachometers, force and vision sensors.The last chapter gives a short presentation of the functional architecture of a robot's control system, including characteristics of the programing environment and the hardware architecture.In conclusion, the book provides a good insight about simulation and control of robot manipulators, with a detailed study of the various control strategies and several interesting and pedagogical applications. This book is an excellent review of the standard knowledge needed not only for graduate students but also for researchers interested in robot manipulators.M Pascal

A magnetic levitation system (Maglev) is a sensitive, multi-parameter, nonlinear, and unstable system that is utilized to levitate a ferromagnetic object in free space. Due to its vast applications, various research studies in the field of control strategy have become extremely important and challenging. This work proposes the design of a nonlinear model predictive (NMPC) control scheme for the object position control against the nonlinearities and uncertainties of a Maglev system. A novel bio-inspired Artificial Protozoa Optimization (APO) algorithm is used to fine-tune the NMPC parameters, which include best weighting matrices ( ), shorter prediction horizons ( ), and shorter time steps ( ) to minimize the objective cost function. The effective performance of the NMPC is verified using simulation-based results in MATLAB. The CasADi toolbox is utilized to solve nonlinear optimization problems and handle the nonlinearity of the Maglev system model. Simulations are implemented for three trajectories tracking (step, sine, and square) with 20% and without Maglev parameters perturbations. To prove the superiority of the proposed controller, comparisons are made with the conventional Linear Quadratic Regulator (LQR) and proportional-integral-derivative (PID) controllers. Two performance indices are introduced, Integral of Squared Error (ISE) and Integral of Absolute Error (IAE), to examine the tracking performances of the NMPC, LQR, and PID controller. The NMPC controller has shown more efficient performance and accurate results than other controllers. The contributions of this work include a new optimization technique of APO, a new engineering application of the APO integrated with NMPC to control a Maglev system, consideration of inherent nonlinearities and system constraints, and robustness improvement under perturbation.

Manuscript provides a key technology, namely Input-Output Feedback Linearization Associates with Linear Quadratic Regulator (for short, IOFLALQR). The objective of this research is to study the possibility of integrating two control strategies, which includes input-output feedback linearization technique (for short, IOFL) and linear quadratic regulator controller (for short, LQR), for stabilization control of Furuta pendulum system. Furuta pendulum system belongs to the group of under-actuated robot systems. In this work, structure of IOFLALQR, control implementation, comparison of IOFLALQR and conventional LQR are adequately studied and discussed. Simulation is completed in MATLAB/Simulink environment and experiment is done on real-time experimental setup. Numerical simulation and experimental results show that the IOFLALQR are implemented on Furuta pendulum successfully. Besides, results have been drawn for demonstrating IOFLALQR better than another classical method.