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Microalgae have been explored as a promising alternative energy source over the last few years, and several control strategies have been developed to maintain their operational conditions. However, these bioprocesses still pose difficult challenges, due to the nonlinearity and uncertainties of microalgal dynamics. This paper addresses the problem of biomass regulation in a continuous culture of the microalga Dunaliella tertiolecta. Our strategy is based on a Proportional-Integral (PI) controller assisted by a Generalized Proportional Integral (GPI) observer, in order to mitigate the impact of disturbances on biomass levels. The proposed design was tested via numerical simulation, using MATLAB/Simulink™ 2020a environment. The robustness of the controller was demonstrated by subjecting the simulated bioreactor to disturbances and changes in reference biomass densities. The proposed strategy effectively tracked the reference within an insignificant deviation ±0.5%. Furthermore, our proposal effectively rejected disturbances that classical PI was unable to counter.

This paper introduces a nonlinear disturbance observer for hybrid dynamical systems with continuous and discrete dynamics. The hybrid dynamical system considered in this work is a bipedal robot. The robot is modeled by a continuous mathematical model connected to a discrete reset functions. The continuous and discrete dynamics are exposed to model parameter uncertainties and external disturbances. The uncertainties and disturbances in the continuous dynamics are lumped into a total disturbance signal, which is estimated through a nonlinear extended state observer (NESO). The disturbance estimation is used to design an active disturbance rejection control (ADRC). To address the reset function uncertainties on the discrete dynamics, a reference trajectory generator is designed to achieve zero tracking error after each reset function using a smooth transition function from the system state to the nominal references. The control strategy proposed in this work is applied to the gait control of a planar, dynamic bipedal robot with point feet, five degrees of freedom, and one degree of underactuation. The gait stability is tested through a linearized Poincare return map.

This document presents an application of Active Disturbance Rejection Control (ADRC) in a secondary frequency regulation problem with an active participation of renewable photovoltaic and wind generators. This problem is known as Load Frequency Control (LFC). The ADRC technique uses a reduced set of information of the model by grouping the effects of non-modeled dynamics, exogenous disturbances, and parameter uncertainties into a generalized equivalent disturbance, which in this case is estimated by an Extended-State Observer. This makes it possible to design a decentralized controller that achieves the bifold control objective of a secondary LFC strategy in each area. The proposed controller is able to regulate the frequency of each area and the tie-line power exchanges in presence of several load disturbances. The simulation scenarios validate the control proposal and show the flexibility and advantages of the application of ADRC-based control techniques as decentralized solutions to an LFC problem.

This study addresses the problem of periodic load mitigation of three-bladed horizontal-axis wind turbines. In periodic load reduction, individual pitch control (IPC) has proved to be effective by means of controllers with an internal model that takes into account the periodic signal frequency. However, the frequency components on the blades vary with the rotor speed of the wind turbine and the above controllers reduce their mitigation performance. This paper proposes a new IPC scheme to mitigate the main frequency components of the periodic disturbances affecting the rotor and structure of wind turbines. The IPC scheme is based on the active disturbance rejection (ADR) philosophy and is formulated in spatial-domain instead of time-domain. The spatial-domain formulation of the controller assures that the disturbance rejection performance is not affected by changes of the rotor speed. A 5 MW reference wind turbine implemented in the FAST (fatigue, aerodynamics, structures and turbulence) code is used for the validation. The results show effective attenuation of the periodic load components of the blades using the proposed ADR scheme.

An Active Disturbance Rejection Control based on Generalized Proportional Integral observer (ADRC with GPI observer) was developed to control the gait of a bipedal robot with five degrees of freedom. The bipedal robot used is a passive point feet which produces an underactuated dynamic walking. A virtual holonomic constraint is imposed to generate online smooth trajectories which were used as references of the control system. The proposed control strategy is tested through numerical simulation on a task of forward walking with the robot exposed to external disturbances. The performance of ADRC with GPI observer strategy is compared with a feedback linearization with proportional-derivative control. A stability test consisting on analyzing the existence of limit cycles using the Poincare's method revealed that asymptotically stable walking was achieved. The proposed control strategy effectively rejects the external disturbances and keeps the robot in a stable dynamic walking.

A digital signal processing approach to estimate and reject disturbances under an active disturbance rejection control (ADRC) methodology is presented. In this paper a technique to assess the current values of the disturbance based on the previous input and output signals is developed. The on-line disturbance estimation is made through the use of a polynomial least squares regression. An excess in the number of data over the order of the polynomial regression is proposed in order to obtain a low pass filter. This estimation allows to simplify the control design in to a linear one. Corresponding performance, stability and robustness are analyzed. The propose approach is tested via numerical simulation in a trajectory tracking task under perturbed linear and nonlinear differentially flat systems. The simulations showed that the technique presented to estimate disturbances is successful in its application to active disturbance rejection control on linear and nonlinear systems.

This work proposes an ADRC (Active Disturbance Rejection Control) for parallel robotic platform, namely the Stewart-Gough configuration. The platform is intended for CNC machining processes where repeatability and accuracy requirements of the robot's motion are of utmost importance. The proposed approach makes use of linear high gain disturbance observation, where model uncertainties and external disturbances are lumped together into a general additive disturbance input that is estimated by Generalized Proportional Integral (GPI) observers and rejected on-line. The GPI control strategy replaces the more common PID controller in the joint control framework, and is used in order to better reject disturbances and non-linearities related with the robot configuration. Simulation results obtained by a co-simulation between Matlab and NX software, where the interaction dynamics and actuator non-linearities of the platform (i.e. saturation and headbands) were taking into account, closely approximate real robot operation and shows that the GPI observer-based linear control presents a better performance tracking trajectories compared with other control schemes, i.e. mixed sensitivity H∞ control.

The problem of Active Disturbance Rejection control for active power filters subject to periodic disturbances is tackled by means of a discrete-time Generalized Proportional Integral (GPI) observer-based control. An extended state observer-based control scheme is proposed for the active filter application according to the Active Disturbance Rejection strategy. In this scheme, model uncertainties and external disturbances are included in a general additive disturbance input which is estimated on-line and subsequently rejected via the controller action. The observer carries out the disturbance estimation, thus reducing the complexity of the controller design. The controller efficiency is tested via realistic computer simulations of a one-phase shunt active power filter, performing a trajectory tracking task under nonlinear and linear loads for power factor correction and harmonic compensation purposes. Performance analysis for varying frequency conditions are also presented.

In this paper, a comparison between the Field-Oriented Control (FOC) scheme and the Generalized Proportional Integral (GPI) controller for a permanent magnet synchronous motor (PMSM) is presented. The GPI controller scheme consists in two stages, the first one is a speed control loop which gives the reference control signals, the second stage is a current controller which generates finally the voltage signals. Experimental results show the characteristics of both control techniques.

A field oriented armature input voltage output feedback control approach is proposed for the robust linear controller design on an induction motor. The scheme simultaneously solves an angular velocity reference trajectory tracking task, and a flux magnitude regulation in the presence of arbitrary time varying load torques and unknown nonlinearities. The field oriented input voltage scheme is combined with linear high gain asymptotic observers, of the Generalized Proportional Integral (GPI) type, and linear, active disturbance rejection, output feedback controllers. The linear observers on-line estimate, in a simultaneous manner, the output phase variables and the lumped effects of a) unknown time-varying load torques and unmodeled frictions and b) rather complex state-dependent nonlinearities present in the electric and magnetic circuits. The field oriented part of the scheme uses the classical flux observer, or simulator. The proposed control laws naturally decouple, while linearizing, the extended second order dynamics for the angular velocity and for the squared flux magnitude. The proposed control scheme is here tested on an experimental induction motor set up.

This article proposes the use of a high gain, Generalized Proportional Integral (GPI), observer for the accurate linear estimation of nonlinear endogenous, and exogenous, disturbance inputs affecting the creation of local sliding regimes, on a given sliding manifold, for Single-Input Single-Output (SISO) systems with limited control authority. Active, online, estimation, and cancelation, of state dependent and time-dependent disturbances, significantly contribute to reducing the required switching control amplitude needed to sustain a sliding regime. This method results in enhanced performance on the controlled variable. Illustrative simulation examples are presented which validate the proposed approach.

A linear output feedback controller is developed for trajectory tracking problems defined on a modified version of Chua's circuit. The circuit modification considers the introduction of a suitable external control input channel guided by a) the induction of the flatness property on a measurable output signal of the circuit and b) the physical viability of the control input. A linear active disturbance rejection control, based on a high gain linear disturbance observer, is implemented on a laboratory prototype. We show that the state-dependent disturbance can be approximately, but arbitrarily closely, estimated through a linear, high-gain, observer, called a Generalized Proportional Integral (GPI) observer, which contains a linear combination of a sufficient number of extra iterated integrals of the output estimation error. Experimental results are presented in the output reference trajectory tracking of a signal generated by an unrelated chaotic system of the Lorenz type. Laboratory experiments illustrate the proposed linear methodology for effectively controlling chaos.

In this article, we propose a fast, on-line, algebraic identification scheme for the determination of some relevant induction motor parameters. The estimated values, given by the algebraic identification methodology, are here tested in a self-tuning output feedback control, subject to constant perturbation load torques while solving a reference trajectory tracking task. An output feedback controller of the classical, Field Oriented, Proportional Integral (PI) type, is proposed for the perturbed output trajectory tracking problem. Experimental results validate the effectiveness of the proposed approach.

In this article, we propose a new discontinuous feedback controller design approach for the asymptotic sliding mode control of a large class of linear switched systems. The method is devoid of state measurements and efficiently extends the sliding mode control methodology to traditional input-output descriptions of the plant. The approach is based on regarding the average Generalized Proportional Integral (GPI) output feedback controller design as a guide for defining the sliding mode features. Throughout, it is assumed that the available output signal coincides with the system's flat output, an output capable of completely differentially parameterizing all the variables in the system (inputs, original outputs and state variables) and exhibits no zero dynamics. Encouraging simulation results are presented in connection with a tutorial example. Experimental results are also presented for the trajectory tracking problem on a popular DC-to-DC switched power converter of the “buck” type.

The problem of controlling load perturbed induction motors is tackled by means of an observer based robust discrete-time control. In this scheme, model uncertainties and external disturbances are included in a general additive disturbance input which is to be on-line estimated and subsequently rejected via the controller actions. The observer carries out the disturbance estimation, thus reducing the complexity of the controller design. The controller efficiency is tested via some numerical simulations, performing a trajectory tracking task under severe load variations.

In this article, we propose an identification-based control scheme for a DC Brushless motor drive. The identification scheme is based on the algebraic identification method which allows for fast parameter identification whose, on line, computed values are used in canceling out the nonlinearities of the system dynamics thus reducing the control problem to that of a pure integration system. The control scheme consists of two stages: the first one is a outer loop current control which generates the required reference signal for the inner loop velocity control. A Generalized Proportional Integral control scheme is used in both loops, obtaining accurate, feasible, results as demonstrated by numerical simulations.

In this article, we propose a state-free discontinuous feedback controller design approach for the asymptotic sliding mode control of a large class of linear switched systems. The method is devoid of state measurements and efficiently extends the sliding mode control methodology to traditional input-output descriptions of the plant. The approach is based on regarding the average Generalized Proportional Integral (GPI) controller design as a guide for inducing the sliding mode features through the switching controller. Throughout, it is assumed that the available output signal coincides with the system's flat output, an output capable of completely differentially parameterizing all the variables in the system (inputs, original outputs and state variables) and exhibits no zero dynamics. Encouraging simulation results are presented in connection with the tutorial example. Experimental results are also presented for the trajectory tracking problem on a popular DC-to-DC switched power converter of the “buck” type.

In this paper, the noise filtering problem (“de-noising” problem) is approached via a suitable modification of the traditional Luenberger observer approach, also known as the “high gain observer” approach (HGO). The HGO observer is, fundamentally, a Luenberger observer with large stable eigenvalues of the output estimation error dynamics. HGO and some of its modifications have been particularly useful in the linear based control of perturbed linear and nonlinear systems. HGO are, however, inappropriate to deal with noisy injection signals and noisy plants. To overcome this fact, the structure of the Luenberger state estimator reconstructing the time derivatives of the given signal is enhanced against the effects of noise by means of an algebraic filtering scheme. The algebraic filtering consists in a suitable modification of the recently introduced algebraic parameter identification methodology. The proposed approach is capable of attenuating the noise effects significantly. The proposed strategy is illustrated via numerical simulations.

We tackle the problem of controlling a mechanical system by means of a robust discrete-time linear predictive control which is the discrete time version of the Robust Generalized Proportional Integral Control. It is assumed that the model uncertainties and external disturbances are bounded and bandlimited, so that they can be modeled by means of a polynomial approximation which needs to be rejected. The controller efficiency is proven by means of experimental results in a trajectory tracking task under disturbance inputs.

In this article, we propose a two stage control design scheme for simultaneous flux regulation and angular position reference trajectory tracking in induction motors. The first outer loop design stage uses a linear GPI observer based robust control, aimed at on-line load torque estimation, thus making possible its cancelation from the controller. The stator currents act as auxiliary control input variables, within a field oriented control scheme, which uses a nonlinear asymptotic flux reconstructor. The designed current signals are used then as reference trajectories for the second, inner loop, design stage, corresponding to a switched stator input voltage strategy based on an average Generalized Proportional Integral control design. This average design defines a discontinuous control input by means of a properly set sign function on the input tracking error. The second controller design stage, largely overcomes the effects of nonlinearities, including unknown motor parameters, present in the rotor voltages-to-rotor currents multi-variable dynamics.

In this article, we propose a field oriented control scheme of two stages. The first stage keeps the tracking of the angular velocity and simultaneously, regulates the flux modulus by means of the stator currents. These designed current signals are used as reference trajectories for the second stage. Both stages use observer based controllers of Generalized Proportional Integral (GPI) nature. The trajectory tracking task is defined on the angular velocity of a complete model of an induction motor subject to a completely unknown, but bounded, load torque perturbation input. The robustness is tested under deviation of system parameter, additive unknown perturbations and high frequency measurement noises in the closed loop system. A numerical simulation verifies the effectiveness of the proposed scheme.

We tackle the problem of synchronization of two oscillators as a control problem. The system to control is taken as a chain of integrators control where the remainder of the dynamics is considered as an additive disturbance. This disturbance is locally approximated by a m-order time polynomial and then it is cancelled out by means of a robust Generalized Proportional Integral controller. Two examples are shown. The first one is a Duffing system as a reference and a controlled Van Der Pol as a tracker, and the second example is the synchronization of two Rosslerpsilas systems. Some numerical results are shown.

This work deals with the control, and the on line algebraic identification, for an unknown perturbed 1 degree of freedom (DOF) suspension system. The algebraic identifier is provided with an automatic disconnection strategy of the fast on-line identification subsystem. The automatic disconnection is achieved by assessing an extra auxiliary parameter, called the ldquosentinelrdquo parameter, that monitors the convergence of the rest of the system parameters estimation process. The estimated values of mass, stiffness and damping is realized via an adaptive algebraic estimator, with great rapidity and robustness to noise process signals present in the input and output signals measurements. A generalized proportional integral (GPI) controller was designed for the trajectory tracking task and for the rejection of a constant disturbance input. The switched implementation of the average input in the form of a bounded discontinuous control signal is based on the use of a Sigma-Delta sliding mode based modulator. In an average sense, this modulation allows us preserve the desirable features of the dynamic output feedback controller and to be close to a real implementation. The efficiency of the complete procedure is demonstrated via digital computer simulations.