Design of shifting output-feedback controllers for LPV systems subject to time-varying saturations

This paper considers the problem of designing a shifting output-feedback controller for polytopic linear parameter-varying (LPV) systems subject to time-varying saturations. By means of the LPV framework and the use of the Lyapunov theory, the shifting paradigm concept, and the ellipsoidal invariant theory, a linear matrix inequality (LMI)-based methodology for the controller's design is proposed. The resulting gain-scheduled controller holds the control action in the linearity region of the actuators and regulates online the closed-loop convergence taking into account the instantaneous saturation limit values. The proposed approach is validated by means of an illustrative example.This work has been partially funded by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SaCoAV (ref. PID2020-114244RB-I00). This work has also been partially funded by AGAUR of Generalitat de Catalunya through the Advanced Control Systems (SAC) group grant (2017 SGR 482) and by the University of Stavanger through the project IN-12267. A. Ruiz is also supported by the Secretaria d’Universitats i Recerca de la Generalitat de Catalunya, the European Social Fund (ESF) and AGAUR under a FI SDUR grant (ref. 2020 FI-SDUR 00097).Peer ReviewedPostprint (published version

Analysis and design of quadratic parameter varying (QPV) control systems with polytopic attractive region

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper proposes a gain-scheduling approach for systems with a quadratic structure. Both the stability analysis and the state-feedback controller design problems are considered for quadratic parameter varying (QPV) systems. The developed approach assesses/enforces the belonging of a polytopic region of the state space to the region of attraction of the origin, and relies on a linear matrix inequality (LMI) feasibility problem. The main characteristics of the proposed approach are illustrated by means of examples, which confirm the validity of the theoretical results.Peer ReviewedPostprint (author's final draft

LPV control and virtual-sensor-based fault tolerant strategies for a three-axis gimbal system

This paper deals with the LPV control of a three-axis gimbal including fault-tolerant capabilities. First, the derivation of an analytical model for the considered system based on the robotics Serial-Link (SL) theory is derived. Then, a series of simplifications that allow obtaining a quasi-LPV model for the considered gimbal is proposed. Gain scheduling LPV controllers with PID structure are designed using pole placement by means of linear matrix inequalities (LMIs). Moreover, exploiting the sensor redundancy available in the gimbal, a virtual-sensor-based fault tolerant control (FTC) strategy is proposed. This virtual sensor uses a Recursive Least Square (RLS) estimation algorithm and an LPV observer for fault detection and estimation. Finally, the proposed LPV control scheme including the virtual sensor strategy is tested in simulation in several scenarios.Peer ReviewedPostprint (published version

Flexible-Link Robot Control Using a Linear Parameter Varying Systems Methodology

This paper addresses the issues of the Linear Parameter Varying (LPV) modelling and control of flexible-link robot manipulators. The LPV formalism allows the synthesis of nonlinear control laws and the assessment of their closed-loop stability and performances in a simple and effective manner, based on the use of Linear Matrix Inequalities (LMI). Following the quasi-LPV modelling approach, an LPV model of a flexible manipulator is obtained, starting from the nonlinear dynamic model stemming from Euler-Lagrange equations. Based on this LPV model, which has a rational dependence in terms of the varying parameters, two different methods for the synthesis of LPV controllers are explored. They guarantee the asymptotic stability and some level of closed-loop ℒ 2 -gain performance on a bounded parametric set. The first method exploits a descriptor representation that simplifies the rational dependence of the LPV model, whereas the second one manages the troublesome rational dependence by using dilated LMI conditions and taking the particular structure of the model into account. The resulting controllers involve the measured state variables only, namely the joint positions and velocities. Simulation results are presented that illustrate the validity of the proposed control methodology. Comparisons with an inversion-based nonlinear control method are performed in the presence of velocity measurement noise, model uncertainties and high-frequency inputs

Joint control of a robotic arm using particle swarm optimization based H2/H∞ robust control on arduino

This paper proposes a small structure of robust controller to control robotic arm’s joints where exist some uncertainties and unmodelled dynamics. Robotic arm is widely used now in the era of Industry 4.0. Nevertheless, the cost for an industry to migrate from a conventional automatic machine to industrial robot still very high. This become a significant challenge to middle or small size industry. Development of a low cost industrial robotic arm can be one of good solutions for them. However, a low-cost manipulator can bring more uncertainties. There might be exist more unmodelled dynamic in a low-cost system. A good controller to overcome such uncertainties and unmodelled dynamics is robust controller. A low-cost robotic arm might use small or medium size embedded controller such as Arduino. Therefore, the control algorithm should be a small order of controller. The synthesized controller was tested using MATLAB and then implemented on the real hardware to control a robotic manipulator. Both the simulation and the experiment showed that the proposed controller performed satisfactory results. It can control the joint position to the desired position even in the presence of uncertainties such as unmodelled dynamics and variation of loads or manipulator poses

Condition-based design of variable impedance controllers from user demonstrations

This paper presents an approach to ensure conditions on Variable Impedance Controllers through the off-line tuning of the parameters involved in its description. In particular, we prove its application to term modulations defined by a Learning from Demonstration technique. This is performed through the assessment of conditions regarding safety and performance, which encompass heuristics and constraints in the form of Linear Matrix Inequalities. Latter ones allow to define a convex optimisation problem to analyse their fulfilment, and require a polytopic description of the VIC, in this case, obtained from its formulation as a discrete-time Linear Parameter Varying system. With respect to the current state-of-art, this approach only limits the term definition obtained by the Learning from Demonstration technique to be continuous and function of exogenous signals, i.e. external variables to the robot. Therefore, using a solution-search method, the most suitable set of parameters according to assessment criteria can be obtained. Using a 7-DoF KinovaGen3 manipulator, validation and comparison against solutions with relaxed conditions are performed. The method is applied to generate Variable Impedance Controllers for a pulley belt looping task, inspired by the Assembly Challenge for Industrial Robotics in World Robot Summit 2018, to reduce the exerted force with respect to a standard (constant) Impedance Controller. These controllers fulfil a set of safety constraints, namely stability, bounds on task variables and maximum response overshooting; and their performance is determined by the User Preference heuristic, which allows to intuitively define the desired compliant behaviour along the task. In the context of the task, this is used to generate new controllers for one-off modifications of the nominal belt looping task setup without new demonstrations.This work is partially supported by MCIN/ AEI /10.13039/501100011033 and by the ”European Union NextGenerationEU/PRTR” under the project ROB-IN (PLEC2021-007859); and by MCIN/ AEI /10.13039/ 501100011033, Spain, under the project CHLOE-GRAPH (PID2020- 119244GB-I00). Authors also want to thank Adriá Colomé and Edoardo Caldarelli for their comments and help throughout this work.Peer ReviewedPostprint (published version

Design of shifting output-feedback controllers for LPV systems subject to time-varying saturations

This paper considers the problem of designing a shifting output-feedback controller for polytopic linear parameter-varying (LPV) systems subject to time-varying saturations. By means of the LPV framework and the use of the Lyapunov theory, the shifting paradigm concept, and the ellipsoidal invariant theory, a linear matrix inequality (LMI)-based methodology for the controller's design is proposed. The resulting gain-scheduled controller holds the control action in the linearity region of the actuators and regulates online the closed-loop convergence taking into account the instantaneous saturation limit values. The proposed approach is validated by means of an illustrative example.acceptedVersio

A recursive LMI-based algorithm for efficient vertex reduction in LPV systems

This paper proposes a new algorithm to reduce the number of gains of a polytopic LPV controller considering generic tuples of vertices, for which a common controller gain can be used. The use of Frobenius norm and the inclusion of the input matrix in the LMIs perturbation matrix allows decreasing the conservativeness to select vertices which are combinable, with respect to a previous approach based on Gershgorin circles. A combinability metric that can be applied to an arbitrary partition of the set of vertices is defined. Then, a recursive algorithm finds a lesser-fragmented combinable partition at each iteration by combining together two elements of a partition. The algorithm aims at finding combinable partitions with minimal cardinality in fewer attempts, always preserving the original control performance specifications. The proposed method is validated using numerical examples, a twin rotor MIMO system and a two-link robotic manipulator.This work has been co-financed by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SCAV (ref. MINECO DPI2017-88403-R), by the European Regional Development Fund of the European Union in the framework of the ERDF Operational Program of Catalonia 2014-2020 (ref. 001-P-001643 Looming Factory) and by the DGR of Generalitat de Catalunya (SAC group ref. 2017/SGR/482).Peer ReviewedPostprint (author's final draft

Linear Parameter-Varying Embedding of Nonlinear Models with Reduced Conservativeness

In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are approximated using multivariate polynomial regression. Taking into account the residuals of the approximation as the potential scheduling parameters, a principle component analysis (PCA) is conducted to introduce a limited set of auxiliary scheduling parameters in coping with the trade-o? between model accuracy and complexity. In this way, LPV embedding of the nonlinear systems and scheduling variable selection are jointly performed such that a good trade-o? between complexity and conservativeness can be found. The developed LPV model depends polynomially on some of the state variables and affinely on the introduced auxiliary scheduling variables, which all together comprise the overall scheduling vector. The methodology is applied to a two-degree of freedom (2-DOf) robotic manipulator in addition to an academic example to reveal the effectiveness of the proposed method and to show the merits of the presented approach compared with some available results in the literature.Comment: 7 pages, 2 figures, IFAC World Congress, Berlin, 202

Observer-based robust fault estimation for fault-tolerant control

A control system is fault-tolerant if it possesses the capability of optimizing the system stability and admissible performance subject to bounded faults, complexity and modeling uncertainty. Based on this definition this thesis is concerned with the theoretical developments of the combination of robust fault estimation (FE) and robust active fault tolerant control (AFTC) for systems with both faults and uncertainties.This thesis develops robust strategies for AFTC involving a joint problem of on-line robust FE and robust adaptive control. The disturbances and modeling uncertainty affect the FE and FTC performance. Hence, the proposed robust observer-based fault estimator schemes are combined with several control methods to achieve the desired system performance and robust active fault tolerance. The controller approaches involve concepts of output feedback control, adaptive control, robust observer-based state feedback control. A new robust FE method has been developed initially to take into account the joint effect of both fault and disturbance signals, thereby rejecting the disturbances and enhancing the accuracy of the fault estimation. This is then extended to encompass the robustness with respect to modeling uncertainty.As an extension to the robust FE and FTC scheme a further development is made for direct application to smooth non-linear systems via the use of linear parameter-varying systems (LPV) modeling.The main contributions of the research are thus:- The development of a robust observer-based FE method and integration design for the FE and AFTC systems with the bounded time derivative fault magnitudes, providing the solution based on linear matrix inequality (LMI) methodology. A stability proof for the integrated design of the robust FE within the FTC system.- An improvement is given to the proposed robust observer-based FE method and integrated design for FE and AFTC systems under the existence of different disturbance structures.- New guidance for the choice of learning rate of the robust FE algorithm.- Some improvement compared with the recent literature by considering the FTC problem in a more general way, for example by using LPV modeling