Embedded Model Control Research Articles

Embedded model control of networked control systems: An experimental robotic application

In Networked Control System (NCS), the absence of physical communication links in the loop leads to relevant issues, such as measurement delays and asynchronous execution of the control commands. In general, these issues may significantly compromise the performance of the NCS, possibly causing unstable behaviours. This paper presents an original approach to the design of a complete digital control unit for a system characterized by a varying sampling time and asynchronous command execution. The approach is based on the Embedded Model Control (EMC) methodology, whose key feature is the estimation of the disturbances, errors and nonlinearities affecting the plant to control and their online cancellation. In this way, measurement delays and execution asynchronicity are treated as errors and rejected up to a given frequency by the EMC unit. The effectiveness of the proposed approach is demonstrated in a real-world case-study, where the NCS consists of a differential-drive mobile robot (the plant) and a control unit, and the two subsystems communicate through the web without physical connection links. After a preliminary verification using a high-fidelity numerical simulator, the designed controller is validated in several experimental tests, carried out on a real-time embedded system incorporated in the robotic platform.

Drag-free design based on Embedded Model Control for TianQin project

With the ability to detect low-frequency gravitational waves (GWs), space-borne detectors will play an important role in exploring the universe in the future. The TianQin project proposed in China participates in this challenge by aiming to detect millihertz GWs. The TianQin GW detector consists of three spacecraft forming a triangular constellation. Each spacecraft carries a pair of test masses (TM) which, inside shielding cages, are left to free fall along the local geodesic. In this way, a pair of TMs on two separate spacecraft can be each other aligned to become the gravitational references of the GW detector, made by an inter-satellite laser interferometer. Each free-falling TM is limited by parasitic forces to be appropriately bounded. The relevant acceleration bound has been fixed to 10−15 m/s2/Hz within the TianQin measurement bandwidth (MBW) ranging from 0.1mHz to 0.1Hz. In turn, TM to cage fluctuations must be kept below 4nm/Hz to limit the stiffness coupling with the spacecraft displacement caused by non-gravitational disturbances, such as solar radiations and the thruster noise. Suppression of such disturbances calls for a challenging drag-free control technology, since the center of mass (CoM) of a single spacecraft cannot track the separated CoMs of two TMs simultaneously, and consequently tracking must be limited to three degrees of freedom (DoF): two non-orthogonal sensitive axes (one for each TM) and the perpendicular direction to their plane. Control design and simulated tests of this paper will be restricted to the drag-free control along the sensitive axes. The remaining nine DoFs of the two TMs (position and attitude) are controlled by electrostatic suspensions, not to be treated here, but accounted for in the simulated trials. The design of the two-DoF drag-free control relies on a model-based control methodology, the Embedded Model Control (EMC), capable of predicting and suppressing unknown disturbances within the required bandwidth and of decoupling the TM dynamics along the non-orthogonal sensitive axes. The paper starts with the nonlinear model of the TM to cage dynamics, followed by the relevant EMC design, restricted to the sensitive axes. Numerical simulations are employed to validate closed-loop performance and robust stability. Simulated results show that the residual TM to cage fluctuations can be kept below 3nm/Hz, which leaves a margin within the required spectral bound. The EMC methodology discussed in the paper can provide a reference for future developments and implementations.

Embedded model control for underactuated systems: An application to Furuta pendulum

The main goal of the paper is to test the Embedded Model Control (EMC) design and implementation on a typical underactuated apparatus, like the Furuta pendulum, by comparing experimental results with a Linear Quadratic Regulator (LQR). EMC can be considered as a disturbance rejection control strategy, since the state predictor is extended to explicitly include disturbance dynamics, in charge of predicting the uncertainty to be rejected by control law. Essential in EMC design is the separation between controllable and not controllable dynamics, a task which allows us to find the controllable channel of underactuated systems from the low-dimensional command to the whole system degrees of freedom (DF). Pursuing this objective, a rather generic method is shown, which is applicable to other underactuated systems. The result is a very simple controllable dynamics from the single pendulum command to pendulum DF arranged in a single series of controllable integrators. The neglected feedback channels, including the unstable gravity feedback, are treated as unknown thus posing a challenge to disturbance prediction and closed loop stability. Typical in EMC, closed loop eigenvalues are chosen to guarantee stability, a pre-requisite to performance. Experimental results point out effectiveness and advantage, with respect to LQR, of design and implementation under adverse conditions, due to a disturbance pulse, in which command saturates.

Control Design for UAV Quadrotors via Embedded Model Control

In this paper, a control system for unmanned aerial vehicles (UAVs) is designed, tested in simulation by means of a high-fidelity simulator, and then applied to a real quadrotor UAV. A novel approach is proposed for the control design, based on the combination of two methodologies: feedback linearization (FL) and embedded model control (EMC). FL allows us to properly transform the UAV dynamics into a form suitable for EMC; EMC is then used to control the transformed system. A key feature of EMC is that it encompasses a so-called extended state observer (ESO), which not only recovers the system state but also gives a real-time estimate of all the disturbances/uncertainties affecting the system. This estimate is used by the FL-EMC control law to reject the aforementioned disturbances/uncertainties, including those collected via the FL, allowing a robustness and performance enhancement. This approach allows us to combine FL and EMC strengths. Most notably, the entire process is made systematic and application oriented. To set-up a reliable UAV attitude observer, an effective attitude sensors fusion is proposed and also benchmarked with an enhanced complementary filter. Finally, to enhance the closed-loop performance, a complete tuning procedure, encompassing frequency requirements, is outlined, based on suitably defined stability and performance metrics.

UAV quadrotor attitude control: An ADRC-EMC combined approach

This study presents an original approach to the design of a complete digital attitude control unit for a UAV quadrotor. The approach is developed within the framework of Active Disturbance Rejection Control (ADRC) and Embedded Model Control (EMC), two well-established control design methodologies, both based on the estimation of the disturbances/uncertainties affecting the plant to control, and on their online cancellation. The attitude control design carried out in this paper demonstrates the possibility of adopting a simple input–output model to control the UAV attitude, while relying on the disturbance rejector to bridge the gap between model and plant reality. The designed attitude control unit encompasses an attitude state predictor, a control law, and a model-based reference generator. A multi-step test strategy is proposed to assess the performance of this disturbance-rejection-based attitude controller. Consequently, the presented experimental results are obtained both using a high-fidelity numerical simulator and in several experimental tests, carried out either on a laboratory single-axial test-bench or in-flight. Finally, the control unit performance is benchmarked, in simulation, against a state-of-the-art high-performance UAV attitude controller.

Embedded model control: Reconciling modern control theory and error-based control design

The paper addresses the problem of reconciling the modern control paradigm developed by R. Kalman in the sixties of the past century, and the centenary error-based design of the proportional, integrative and derivative (PID) controllers. This is done with the help of the error loop whose stability is proved to be necessary and sufficient for the close-loop plant stability. The error loop is built by cascading the uncertain plant-to-model discrepancies (causal, parametric, initial state, neglected dynamics), which are driven by the design model output and by arbitrary bounded signals, with the control unit transfer functions. The embedded model control takes advantage of the error loop and its equations to design appropriate algorithms of the modern control theory (state predictor, control law, reference generator), which guarantee the error loop stability and performance. A simulated multivariate case study shows modeling and control design steps and the coherence of the predicted and simulated performance.

Embedded model control GNC for the Next Generation Gravity Mission

A Next Generation Gravity Mission (NGGM) concept for measuring the Earth's variable gravity field has been recently proposed by ESA. The mission objective consists in measuring the temporal variations of the Earth gravity field over a long-time span, with very high spatial and temporal resolutions.This paper focuses on the guidance, navigation and control (GNC) design for the science phase of the NGGM mission. NGGM will consist of a two-satellite long-distance formation like GRACE, where each satellite will be controlled to be drag-free like GOCE. Satellite-to-satellite distance variations, encoding gravity anomalies, will be measured by laser interferometry. The formation satellites, distant up to 200 km, will fly in a quasi-polar orbit at an Earth altitude between 300 and 450 km.Orbit and formation control counteract bias and drift of the residual drag-free accelerations, in order to reach orbit/formation long-term stability. Drag-free control allows the formation to fly counteracting the atmospheric drag, ideally subject only to gravity.Orbit and formation control, designed through the innovative Integrated Formation Control (IFC), have been integrated into a unique control system, aiming at stabilizing the formation triangle consisting of satellites and Earth Center of Masses.In addition, both spacecraft must align their control axis to the satellite-to-satellite line (SSL) with micro-radian accuracy. This is made possible by specific optical sensors and the inter-satellite laser interferometer, capable of materializing the SSL. Such sensors allow each satellite to pursue an autonomous alignment after a suitable acquisition procedure. Pointing control is severely constrained by the angular drag-free control, which must ideally zero the angular acceleration vector, in the science frequency band.The control unit has been designed according to the Embedded Model Control methodology and is organized in a hierarchical way, where the drag-free control plays the role of a wide-band inner loop, and orbit/formation and attitude/pointing controls are the narrow band outer loops. The relevant state equations were converted to discrete time providing the embedded model, a fundamental part of the control unit. The state predictor, control law and reference generator were built on and interfaced to the embedded model.Simulated results, via a high-fidelity simulator, prove the concept validity and show that the control performances are in agreement with the defined mission requirements. Indeed, the presented control strategy is shown to be capable of keeping the attitude and formation variables stable within the required boundaries, all over the 10-year mission, through a low-thrust authority in the order of a few milli-Newton.

The four-tank control problem: Comparison of two disturbance rejection control solutions

The paper aims to compare and prove a pair of disturbance/uncertainty rejection control laws for the well-known four-tank control problem. The control requirements are expressed in terms of a set point sequence as usual in the literature. The uncertainty class is defined as the union of four sub-classes: unknown disturbance, parametric uncertainty, measurement errors and neglected dynamics. Modelling and design give insight on the dynamic properties of the problem. Two theorems, which fix the range of application, are presented. These theorems are confirmed by the simulated results, and indicate the correct way to further broaden the control design applicability. The disturbance rejection design is deployed using the Embedded Model Control methodology. Accordingly, only the unknown disturbance and parametric uncertainty can be rejected, whereas the effects of neglected dynamics must be filtered. As a result, simple performance and stability inequality can be formulated in the frequency domain: they guide the closed-loop pole placement. These inequalities reveal whether pole placement is feasible and how feasibility can be recovered. The latter is an issue, which at the authors’ knowledge, is rarely encountered in the literature. Simulated runs prove the effectiveness of the design procedure.

Embedded model control, performance limits: A case study

Este trabajo presenta el análisis e implementación de dos leyes de control aplicadas en un caso de estudio. La primera y el enfoque principal de este trabajo es el control a modelo embebido cuyas características fundamentales son la cancelación activa de disturbios y el manejo de incertidumbres. Aquí se prueban diferentes configuraciones para los parámetros del control logrando que los límites en el desempeño queden expuestos debido a las limitaciones del modelo. Por otro lado se encuentra la ley de control PID clásica basada en acciones sobre el error de trayectoria como un paradigma de control que no requiere de un modelo para su ejecución. La implementación y pruebas se hacen en una planta didáctica comercial, donde se verifican las propiedades de desempeño y rechazo a perturbaciones mostrando que aun en este simple proceso el desempeño puede verse degradado debido a la ausencia de un modelo de la planta embebido en la ley de control

Proportional electro-hydraulic valves: An Embedded Model Control solution

Hierarchical control architectures are a common approach when hydraulic systems are under study; provided their multi-domain nature, the control scheme is commonly split into different hierarchical levels each one associated with a particular physical domain. This paper presents the application of a model-based control structure called Embedded Model Control (EMC) when a hierarchical scheme is implemented on an electro-hydraulic proportional valve. The overall control consists of two hierarchical loops: the inner loop is the solenoid current regulator with a closed loop bandwidth close to 1kHz. The outer loop is a position tracking control, in charge of the accurate positioning of the spool with respect to valve openings. The paper addresses the outer loop, i.e., the tracking of mechanical spool position by using the EMC. Analysis and synthesis are presented as well as experimental results obtained from a test rig provided by an industrial manufacturer.

A Novel Controller Design for the Next Generation Space Electrostatic Accelerometer Based on Disturbance Observation and Rejection.

The state-of-the-art accelerometer technology has been widely applied in space missions. The performance of the next generation accelerometer in future geodesic satellites is pushed to , which is close to the hardware fundamental limit. According to the instrument noise budget, the geodesic test mass must be kept in the center of the accelerometer within the bounds of 56 by the feedback controller. The unprecedented control requirements and necessity for the integration of calibration functions calls for a new type of control scheme with more flexibility and robustness. A novel digital controller design for the next generation electrostatic accelerometers based on disturbance observation and rejection with the well-studied Embedded Model Control (EMC) methodology is presented. The parameters are optimized automatically using a non-smooth optimization toolbox and setting a weighted H-infinity norm as the target. The precise frequency performance requirement of the accelerometer is well met during the batch auto-tuning, and a series of controllers for multiple working modes is generated. Simulation results show that the novel controller could obtain not only better disturbance rejection performance than the traditional Proportional Integral Derivative (PID) controllers, but also new instrument functions, including: easier tuning procedure, separation of measurement and control bandwidth and smooth control parameter switching.

Embedded Model Control for UAV Quadrotor via Feedback Linearization

This study investigates the use of the feedback linearization approach as a novel way to design the internal model for Embedded Model Control (EMC). The feedback linearization allows to collect all the nonlinearities at command level. EMC, by means of a disturbance dynamics model, makes possible to estimate and then reject the non-linear terms through the control law. This idea is applied to the control of an Unmanned Aerial Vehicle: the Borea project quadrotor. Embedded Model Control methodology implies the design of an internal model (Embedded Model) coded into the control unit and running in parallel with the plant. The attitude reconstruction problem is faced by means of a state observer developed on purpose and fully integrated with the model. A two-modes control strategy is proposed in order to reject systematic sensor errors, thus enhancing the attitude estimation capability. Using a high-fidelity numerical simulator, the feasibility of the proposed control strategy was demonstrated. This indicates that a feedback linearization approach allows the extension of EMC techniques to non-linear systems control. What is more, the EMC was successfully applied to the control of the Borea quadrotor.

Stochastic modelling and prediction for spacecraft drag-free control

Spacecraft drag-free control is an effective way to make satellite orbit only shaped by gravity and to achieve accurate and quiet alignment of the spacecraft axes to their reference. Essential measurements come from fine accelerometers. Exploiting the experience of the GOCE satellite drag-free and attitude control, the paper provides an integrated modelling and control design procedure which encompasses accelerometer and spacecraft control. Essential to this framework is the stochastic modelling and prediction of the unknown disturbance class to be counteracted. Stochastic modelling of disturbance is the key asset of the Embedded Model Control methodology. Among other advantages it allows robust decoupling of state prediction and control for complex dynamic systems

Satellite-to-satellite attitude control of a long-distance spacecraft formation for the Next Generation Gravity Mission

The paper presents the design and some simulated results of the attitude control of a satellite formation under study by the European Space Agency for the Next Generation Gravity Mission. The formation consists of two spacecrafts which fly more than 200km apart at an altitude from the Earth׳s ground of between 300 and 400km. The attitude control must keep the optical axes of the two spacecraft aligned with a microradian accuracy (pointing control). This is made possible by specific optical sensors accompanying the inter-satellite laser interferometer, which is the main payload of the mission. These sensors allow each spacecraft to actuate autonomous alignment after a suitable acquisition procedure. Pointing control is constrained by the angular drag-free control, which is imposed by mission science (Earth gravimetry at a low Earth orbit), and must zero the angular acceleration vector below 0.01μrad/s2 in the science frequency band. This is made possible by ultrafine accelerometers from the GOCE-class, whose measurements must be coordinated with attitude sensors to achieve drag-free and pointing requirements. Embedded Model Control shows how coordination can be implemented around the embedded models of the spacecraft attitude and of the formation frame quaternion. Evidence and discussion about some critical requirements are also included together with extensive simulated results of two different formation types.

Digital current regulator for proportional electro-hydraulic valves with unknown disturbance rejection

Solenoid current regulation is well-known and standard in any proportional electro-hydraulic valve. The goal is to provide a wide-band transfer function from the reference to the measured current, thus making the solenoid a fast and ideal force actuator within the limits of the power supplier. The power supplier is usually a Pulse Width Modulation (PWM) amplifier fixing the voltage bound and the Nyquist frequency of the regulator. Typical analog regulators include three main terms: a feedforward channel, a proportional feedback channel and the electromotive force compensation. The latter compensation may be accomplished by integrative feedback. Here the problem is faced through a model-based design (Embedded Model Control), on the basis of a wide-band embedded model of the solenoid which includes the effect of eddy currents. To this end model parameters must be identified. The embedded model includes a stochastic disturbance dynamics capable of estimating and correcting the electromotive contribution together with parametric uncertainty, variability and state dependence. The embedded model which is fed by the measured current and the supplied voltage becomes a state predictor of the controllable and disturbance dynamics. The control law combines reference generator, state feedback and disturbance rejection to dispatch the PWM amplifier with the appropriate duty cycle. Modeling, identification and control design are outlined together with experimental result. Comparison with an existing analog regulator is also provided.

Control architecture and simulation of the Borea quadrotor

The paper presents modelling, control design and simulated results preliminary to test the Borea quadrotor. Guidance, navigation and control strategy are implemented following the Embedded Model Control (EMC) scheme.

Guidance and control for the propulsion phase of planetary landing

In the propulsion phase of planetary landing, horizontal motion is obtained by tilting and aligning the axial thrust either to the opposite of the velocity vector or to the acceleration vector. The second strategy is assumed here, as it allows free horizontal motion and accurate landing. Instead of designing a hierarchical guidance and control in which horizontal acceleration becomes the attitude reference, a unique control system is designed based on a fourth-order state equation per degree-of-freedom from angular acceleration to position coordinate. Following the Embedded Model Control methodology, a unique discrete-time state equation is derived and employed by guidance, navigation and control. Here guidance and control are outlined. The whole guidance, navigation and control algorithm has been tested on a high-fidelity descent simulator. The results of Monte Carlo runs for assessing performance versus requirements that are typical of accurate landing are presented and discussed.

Embedded model control calls for disturbance modeling and rejection

Robust control design guarantees closed-loop stability of a model-based control law in the presence of parametric uncertainties. Stability is guaranteed by introducing some ignorance coefficients and restricting the feedback control effort. Embedded Model Control shows that the model-based control law can be kept intact in the case of uncertainty, if the controllable dynamics is complemented by a suitable disturbance dynamics. The disturbance state must be driven by an unpredictable input vector, the noise, which can only be estimated from the model error i.e. the difference between plant and model output. The uncertainty-based design concerns the noise estimator, so as to prevent the model error from conveying uncertainty components which are command-dependent and thus prone to destabilizing the controlled plant. Separation of the components in the low and high frequency domain by the noise estimator itself allows stability recovery and guarantee, and the rejection of low frequency components. Two simple case studies help to understand the key assets of the methodology.

Embedded model control: Submicroradian horizontality of the nanobalance thrust-stand

Pendulum tilt, with respect to local gravity, is affected by the tilt and lateral acceleration of the supporting structure. A differential pendulum, such as the Nanobalance thrust-stand, would be immune only in the ideal case of perfectly balanced pendulums. In the actual case, the equivalent tilt must be zeroed in the measuring bandwidth by an active control system. This paper outlines requirements, technology, modeling, and robust control strategies to ensure instrument horizontality, achieving submicroradian accuracy in a frequency band from 0.1 mHz to 1 Hz. Control strategies, including the coordination of slow and fast motors, have been designed and implemented following the embedded model control methodology. The results of commissioning tests are given and discussed, pointing out the limits of the available technology.

Drag-free and attitude control for the GOCE satellite

The paper concerns Drag-Free and Attitude Control of the European satellite Gravity field and steady-state Ocean Circulation Explorer (GOCE) during the science phase. Design has followed Embedded Model Control, where a spacecraft/environment discrete-time model becomes the real-time control core and is interfaced to actuators and sensors via tuneable feedback laws. Drag-free control implies cancelling non-gravitational forces and all torques, leaving the satellite to free fall subject only to gravity. In addition, for reasons of science, the spacecraft must be carefully aligned to the local orbital frame, retrieved from range and rate of a Global Positioning System receiver. Accurate drag-free and attitude control requires proportional and low-noise thrusting, which in turn raises the problem of propellant saving. Six-axis drag-free control is driven by accurate acceleration measurements provided by the mission payload. Their angular components must be combined with the star-tracker attitude so as to compensate accelerometer drift. Simulated results are presented and discussed.