Pedro Jesus Rodriguez-Ayerbe - Academia.edu (original) (raw)

Papers by Pedro Jesus Rodriguez-Ayerbe

IFAC-PapersOnLine, 2017

In sensorless control for synchronous machines at low speed and standstill, the position estimati... more In sensorless control for synchronous machines at low speed and standstill, the position estimation can be sensitive to the choice of the carrier frequency of the injection method. Moreover, electromagnetic saturation or temperature variation in the machine might also affect the estimation error. In order to better describe the high-frequency (HF) behaviour of the machine, the effective HF inductances and resistances are presented in this paper. Then, the analytical expression for the carrier frequency dependent error is explained using the calculated HF-equivalent model and is proposed to be integrated into the sensorless control scheme when a rotating HF voltage injection is employed. Numerical simulations highlight the frequency dependent error and prove the satisfactory operation of the compensation.

Bulletin Mathematique De La Societe Des Sciences Mathematiques De Roumanie, 2018

The control design techniques for linear or hybrid systems under constraints lead often to off-li... more The control design techniques for linear or hybrid systems under constraints lead often to off-line state-space partitions with non-overlapping convex polyhedral regions. This corresponds to a piecewise affine (PWA) state feedback control laws associated to polyhedral partition of the state-space. The aim of this paper is to consider perturbation in the representation of the vertices of such polyhedral regions. Another idea behind this study is to perform a quantization operation on the representation of the state-space regions and the associated PWA control laws in order to reduce the hardware requirements in terms of processor speed and memory unit. The quantized state-space partitions lose some of the important properties of the explicit controllers: non-overlapping, convexity and invariant characterization. The major contribution of this work is to analyze to what extend the non-overlapping and the invariance characteristics of the PWA controller can be preserved when perturbati...

Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics Service, 2008

The procedure of system identification of multi-mass servo system using different methods is desc... more The procedure of system identification of multi-mass servo system using different methods is described in this paper. Different black-box models are identified. Previous experimental results show that a model consisting of three-masses connected by springs and dampers gives an acceptable description of the dynamics of the servo system. However, this work shows that a lower order black-box model, identified using off-line or on-line experiments, gives better fit. The purpose of this contribution is to present experimental identification of a multi-mass servo system using different algorithms.

Journal of Dynamic Systems, Measurement, and Control, 2021

This article presents an approach to efficiently control grippers/multifingered hands for dextero... more This article presents an approach to efficiently control grippers/multifingered hands for dexterous manipulation according to a task, i.e., a predefined trajectory in the object space. The object motion is decomposed using a basis of predefined object motions equivalent to object-level coordinate couplings and leading to the definition of the task-level space. In the proposed approach, the decomposition of the motion in the task space is associated with a robust control design based on linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Eigenvalue placement ensures the robustness of the system to geometric uncertainties and eigenvector placement decouples the system according to task specifications. A practical evaluation of the proposed control strategy is provided with a two-fingers' and six degrees-of-freedom robotic system manipulating an object in the horizontal plane. Results show a better trajectory tracking and the robustness of the control law acc...

2019 18th European Control Conference (ECC), 2019

This article presents a stability analysis of object grasping with a compliant multi-fingered rob... more This article presents a stability analysis of object grasping with a compliant multi-fingered robot hand. This stability analysis is based on an energetic approach, in which we aim to compute the maximum amount of energy that can be stored by a compliant hand-object system about a stable equilibrium before being destabilized. More specifically, the case of external disturbance wrenches is investigated. This analysis admits several applications, two of which are illustrated in this article on a case study. First the quality of a given grasp can be quantified in terms of maximum allowed disturbance force and the associated displacement around the initial equilibrium, with applications in trajectory design for the robot arm that holds the hand-object system. Conversely, given a task specified in terms of known disturbance wrenches set, the proposed approach helps determining the optimal grasp for an enhanced stability, e.g. the contact points locations, joint compliance or internal forces levels.

2016 18th European Conference on Power Electronics and Applications (EPE'16 ECCE Europe), Sep 1, 2016

The paper presents a detailed description of the prediction model for Predictive Power Control ba... more The paper presents a detailed description of the prediction model for Predictive Power Control based on Virtual Flux (MPPC-VF) scheme for control grid connected three-level neutral-point clamped inverter (3L-NPC). The controller uses a model to calculate predictions of the future values of the virtual flux, grid currents and DC-link capacitor voltages for all possible voltage vectors. The active and reactive power can be estimated based on the virtual flux and the current. The cost function is defined to minimize the error between the active, reactive power and their references, balance the DC-link capacitor voltage and reduce the switching frequency. The optimal switching state that minimizes the cost function is selected and applied to the inverter. Simulation results under different conditions are presented and compared with conventional Direct Power Control and Space Vector Modulation (DPC-SVM). The obtained results show the better performances of the proposed control method.

2017 21st International Conference on Control Systems and Computer Science (CSCS), May 1, 2017

The control design techniques for linear or hybrid systems (e.g. anti-wind up, MPC) lead often to... more The control design techniques for linear or hybrid systems (e.g. anti-wind up, MPC) lead often to off-line state-space partitions with non-overlapping convex polyhedral regions. This corresponds to a piecewise state feedback control laws associated to polyhedral partition of the state-space. In this work, we consider the perturbation in the representation of the vertices of the polyhedral regions. For such control laws, this problem is of particular interest with respect to the reduced precision representation of the state-space partition. The perturbed state-space partitions might lose one of the important property of the explicit controllers: the "non-overlapping" characterization. We derive a set called vertex sensitivity region to determine the admissible perturbation independently for each vertex of the polyhedral partition. A perturbation is deemed admissible if the non-overlapping property of the polyhedral regions is preserved. In the present work, the analysis of the sensitivity of each vertex is done under the assumption that the rest of the partition remains on the nominal configuration.

Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics Service, 2008

An off-line technique enabling to robustify an initial Model Predictive Control (MPC) for multiva... more An off-line technique enabling to robustify an initial Model Predictive Control (MPC) for multivariable systems via the convex optimization of a Youla parameter is presented. Firstly, a multivariable predictive controller is designed for a nominal system and then robustified towards unstructured uncertainties, while guaranteeing stability properties over a specified polytopic domain of uncertainties. This condition leads to verify a Bilinear Matrix Inequality (BMI) for each vertex of the polytopic domain. This BMI can be mathematically relaxed to semi-definite programming (SDP) using a Sum of Squares (SOS) strategy, with a significant increase of the number of scalar decision variables. To overcome this inconvenient, an alternative tractable sub-optimal solution for the BMI is proposed, based on the elaboration of a stable solution obtained by minimization of the complementary sensitivity function.

IEEE Access, 2019

In this paper, a new power control strategy based on a model predictive power control for the gri... more In this paper, a new power control strategy based on a model predictive power control for the grid-tie three-level neutral point clamped inverter is presented. A dynamical model based on the orientation of grid voltage is used to predict the performance of control variables required for the system. A cost function that includes the tracking power ability, the neutral-point voltage balancing and switching frequency reduction is used to achieve the optimal switching state. A proposed selection scheme of control input is introduced to comprehend the stability of the closed-loop system and reduce the computational cost. At each sampling time, only candidate switching state inputs that guarantee the stability condition through a control Lyapunov function is evaluated in the cost function of the MPC algorithm. Thus, the execution time is remarkably decreased by 26% in comparison with traditional model predictive control. Moreover, the deadtime effect is compensated by incorporating its influence in the proposed prediction model. Simulation and experimental results compared with the traditional model predictive control are used to confirm the effectiveness of the proposed scheme. INDEX TERMS Computational burden, control Lyapunov function, dead-time compensation, finite control set model predictive control, stability conditions, three-level neutral-point-clamped inverter. NOMENCLATURE C 1 , C 2 , C dc DC-link capacitance. i g , u g Grid current and voltage. i z Neutral-point current. K d , K q Positive gains of Lyapunov function. L f , R f Filter inductance and resistance. ω Grid voltage angular frequency. θ Grid voltage angle in the stationary frame. λ uz , λ sw Weighting factor of voltage balance, switching frequency reduction. P g , Q g Grid active and reactive powers. The associate editor coordinating the review of this manuscript and approving it for publication was Alfeu J. Sguarezi Filho. S x Switching state of the 3L-NPC inverter. t d , t on , t off Dead-time, turn-on/off time of IGBT. T s Sampling time of the controller. u inv Inverter output voltage. U dc DC-bus voltage. u z Neutral-point voltage. SUPERSCRIPTS * Reference value. p Predicted value. SUBSCRIPTS d, q d, q axis of grid voltage oriented reference frame. α, β α, β axis of stationary reference frame.

The International Journal of Advanced Manufacturing Technology, 2018

This paper presents an Off-line Gain Adjustment (OGA) approach to reduce contour error in 5-axis ... more This paper presents an Off-line Gain Adjustment (OGA) approach to reduce contour error in 5-axis high speed machining. The proposed contour error formulation is based on the estimation of tool contact points and the OGA is inspired from the idea of Model Predictive Control (MPC). The control gains used in the position loop of servo drives are optimally adjusted off-line to reduce the contour error for the considered trajectory. The obtained gain profiles are computed preserving axis kinematic limitations, stability criterion of servo drives and the motor current constraints. The OGA is developed thanks to a validated machine simulator. The simulation results prove that the OGA reduces significantly the contour error in 5-axis high speed machining.

International Journal of Intelligent Robotics and Applications, 2018

This work proposes a design and performance quantification methodology for observer-based impact ... more This work proposes a design and performance quantification methodology for observer-based impact detection in serial robot manipulators in presence of modelling errors and without force/torque sensor. After expressing the modelling errors between the physical robot and its inverse dynamic model as the sum of contributions due to dynamic parameters uncertainties and numerical differentiation errors for a given trajectory, an observer of the external disturbance torque is designed based on the inverse dynamic model and using a Kalman filter. The influence of each design parameter of the observer on the quality of the external torque estimation is studied first based on simulation results. Then a frequency analysis is conducted to distinguish between the influence of the exact external torque, the modelling uncertainties and the measurement noise on the estimated external torque. Finally a methodology is proposed to determine the optimal design corresponding to the shortest detection time depending on the expected sensitivity.

Automatica, 2017

This paper presents a new approach for control design of constrained linear systems affected by b... more This paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties. This method hinges on so-called convex liftings which emulate control Lyapunov function by providing a constructive framework for optimization based control implementation. It will be shown that this method can guarantee the recursive feasibility and robust stability in the sense of Lyapunov. Finally, a numerical example will be presented to illustrate this method.

2016 20th International Conference on System Theory, Control and Computing (ICSTCC), 2016

This paper deals with the class of discrete-time linear dynamics affected by polytopic uncertaint... more This paper deals with the class of discrete-time linear dynamics affected by polytopic uncertainty in closed loop with contractive piecewise affine (PWA) control law. Starting from the hypothesis that the synthesis ensures a λ-contractive PWA control law for the nominal model, the objective is to calculate the robustness margin guaranteeing the contractivity (and consequently the asymptotic stability) of the closed loop dynamics. The robustness margin is represented as a subset of parameters within the set describing the polytopic uncertainty. For all these parameters, the λ-contractive behavior of the trajectories can be certified. This set of parameters is then compared to the set assuring the invariance of the considered closed-loop PWA dynamics which represents a limit case of the robustness study presented here.

Journal of Optimization Theory and Applications, 2016

Parametric convex programming has received a lot of attention, since it has many applications in ... more Parametric convex programming has received a lot of attention, since it has many applications in chemical engineering, control engineering, signal processing, etc. Further, inverse optimality plays an important role in many contexts, e.g., image processing, motion planning. This paper introduces a constructive solution of the inverse optimality problem for the class of continuous piecewise affine functions. The main idea is based on the convex lifting concept. Accordingly, an algorithm to construct convex liftings of a given convexly liftable partition will be put forward. Following this idea, an important result will be presented in this article: any continuous piecewise affine function defined over a polytopic partition is the solution of a parametric linear/quadratic programming problem. Regarding linear optimal control, it will be shown that any continuous piecewise affine control law can be obtained via a linear optimal control problem with the control horizon at most equal to 2 prediction steps.

2008 IEEE International Conference on Computer-Aided Control Systems, 2008

Abstract Robustness of Model Predictive Control (MPC) has been extensively investigated, consider... more Abstract Robustness of Model Predictive Control (MPC) has been extensively investigated, considering both on-line and off-line strategies. However the implementation of the theoretical background required within such methodologies may appear complicated to ...

2015 20th International Conference on Process Control (PC), 2015

This paper presents a detailed description of Finite Control Set Model Predictive Control (FCS-MP... more This paper presents a detailed description of Finite Control Set Model Predictive Control (FCS-MPC) applied to three-level neutral point clamped inverter (3L-NPC). The controller uses a model of the converter, DC link and load to calculate predictions of the future values of the load currents and DC-link capacitor voltages for all possible voltage vectors. The cost function is defined to minimize the error between the reference currents and predicted load currents, balance the DClink capacitor voltage and reduce the switching frequency. The optimal switching state that minimizes the cost function is selected and applied to the converter. Furthermore, the quality of the current and voltage are improved by using a two prediction steps procedure. Simulation results for the one and two prediction step are presented and compared with linear current controller and space-vector modulation (PI-SVM). The obtained results show the better performances of the proposed control method.

2007 Mediterranean Conference on Control & Automation, 2007

Through many industrial applications, predictive control has proven its ability to give better pe... more Through many industrial applications, predictive control has proven its ability to give better performance while keeping its implementation relatively easy. From the basic version, several approaches have been developed to robustify an initial predictive law towards unstructured uncertainties. However, most of them provide high robustness bounds but penalize the disturbance rejection performance, and are built under the transfer function formalism difficult to extend to multivariable systems. To overcome these difficulties, this paper presents a methodology for enhancing the robustness of a GPC controlled system by convex optimization of the Youla parameter. This methodology, completely formulated with the state-space representation, starts with the design of an initial stabilizing GPC controller; this controller is then robustified off-line using LMI techniques to find the best trade-off between stability robustness and nominal performance, which represents the original contribution. The developed robustified GPC controller is finally applied to the velocity control of an induction machine, aiming at reducing the impact of additive unstructured uncertainties on the system, while respecting a time-domain template for the disturbance rejection.

2011 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), 2011

ABSTRACT This paper presents an effective model-based pre- dictive approach for the precise traje... more ABSTRACT This paper presents an effective model-based pre- dictive approach for the precise trajectory tracking of an anthropomorphic robot arm. The proposed control strategy is based on feedback linearization and linear Generalized Predictive Control, requiring no on-line optimization proce- dure. Experimental evaluation of the proposed method and its comparison with two classic robot control approaches illustrate its tracking performances and robustness with respect to non- compensated load variations. I. INTRODUCTION Over the last few decades, the efficiency of the Model Predictive Control (MPC) has been demonstrated through a large number of industrial applications (1), (2). Such a strategy is of interest when a plant model is available and the reference trajectory is known, which makes it relevant for precise trajectory tracking by a robot manipulator. The difficulty of the implementation of a MPC approach in this context lies in the highly nonlinear, fast dynamic behavior of the manipulator and the limited computation time in real- time controllers. Indeed, in nonlinear MPC the control signal is computed by solving a nonlinear optimization problem at each sampling period. Existing MPC approaches for robot motion control there- fore tend to avoid the on-line optimization process by provid- ing an analytical solution of the predictive control algorithm. This is usually achieved either by using an approximated model of the manipulator, or by applying linear MPC on a robot first linearized by feedback. Examples of the first strategy can be found in (3) and (4), where closed-form expressions of the predictive controller are obtained using Taylor series expansions of the robot nonlinear model. A computationally-efficient simplified predictive controller is proposed in (5), illustrated by an experimental implementa- tion on a 6 degrees-of-freedom (dof) parallel manipulator. In the feedback linearization approach, several predictive laws have been proposed for the outer-loop controller, such as the Dynamic Matrix Control (DMC) in (6), or the Predictive Functional Control (PFC) in (7). The latter has been exper- imentally demonstrated on a parallel 4-dof mechanism (8), requiring however an intermediary re-identification and sta- bilization of the linearized system.

Proceedings of the 2010 American Control Conference, 2010

This paper presents a new methodology for Youla-Kučera parameter synthesis using invariant sets ... more This paper presents a new methodology for Youla-Kučera parameter synthesis using invariant sets techniques. For a linear discrete-time system affected by perturbations and constraints and with the state derived by means of an observer, the proposed method gives the best Youla parameter in terms of finding the maximal invariant ellipsoid satisfying the constraints. As a result of this technique that combines the advantages of the Youla parameter and the invariant set, a larger maximal ellipsoid is derived together with an improved sensitivity function compared to the ones obtained for the system with observer only. In order to improve also performances, considering complementary sensitivity function and transient response toward output disturbances, a new bound is imposed to the Lyapunov function. This approach is finally validated in simulation considering position control of an induction motor.

IFAC-PapersOnLine, 2017

In sensorless control for synchronous machines at low speed and standstill, the position estimati... more In sensorless control for synchronous machines at low speed and standstill, the position estimation can be sensitive to the choice of the carrier frequency of the injection method. Moreover, electromagnetic saturation or temperature variation in the machine might also affect the estimation error. In order to better describe the high-frequency (HF) behaviour of the machine, the effective HF inductances and resistances are presented in this paper. Then, the analytical expression for the carrier frequency dependent error is explained using the calculated HF-equivalent model and is proposed to be integrated into the sensorless control scheme when a rotating HF voltage injection is employed. Numerical simulations highlight the frequency dependent error and prove the satisfactory operation of the compensation.

Bulletin Mathematique De La Societe Des Sciences Mathematiques De Roumanie, 2018

The control design techniques for linear or hybrid systems under constraints lead often to off-li... more The control design techniques for linear or hybrid systems under constraints lead often to off-line state-space partitions with non-overlapping convex polyhedral regions. This corresponds to a piecewise affine (PWA) state feedback control laws associated to polyhedral partition of the state-space. The aim of this paper is to consider perturbation in the representation of the vertices of such polyhedral regions. Another idea behind this study is to perform a quantization operation on the representation of the state-space regions and the associated PWA control laws in order to reduce the hardware requirements in terms of processor speed and memory unit. The quantized state-space partitions lose some of the important properties of the explicit controllers: non-overlapping, convexity and invariant characterization. The major contribution of this work is to analyze to what extend the non-overlapping and the invariance characteristics of the PWA controller can be preserved when perturbati...

Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics Service, 2008

The procedure of system identification of multi-mass servo system using different methods is desc... more The procedure of system identification of multi-mass servo system using different methods is described in this paper. Different black-box models are identified. Previous experimental results show that a model consisting of three-masses connected by springs and dampers gives an acceptable description of the dynamics of the servo system. However, this work shows that a lower order black-box model, identified using off-line or on-line experiments, gives better fit. The purpose of this contribution is to present experimental identification of a multi-mass servo system using different algorithms.

Journal of Dynamic Systems, Measurement, and Control, 2021

This article presents an approach to efficiently control grippers/multifingered hands for dextero... more This article presents an approach to efficiently control grippers/multifingered hands for dexterous manipulation according to a task, i.e., a predefined trajectory in the object space. The object motion is decomposed using a basis of predefined object motions equivalent to object-level coordinate couplings and leading to the definition of the task-level space. In the proposed approach, the decomposition of the motion in the task space is associated with a robust control design based on linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Eigenvalue placement ensures the robustness of the system to geometric uncertainties and eigenvector placement decouples the system according to task specifications. A practical evaluation of the proposed control strategy is provided with a two-fingers' and six degrees-of-freedom robotic system manipulating an object in the horizontal plane. Results show a better trajectory tracking and the robustness of the control law acc...

2019 18th European Control Conference (ECC), 2019

This article presents a stability analysis of object grasping with a compliant multi-fingered rob... more This article presents a stability analysis of object grasping with a compliant multi-fingered robot hand. This stability analysis is based on an energetic approach, in which we aim to compute the maximum amount of energy that can be stored by a compliant hand-object system about a stable equilibrium before being destabilized. More specifically, the case of external disturbance wrenches is investigated. This analysis admits several applications, two of which are illustrated in this article on a case study. First the quality of a given grasp can be quantified in terms of maximum allowed disturbance force and the associated displacement around the initial equilibrium, with applications in trajectory design for the robot arm that holds the hand-object system. Conversely, given a task specified in terms of known disturbance wrenches set, the proposed approach helps determining the optimal grasp for an enhanced stability, e.g. the contact points locations, joint compliance or internal forces levels.

2016 18th European Conference on Power Electronics and Applications (EPE'16 ECCE Europe), Sep 1, 2016

The paper presents a detailed description of the prediction model for Predictive Power Control ba... more The paper presents a detailed description of the prediction model for Predictive Power Control based on Virtual Flux (MPPC-VF) scheme for control grid connected three-level neutral-point clamped inverter (3L-NPC). The controller uses a model to calculate predictions of the future values of the virtual flux, grid currents and DC-link capacitor voltages for all possible voltage vectors. The active and reactive power can be estimated based on the virtual flux and the current. The cost function is defined to minimize the error between the active, reactive power and their references, balance the DC-link capacitor voltage and reduce the switching frequency. The optimal switching state that minimizes the cost function is selected and applied to the inverter. Simulation results under different conditions are presented and compared with conventional Direct Power Control and Space Vector Modulation (DPC-SVM). The obtained results show the better performances of the proposed control method.

2017 21st International Conference on Control Systems and Computer Science (CSCS), May 1, 2017

The control design techniques for linear or hybrid systems (e.g. anti-wind up, MPC) lead often to... more The control design techniques for linear or hybrid systems (e.g. anti-wind up, MPC) lead often to off-line state-space partitions with non-overlapping convex polyhedral regions. This corresponds to a piecewise state feedback control laws associated to polyhedral partition of the state-space. In this work, we consider the perturbation in the representation of the vertices of the polyhedral regions. For such control laws, this problem is of particular interest with respect to the reduced precision representation of the state-space partition. The perturbed state-space partitions might lose one of the important property of the explicit controllers: the "non-overlapping" characterization. We derive a set called vertex sensitivity region to determine the admissible perturbation independently for each vertex of the polyhedral partition. A perturbation is deemed admissible if the non-overlapping property of the polyhedral regions is preserved. In the present work, the analysis of the sensitivity of each vertex is done under the assumption that the rest of the partition remains on the nominal configuration.

Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics Service, 2008

An off-line technique enabling to robustify an initial Model Predictive Control (MPC) for multiva... more An off-line technique enabling to robustify an initial Model Predictive Control (MPC) for multivariable systems via the convex optimization of a Youla parameter is presented. Firstly, a multivariable predictive controller is designed for a nominal system and then robustified towards unstructured uncertainties, while guaranteeing stability properties over a specified polytopic domain of uncertainties. This condition leads to verify a Bilinear Matrix Inequality (BMI) for each vertex of the polytopic domain. This BMI can be mathematically relaxed to semi-definite programming (SDP) using a Sum of Squares (SOS) strategy, with a significant increase of the number of scalar decision variables. To overcome this inconvenient, an alternative tractable sub-optimal solution for the BMI is proposed, based on the elaboration of a stable solution obtained by minimization of the complementary sensitivity function.

IEEE Access, 2019

In this paper, a new power control strategy based on a model predictive power control for the gri... more In this paper, a new power control strategy based on a model predictive power control for the grid-tie three-level neutral point clamped inverter is presented. A dynamical model based on the orientation of grid voltage is used to predict the performance of control variables required for the system. A cost function that includes the tracking power ability, the neutral-point voltage balancing and switching frequency reduction is used to achieve the optimal switching state. A proposed selection scheme of control input is introduced to comprehend the stability of the closed-loop system and reduce the computational cost. At each sampling time, only candidate switching state inputs that guarantee the stability condition through a control Lyapunov function is evaluated in the cost function of the MPC algorithm. Thus, the execution time is remarkably decreased by 26% in comparison with traditional model predictive control. Moreover, the deadtime effect is compensated by incorporating its influence in the proposed prediction model. Simulation and experimental results compared with the traditional model predictive control are used to confirm the effectiveness of the proposed scheme. INDEX TERMS Computational burden, control Lyapunov function, dead-time compensation, finite control set model predictive control, stability conditions, three-level neutral-point-clamped inverter. NOMENCLATURE C 1 , C 2 , C dc DC-link capacitance. i g , u g Grid current and voltage. i z Neutral-point current. K d , K q Positive gains of Lyapunov function. L f , R f Filter inductance and resistance. ω Grid voltage angular frequency. θ Grid voltage angle in the stationary frame. λ uz , λ sw Weighting factor of voltage balance, switching frequency reduction. P g , Q g Grid active and reactive powers. The associate editor coordinating the review of this manuscript and approving it for publication was Alfeu J. Sguarezi Filho. S x Switching state of the 3L-NPC inverter. t d , t on , t off Dead-time, turn-on/off time of IGBT. T s Sampling time of the controller. u inv Inverter output voltage. U dc DC-bus voltage. u z Neutral-point voltage. SUPERSCRIPTS * Reference value. p Predicted value. SUBSCRIPTS d, q d, q axis of grid voltage oriented reference frame. α, β α, β axis of stationary reference frame.

The International Journal of Advanced Manufacturing Technology, 2018

This paper presents an Off-line Gain Adjustment (OGA) approach to reduce contour error in 5-axis ... more This paper presents an Off-line Gain Adjustment (OGA) approach to reduce contour error in 5-axis high speed machining. The proposed contour error formulation is based on the estimation of tool contact points and the OGA is inspired from the idea of Model Predictive Control (MPC). The control gains used in the position loop of servo drives are optimally adjusted off-line to reduce the contour error for the considered trajectory. The obtained gain profiles are computed preserving axis kinematic limitations, stability criterion of servo drives and the motor current constraints. The OGA is developed thanks to a validated machine simulator. The simulation results prove that the OGA reduces significantly the contour error in 5-axis high speed machining.

International Journal of Intelligent Robotics and Applications, 2018

This work proposes a design and performance quantification methodology for observer-based impact ... more This work proposes a design and performance quantification methodology for observer-based impact detection in serial robot manipulators in presence of modelling errors and without force/torque sensor. After expressing the modelling errors between the physical robot and its inverse dynamic model as the sum of contributions due to dynamic parameters uncertainties and numerical differentiation errors for a given trajectory, an observer of the external disturbance torque is designed based on the inverse dynamic model and using a Kalman filter. The influence of each design parameter of the observer on the quality of the external torque estimation is studied first based on simulation results. Then a frequency analysis is conducted to distinguish between the influence of the exact external torque, the modelling uncertainties and the measurement noise on the estimated external torque. Finally a methodology is proposed to determine the optimal design corresponding to the shortest detection time depending on the expected sensitivity.

Automatica, 2017

This paper presents a new approach for control design of constrained linear systems affected by b... more This paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties. This method hinges on so-called convex liftings which emulate control Lyapunov function by providing a constructive framework for optimization based control implementation. It will be shown that this method can guarantee the recursive feasibility and robust stability in the sense of Lyapunov. Finally, a numerical example will be presented to illustrate this method.

2016 20th International Conference on System Theory, Control and Computing (ICSTCC), 2016

This paper deals with the class of discrete-time linear dynamics affected by polytopic uncertaint... more This paper deals with the class of discrete-time linear dynamics affected by polytopic uncertainty in closed loop with contractive piecewise affine (PWA) control law. Starting from the hypothesis that the synthesis ensures a λ-contractive PWA control law for the nominal model, the objective is to calculate the robustness margin guaranteeing the contractivity (and consequently the asymptotic stability) of the closed loop dynamics. The robustness margin is represented as a subset of parameters within the set describing the polytopic uncertainty. For all these parameters, the λ-contractive behavior of the trajectories can be certified. This set of parameters is then compared to the set assuring the invariance of the considered closed-loop PWA dynamics which represents a limit case of the robustness study presented here.

Journal of Optimization Theory and Applications, 2016

Parametric convex programming has received a lot of attention, since it has many applications in ... more Parametric convex programming has received a lot of attention, since it has many applications in chemical engineering, control engineering, signal processing, etc. Further, inverse optimality plays an important role in many contexts, e.g., image processing, motion planning. This paper introduces a constructive solution of the inverse optimality problem for the class of continuous piecewise affine functions. The main idea is based on the convex lifting concept. Accordingly, an algorithm to construct convex liftings of a given convexly liftable partition will be put forward. Following this idea, an important result will be presented in this article: any continuous piecewise affine function defined over a polytopic partition is the solution of a parametric linear/quadratic programming problem. Regarding linear optimal control, it will be shown that any continuous piecewise affine control law can be obtained via a linear optimal control problem with the control horizon at most equal to 2 prediction steps.

2008 IEEE International Conference on Computer-Aided Control Systems, 2008

Abstract Robustness of Model Predictive Control (MPC) has been extensively investigated, consider... more Abstract Robustness of Model Predictive Control (MPC) has been extensively investigated, considering both on-line and off-line strategies. However the implementation of the theoretical background required within such methodologies may appear complicated to ...

2015 20th International Conference on Process Control (PC), 2015

This paper presents a detailed description of Finite Control Set Model Predictive Control (FCS-MP... more This paper presents a detailed description of Finite Control Set Model Predictive Control (FCS-MPC) applied to three-level neutral point clamped inverter (3L-NPC). The controller uses a model of the converter, DC link and load to calculate predictions of the future values of the load currents and DC-link capacitor voltages for all possible voltage vectors. The cost function is defined to minimize the error between the reference currents and predicted load currents, balance the DClink capacitor voltage and reduce the switching frequency. The optimal switching state that minimizes the cost function is selected and applied to the converter. Furthermore, the quality of the current and voltage are improved by using a two prediction steps procedure. Simulation results for the one and two prediction step are presented and compared with linear current controller and space-vector modulation (PI-SVM). The obtained results show the better performances of the proposed control method.

2007 Mediterranean Conference on Control & Automation, 2007

Through many industrial applications, predictive control has proven its ability to give better pe... more Through many industrial applications, predictive control has proven its ability to give better performance while keeping its implementation relatively easy. From the basic version, several approaches have been developed to robustify an initial predictive law towards unstructured uncertainties. However, most of them provide high robustness bounds but penalize the disturbance rejection performance, and are built under the transfer function formalism difficult to extend to multivariable systems. To overcome these difficulties, this paper presents a methodology for enhancing the robustness of a GPC controlled system by convex optimization of the Youla parameter. This methodology, completely formulated with the state-space representation, starts with the design of an initial stabilizing GPC controller; this controller is then robustified off-line using LMI techniques to find the best trade-off between stability robustness and nominal performance, which represents the original contribution. The developed robustified GPC controller is finally applied to the velocity control of an induction machine, aiming at reducing the impact of additive unstructured uncertainties on the system, while respecting a time-domain template for the disturbance rejection.

2011 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), 2011

ABSTRACT This paper presents an effective model-based pre- dictive approach for the precise traje... more ABSTRACT This paper presents an effective model-based pre- dictive approach for the precise trajectory tracking of an anthropomorphic robot arm. The proposed control strategy is based on feedback linearization and linear Generalized Predictive Control, requiring no on-line optimization proce- dure. Experimental evaluation of the proposed method and its comparison with two classic robot control approaches illustrate its tracking performances and robustness with respect to non- compensated load variations. I. INTRODUCTION Over the last few decades, the efficiency of the Model Predictive Control (MPC) has been demonstrated through a large number of industrial applications (1), (2). Such a strategy is of interest when a plant model is available and the reference trajectory is known, which makes it relevant for precise trajectory tracking by a robot manipulator. The difficulty of the implementation of a MPC approach in this context lies in the highly nonlinear, fast dynamic behavior of the manipulator and the limited computation time in real- time controllers. Indeed, in nonlinear MPC the control signal is computed by solving a nonlinear optimization problem at each sampling period. Existing MPC approaches for robot motion control there- fore tend to avoid the on-line optimization process by provid- ing an analytical solution of the predictive control algorithm. This is usually achieved either by using an approximated model of the manipulator, or by applying linear MPC on a robot first linearized by feedback. Examples of the first strategy can be found in (3) and (4), where closed-form expressions of the predictive controller are obtained using Taylor series expansions of the robot nonlinear model. A computationally-efficient simplified predictive controller is proposed in (5), illustrated by an experimental implementa- tion on a 6 degrees-of-freedom (dof) parallel manipulator. In the feedback linearization approach, several predictive laws have been proposed for the outer-loop controller, such as the Dynamic Matrix Control (DMC) in (6), or the Predictive Functional Control (PFC) in (7). The latter has been exper- imentally demonstrated on a parallel 4-dof mechanism (8), requiring however an intermediary re-identification and sta- bilization of the linearized system.

Proceedings of the 2010 American Control Conference, 2010

This paper presents a new methodology for Youla-Kučera parameter synthesis using invariant sets ... more This paper presents a new methodology for Youla-Kučera parameter synthesis using invariant sets techniques. For a linear discrete-time system affected by perturbations and constraints and with the state derived by means of an observer, the proposed method gives the best Youla parameter in terms of finding the maximal invariant ellipsoid satisfying the constraints. As a result of this technique that combines the advantages of the Youla parameter and the invariant set, a larger maximal ellipsoid is derived together with an improved sensitivity function compared to the ones obtained for the system with observer only. In order to improve also performances, considering complementary sensitivity function and transient response toward output disturbances, a new bound is imposed to the Lyapunov function. This approach is finally validated in simulation considering position control of an induction motor.