Generalized Proportional Integral Research Articles

A Multiple-Sensor Fault-Tolerant Control of a Single-Phase Pulse-Width Modulated Rectifier Based on MRAS and GPI Observers

Due to their advantages in ensuring low harmonic distortion and high power factors, single-phase Pulse-Width Modulated (PWM) rectifiers are widely employed in several industrial applications. Generally, the conventional control loop of a single-phase PWM rectifier uses both voltage and current sensors. Hence, in case of sensor fault, the performance and the availability of the converter can be seriously compromised. Therefore, diagnosis approaches and fault-tolerant control (FTC) strategies are mandatory to monitor these systems. Accordingly, this paper introduces a novel multiple-sensor FTC scheme for a single-phase PWM rectifier. The proposed fault diagnosis approach relies on joining several Generalized Proportional Integral (GPI) and Model Reference Adaptive System (MRAS) observers with a residual generation technique to detect and isolate sensor faults in a simple and reliable manner. While conventional sensor FTC methods dedicated to PWM rectifiers can only deal with single faults, the suggested approach guarantees a very good effectiveness level of sensor fault detection, isolation (FDI) and FTC of multiple-sensor fault occurrence scenarios. Consequently, the single-phase PWM rectifier can work with only the survivable single sensor with the guarantee of very good performance as in healthy operation mode. The effectiveness of the proposed sensor FDI approach and its control reconfiguration performance are demonstrated through both extensive simulation and experimental results.

GPI observer-based active disturbance rejection control for a morphing quadrotor

Quadrotors are widely used in transportation, aerial photography, agricultural protection, and other important fields. Nevertheless, quadrotors with a fixed structure will face great challenges when crossing through or entering narrow spaces for operations. To improve quadrotor crossing ability in different environments, a morphing quadrotor is designed in this paper, and four servo motors are added to independently change four arm rotation angles. Meanwhile, the dynamic model and dynamic control allocation matrix are established. In addition, considering that the internal dynamic variation caused by morphologic changes and external disturbances may compromise system stability, a control method based on the generalized proportional integral (GPI) observer is proposed to increase the system robustness, and the corresponding stability analysis is provided. Finally, simulation results demonstrate the effectiveness of the proposed GPI observer-based active disturbance rejection control method.

CNC Machines for Rehabilitation: Ankle and Shoulder

Continuous passive motion (CPM) machines are used in the rehabilitation of members that have been injured to recover their range of motion and prevent stiffness. Nowadays, some CPM machines for the knee, ankle, arm, and elbow are available commercially. In this paper, ankle and shoulder rehabilitation robots, based on an X-Y table, are presented. The novelty of these rehabilitation robots is that they have a computerized numerical control system, resulting in low-cost machines. Some G-codes for basic and combined movement routines for ankle and shoulder rehabilitation are presented. In addition, the use of a robust generalized PI controller is also proposed to guarantee safe rehabilitation movements and compensate for passive stiffness in the ankle joint of stroke survivors. Some numerical simulations are included to illustrate the dynamic performance of the robust Generalized Proportional Integral (GPI) controller using the virtual prototype.

Different Active Disturbance Rejection Controllers Based on the Same Order GPI Observer

As the higher order or generalized extended state observer (ESO), generalized proportional-integral (GPI) observer (GPIO) haves been proposed to enhance the active disturbance rejection (ADR) control (ADRC) system's disturbance rejection ability. However, different ADR controllers can be deduced based on the same order GPIO, resulting in different dynamic performances. In this article, ten different ADR controllers based on the fourth order GPIO are present. In order to reveal the relationship between these ADR controllers and the conventional ADR controllers based on the third order ESO, six different third-order-ESO-based ADR controllers are present and compared with the fourth-order-ESO-based ADR controllers. To ease the comparison between different ADRC systems, a common expression is built for different ADR controllers. A novel frequency-domain analysis method is also introduced to reveal how the observer and feedback control law affects the closed-loop control system's dynamic performance. The effectiveness of the proposed method is verified on the test bench based on dSPACE DS1103.

A Robust Controller for Upper Limb Rehabilitation Exoskeleton

In this paper, a portable exoskeleton for the rehabilitation of upper extremities of three degrees of freedom (DOF) is proposed. With these degrees of freedom, the exoskeleton provides the movements of flexion–extension and abduction–adduction of the arm and flexion–extension of the forearm. A robust generalized proportional integral (GPI) controller for trajectory tracking to provide smooth movements for rehabilitation with the exoskeleton is proposed. This controller only requires output measurements and is robust against different types of disturbances. Simulation results are presented in the MSC Adams® software environment in co-simulation with Matlab-Simulink® to show the controller’s performance against different types of disturbances. The results of a PID type controller are also contrasted with the results of the GPI controller.

Integration of CNN in a Dynamic Model-Based Controller for Control of a 2DOF Helicopter With Tail Rotor Perturbations

This paper shows a proposal for a control scheme for the trajectory tracking problem in a Two Degree of Freedom Helicopter (2DOFH). For this purpose, a control scheme based on a feedback linearization combined with a Generalized Proportional Integral (GPI) controller is used. In order to implement linearization by feedback, it is required to know and have access to all the physical 2DOFH parameters, however, angular velocity and viscous friction are often not available. Commonly, state observers are used to know the angular velocity, however, estimating friction results out to be more complex. Therefore, we propose the use of a Convolutional Neural Network (CNN) to estimate viscous friction and angular velocity. The variables estimated by the CNN are entered into both the GPI and feedforward controllers. Thus, the system is brought to a linear representation that directly relates the GPI control to the dynamics of perturbations and non-model parameters. Finally, results of numerical simulations are shown that validate the robustness of our scheme in the presence of disturbances in the tail rotor, as well as the advantages of using a feedforward control based on a CNN.

Controlling the PVTOL Aircraft System with an Inverted Pendular Load by means of Nested Saturation Functions and GPI Controller

This paper presents a control scheme that allows height position regulation and stabilization for an unmanned planar vertical takeoff and landing aircraft system with an inverted pendular load. The proposed controller consists of nested saturations and a generalized proportional integral (GPI). The GPI controls the aircraft height and the roll attitude; the latter is used as the fictitious input control. Next, the system is reduced through linear transformations, expressing it as an integrator chain with a nonlinear perturbation. Finally, the nested saturation function-based controller stabilizes the aircraft’s horizontal position and the pendulum’s angle. Obtaining the control approach was a challenging task due to the underactuated nature of the aircraft, particularly ensuring the pendulum’s upright position. The stability analysis was based on the second method of Lyapunov using a simple candidate function. The numerical simulation confirmed the control strategy’s effectiveness and performance. Additionally, the numerical simulation included a comparison against a PD controller, where its corresponding performance indexes were estimated, revealing that our controller had a better response in the presence of unknown disturbances.

Regulation of Nonlinear Chemical Processes with Variable Dead Time: a Generalized Proportional Integral Controller Proposal

This work shows the development and application of a Generalized Proportional Integral (GPI) Controller based on a First Order Plus Dead Time (FOPDT) approximation for an industrial chemical process. GPI control is a relatively recent advancement in automatic control. Nowadays, several enhancements with the GPI technique come from integral reconstructions of the system states. Chemical engineering processes present numerous challenging control problems, including nonlinear dynamic behavior. GPI can become a new option to consider in industrial applications since, along with the arrival of Industry 4.0, there are many improvements in computers and automation architecture to implement controller algorithms. The new controller's functionality shows significant accessibility of mathematical and logical potential. A comparison between the GPI and a PID controller is made under the same conditions to evaluate their performance. After carrying out some tests, the GPI shows better performance and a smoother controller action when applied to the mixing tank with a variable delay than the PID. Performance indexes as Integral Square Error (ISE) for evaluating the Output Variable and Control Effort Total Variation (TVu) for evaluating the control action are used to measure performance. Finally, designing an appropriate controller like the GPI that recognizes and incorporates nonlinearities is required for chemical processes. Simulations were developed using Simulink-MATLAB.

Experimental implementation of a novel model‐free adaptive fractional‐order sliding mode controller for a flexible‐link manipulator

SummaryThis paper presents an experimental study of a robust control scheme for a single flexible‐link manipulator. Regarding the nonlinear dynamics of flexible manipulators and vibration problems associated with these robots, this study aims to propose a novel fractional‐order controller for efficient reference tracking, even in the presence of noise and total disturbances. In this regard, the control term is formulated by adopting the intelligent proportional–integral–derivative (PID) (iPID) technique and sliding mode control. As for estimating unknown states of the system, and ensuring that time‐variable disturbances are well‐handled and they do not excite vibrating modes, the generalized proportional integral (GPI) observer is utilized. Then, the adaptive reaching laws are derived along with the Lyapunov stability analysis, and finite‐time convergence of the sliding surface is proven. Finally, well‐trajectory tracking and robustness of the system are illustrated by the experimental results. The effectiveness of the fractional calculus in terms of accuracy, control effort, and vibration suppression is depicted as well.

Generalised Proportional Integral Control for Magnetic Levitation Systems Using a Tangent Linearisation Approach

This paper applies a robust generalised proportional integral (GPI) controller to address the problems of stabilisation and position tracking in voltage-controlled magnetic levitation systems, with consideration of the system’s physical parameters, non-linearities and exogenous disturbance signals. The controller has been developed using as a basis a model of the tangent linearised system around an arbitrary unstable equilibrium point. Since the approximate linearised system is differentially flat, it is therefore controllable. This flatness gives the resulting linearised system a relevant cascade characteristic, thus allowing simplification of the control scheme design. The performance of the proposed GPI controller has been analysed by means of numerical simulations and compared with two controllers: (i) a standard proportional integral derivative (PID) control, and (ii) a previously designed exact feedforward-GPI controller. Simulation results show that the proposed GPI control has a better dynamic response than the other two controllers, along with a better performance in terms of the integral squared tracking error (ISE), the integral absolute tracking error (IAE), and the integral time absolute tracking error (ITAE). Finally, experimental results have been included to illustrate the effectiveness of the proposed controller in terms of position stabilisation and tracking performance when appreciable non-linearities and uncertainties exist in the underlying system. Comparative graphs and metrics have shown a superior performance of the proposed GPI scheme to control the magnetic levitation platform.

Improved Low Voltage Ride-Through Capability of DFIG with ESO Controller under Unbalanced Network Conditions

Under unbalanced grid condition, in a Doubly-Fed Induction Generator (DFIG), voltage, current, and flux of the stator become asymmetric. Therefore, active-reactive power and torque will be oscillating. In DFIG controlling Rotor Side Converter (RSC) aims to eliminate power and torque oscillations. However, simultaneous elimination of the power and torque oscillations is not possible. Also, Grid Side Converter (GSC) aims to regulate DC-Link voltage. In this paper, in order to regulate DC-Link voltage, an Extended State Observer (ESO) based on a Generalized Proportional-Integral (GPI) controller, is employed. In this controlling method, DC-Link voltage is controlled without measuring the GSC current, and due to using the GPI controller, the improved dynamic response is resistant against voltage changes, and the settling time is reduced. To improve the transient stability and Low Voltage Fault Ride Through (LVRT) capability of DFIG, Statistic Fault Current Limiter (S-FCL) and Magnetic Energy Storage Fault Current Limiter (MES-FCL) are proposed in this paper. The proposed FCL does not only limit the fault current but also fasten voltage recovery. The simulations are implemented by MATLAB software in the synchronous positive and negative sequence reference (d-q).

Control of Doubly-fed Induction Generator with Extended State Observer under Unbalanced Grid Conditions

Under unbalanced grid condition, in a doubly-fed induction generator (DFIG), voltage, current, and flux of the stator become asymmetric. Therefore, active-reactive power and torque will be oscillating. In DFIG controlling rotor side converter (RSC) aims to eliminate power and torque oscillations. However, simultaneous elimination of the power and torque oscillations is not possible. Also, grid side converter (GSC) aims to regulate DC-Link voltage. In this paper, in order to regulate DC-Link voltage, an extended state observer (ESO) based on a generalized proportional-integral (GPI) controller, is employed. In this controlling method, DC-Link voltage is controlled without measuring the GSC current, and due to using the GPI controller, the improved dynamic response is resistant against voltage changes, and the settling time is reduced. A versatile rotor position computation algorithm (RPCA) is utilized to measure the rotor speed. This algorithm is simple, yet it is accurate and is resistant to changes in the resistance of the rotor and stator. The simulations are implemented by MATLAB software in the synchronous positive and negative sequence reference (d-q).

FPGA‐based active disturbance rejection velocity control for a parallel DC/DC buck converter‐DC motor system

This study deals with the robust velocity controller of a DC motor driven by means of parallel DC/DC buck power converters with equal current distribution, from the perspective of a generalised proportional–integral (GPI)-observers-based active disturbance rejection controller (ADRC). The multivariable system is subject to constant torque load demands and changes in the internal parameters. The linear output feedback controllers actively counteract the exogenous and endogenous disturbances that result from the cascading parallel converter and the DC motor. A rapid prototyping tool is used for synthetising the proposed controller into a field-programmable gate array (FPGA) which is based on Matlab/Simulink and a Xilinx System Generator. The robustness of the proposed ADRC system is analysed. The FPGA-based implementation setup is presented with the purpose of validating the theoretical calculations of the proposed DC motor velocity control.

Controlador robusto para el seguimiento de trayectorias para un exoesqueleto de extremidades inferiores

Currently, robotics has shown that it can increase the efficiency in the specific rehabilitation of some of the limbs of the human body, in this case assisting people who have suffered a stroke, by using devices such as exoskeletons, to provide continuous, smooth and controlled movements. Stroke is the result of a shortage of the brain that leads in just a few minutes to cell death, causing severe damage to the human body, even death of the patient. People who have suffered a stroke have difficulty rising from a chair. An exoskeleton is a mechanical structure designed to be used on the human body as a garment, it serves as a support and is used to assist movements or accentuate strength as a support in a person. Lower extremity exoskeleton can assist patients with hemiplegia to get up or sit on a chair, thus avoiding muscle atrophy and possible spasticity. This paper proposes the use of a robust Generalized Proportional Integral (GPI) controller for trajectory tracking for controlling a six degrees of freedom exoskeleton, to assist patients when getting up and sitting down from a chair. Simulation results obtained with the virtual prototype of the exoskeleton, under the environment of the MSC Adams software in co-simulation with Matlab are presented.

Passivity-based tracking control of an omnidirectional mobile robot using only one geometrical parameter

This paper presents an output feedback tracking control scheme for a three-wheeled omnidirectional mobile robot, based on passivity property and a modified generalized proportional integral (GPI) observer. The proposed control approach is attractive from an implementation point of view, since only one robot geometrical parameter (i.e., contact radius) is required. Firstly, a nominal dynamic model is given and the passivity property is analyzed. Then the controller is designed based on passivity property and a modified GPI observer. The controller design objective is to preserve the passivity property of the robot system in the closed-loop system, which is conceptually different from the traditional model-based control methodology. Particularly, the designed control system takes full advantage of the robot natural damping. Therefore, only considerably small or non differential feedback is needed. In addition, theoretical analysis is given to show the closed-loop stability behavior. Finally, experiments are conducted to validate the effectiveness of the proposed control system design in both tracking and robustness performance.

Control Algorithm for Taking off and Landing Manoeuvres of Quadrotors in Open Navigation Environments

This paper presents a control algorithm for the taking off and landing manoeuvres of a quadrotor aircraft in open navigation environments. For this purpose, a combination of controllers based on nested saturations and a generalised proportional integral (GPI) controller is used. The first controller limits both the angular positions and angular velocities in a small compact set, which defines the closed-loop stability domain and guarantees the total convergence of the state, whereas the second is designed for the translational aspect, considering the presence of disturbances during landing. The proposed controller is designed considering the presence of disturbances; therefore, greater robustness is obtained regarding perturbations that may occur in open navigation environments. The algorithm convergence is proven by means of Lyapunov’s second method. Several numerical simulations are presented to demonstrate the effectiveness of our proposed algorithm, and a comparison test against an effective method for indoor environments is provided to illustrate its superior performance.

Robust compound control of dynamic bipedal robots

This paper presents a robust compound control strategy to produce a stable gait in dynamic bipedal robots under random perturbations. The proposed control strategy consists of two interactive loops: an adaptive trajectory generator and a robust trajectory tracking controller. The adaptive trajectory generator produces references for the robot controlled joints without a-priori knowledge of the terrain features and minimizes the effects of disturbances and model uncertainties during the gait, particularly during the support-leg exchange. The trajectory tracking controller is a non-switching robust multivariable generalized proportional integral (GPI) controller. The GPI controller rejects external disturbances and uncertainties faced by the robot during the swing walking phase. The proposed control strategy was evaluated on the numerical model of a five-link planar bipedal robot with one degree of under-actuation, four actuators, and point feet. The results showed robust performance and stability under external disturbances and model parameter uncertainties on uneven terrain with uphills and downhills. The stability of the gait was proven through the computation of a Poincaré return map for a hybrid zero dynamics with uncertainties (HZDU) model, which shows convergence to a bounded neighborhood of a nominal orbital periodic behavior.

Linear active disturbance rejection control for a raceway photobioreactor

In this paper, the problem of pH regulation in photobioreactors has been addressed by using a robust Proportional–Integral controller in combination with a linear active disturbance rejection approach. This formulation is based on the Generalized Proportional–Integral (GPI) observers design to estimate online external disturbances and non-modeled dynamics. The methodology uses a model reference optimization procedure with tracking and regulatory target closed-loop transfer functions for first-order plus dead-time models. The proposed controller is validated on a full-scale Raceway photobioreactor, whose results show a significant improvement in the accuracy of pH regulation and, consequently, a positive influence on biomass production. Moreover, a classical feedforward approach has been used for comparison purposes. The performance of the robust technique is evaluated with different indexes, whose results confirm the good performance of the proposed active disturbance rejection control scheme.

Active Disturbance Rejection Control of the Inertia Wheel Pendulum through a Tangent Linearization Approach

A flatness based approach is proposed for the linear Active Disturbance Rejection Control (ADRC) stabilization of a nonlinear inertia wheel pendulum (IWP) around its unstable equilibrium point, subject to unmodelled dynamics and disturbances. The approach exploits the cascade structure, provided by the flatness property, of the tangent linearization of the underactuated system which allows designing a high gain linear cascaded Extended State Observer (ESO) of the Generalized Proportional Integral (GPI) type. This class of linear observers is employed to build an Active Disturbance Rejection Control controller with a lower order of complexity regarding other ADRC classic schemes. Experimental results demonstrate the effectiveness and feasibility of the proposed approach, as well as a better behavior with respect to a classic control technique in the presence of disturbances.

From flatness, GPI observers, GPI control and flat filters to observer-based ADRC

In this article, we establish the route taken by the author, and his research group, to bring differential flatness to the realm of active disturbance rejection control (ADRC). This avenue entitled: 1) generalized proportional integral observers (GPIO), as natural state and disturbance observers for flat systems, 2) generalized proportional integral (GPI) control, provided with extra integrations, to produce a modular controller known as flat filters (FF’s) and, finally, 3) the establishing of an equivalence of observer based ADRC with FF’s. The context is that of pure integration systems. The obtained controllers depend only on the order of the flat system and they are to be directly used on the basis of the available flat output signal in a universal, modular, fashion. The map is complemented with the relevant references where the intermediate techniques were illustrated and developed, over the years, in connection with laboratory experimental implementations.