Generalized Proportional Integral Observer Research Articles

Single-Loop Robust Model Predictive Speed Regulation of PMSM Based on Exogenous Signal Preview

Speed regulation problem of permanent magnet synchronous motor (PMSM) with overcurrent protection is addressed in this paper by using a single-loop robust model predictive control (MPC) approach. The unique feature of this new disturbance rejection MPC method is the utilization of the preview information of lumped exogenous signal. Different from most of the existing disturbance observer-based MPC approaches, the reference inputs, the lumped disturbances in PMSM, and their higher-order differences are explicitly considered as a part of this new concept of lumped exogenous signal by exploiting output regulation theory. Preview of the possible future behaviors of this exogenous signal is conducted based upon the development of two generalized proportional integral observers (GPIOs). An accuracy enhanced prediction model is obtained by exploiting the estimation and preview of the exogenous signal during the prediction horizon. Speed regulation problem of the PMSM is transformed into an error stabilization problem by means of regulator equations and preview information where the faster time-varying exogenous signal is considered. The overcurrent protection problem is also taken into account throughout the receding horizon optimization process. Experimental studies show that the proposed method achieves effective functionality in overcurrent protection, and much better dynamic performance against time-varying exogenous inputs.

Saturated formation containment control for a heterogeneous multi-agent system with unknown perturbations

This work addresses formation containment control for a heterogeneous multi-agent system composed of first-order (FO) and second-order (SO) agents that can be either leader or follower agents. It is assumed that unknown but bounded disturbances perturb its dynamical model. An error-based version of a generalized proportional–integral observer (GPIO) is proposed to estimate these perturbations, and saturation functions, based on position measurement and estimated velocity errors, are designed to achieve the control objective. Specifically, it is shown that the leader agents converge to a desired geometric pattern following a desired trajectory simultaneously. Furthermore, the follower agents converge to the convex hull spanned by the leaders. The result applies to a group of robots in which a directed spanning tree gives the communication topology among the leaders with a root in the main leader. At the same time, each follower receives information from at least one leader agent, and the communication is directed. Real-time experiments and a comparison with a robust control technique exhibit the excellent performance of the proposed GPIO and control strategy in achieving formation containment control.

GPIO-based nonsingular terminal sliding mode control for high-pressure common rail systems

The ideal fuel rail pressure is a significant component to keep the high-pressure common rail (HPCR) system work stably. The influence of time-varying fuel injection disturbance of the HPCR system is neither fully considered nor well dealt with in traditional rail pressure control approaches. To this end, the rail pressure tracking problem of an HPCR system is investigated in this paper using a generalized proportional integral observer (GPIO)-based composite control algorithm. A nonlinear model of the HPCR system is first established based on fluid dynamics and mechanics laws. Then, a GPIO is utilized to observe the time-varying fuel injection disturbance. Based on the design of a nonlinear sliding surface using the disturbance estimation, a GPIO-based nonsingular terminal sliding mode control (NTSMC) method is proposed to achieve a better rail pressure tracking control performance and a stronger robustness. Finally, a group of simulations in the MATLAB/Simulink environment and experiments in a more realistic Advanced Modeling Environment for performing Simulation of engineering systems (AMESim) environment are conducted, the results of which demonstrate the advantage and effectiveness of the proposed method.

Smooth collision avoidance for the formation control of first order multi-agent systems

This work addresses collision avoidance in the formation control of a group of mobile robots with first-order dynamics perturbed by lateral and longitudinal slipping parameters. A Generalized Proportional–Integral Observer (GPIO) is designed to estimate these perturbations. Then, an Active Disturbance Rejection Control (ADRC) is proposed to solve the well-known formation control avoiding collisions among the agents. The control strategy only depends on the agents’ position measurements. On the other hand, Continuous Repulsive Vector Fields (C-RVFs) are developed to avoid collisions among the agents. For this purpose, a parameter depending on the inter-robot distance is developed to scale the RVFs properly. By proposing C-RVFs, the chattering is eliminated when using Discontinuous RVFs (D-RVFs). Numerical simulations and real-time experiments illustrate the agents’ performance when they are at risk of collision.

Adaptive Fixed-Time Position Precision Control for Magnetic Levitation Systems

A novel adaptive fixed-time controller (AFTC) based on disturbance compensation technology is proposed to achieve high performance position precision control for magnetic levitation system in this paper. Firstly, the dynamic model of the magnetic levitation system is established and a fixed-time controller (FTC) is designed to realize the closed-loop control. However, this approach usually requires a large switching gain to suppress interference, resulting in chattering. In view of this, the generalized proportional integral observer (GPIO) is introduced to estimate and compensate the time-varying interference, which can not only improve the anti-interference ability, but also reduce the chattering by choosing a smaller switching gain. Nevertheless, these two performance improvements come at the cost of the dynamic response rate. In order to improve steady state performance without sacrificing dynamic performance, an adaptive fixed-time controller based on GPIO is proposed, which has a significant advantage because of the adjustable switching gain. Specifically, when the system state is far from the sliding mode surface, a larger switching gain is adjusted to improve the convergence rate. When the system state is close to the sliding mode surface, a smaller switching gain is adjusted to reduce chattering. Simulation and experimental results demonstrate the superiority of the proposed AFTC-GPIO method qualitatively and quantitatively. Note to Practitioners–As a highly nonlinear system easily affected by external disturbances and system uncertainty, high precision position control of magnetic levitation system is a great challenge. In this paper, based on the accurate estimation of lumped time-varying interference by GPIO, an adaptive fixed time sliding mode controller is designed to suppress the disturbance and achieve the high precision control. Traditional sliding mode control inevitably has to choose between improving convergence rate and suppressing chattering, and the dynamic and steady performance of the system cannot be considered simultaneously. In view of this issue, this paper combines sliding mode control with adaptive control, and an adaptive and adjustable switching gain is designed, so that the system has the performance of fast convergence and small chattering. Simulation and experimental results verify the effectiveness of the proposed method. The reported AFTC-GPIO idea can also be extended to control of other types of systems.

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.

Continuous output feedback sliding mode control for underactuated flexible-joint robot

The tracking control based on output feedback for a category of flexible-joint robot (FJR) systems is investigated in this brief. Control performance of the systems is inevitably bearing the brunt of various unknown time-varying disturbances, which can be categorized to be matched and mismatched and generally cover internal parameter uncertainties, couplings, unmodelled dynamics, and external load or changing operating environments. To cope with these disturbances, the mismatched disturbances are first transferred to the matched ones by a flatness method, which eliminates the computational cost of estimating mismatched disturbances. Then, a generalized proportional integral observer (GPIO) is constructed to estimate the unavailable states and disturbances. By integrating the estimated disturbance and states provided by the GPIO, a novel dynamic sliding surface is constructed. Finally, a continuous sliding mode control (CSMC)-based output feedback control framework is further designed. The presented control strategy only requires link position information and is continuous, which can effectively reduce the chattering driven by the high-frequency switching item in the traditional SMC method. Asymptotic convergence of output tracking error is guaranteed by theoretical analysis under some mild conditions. Comparative tests on a two-link FJR verify the claimed control performance.

Composite fractional-order sliding mode controller for PMSM drives based on GPIO

In order to optimize the performance of permanent magnet synchronous motor (PMSM) drives, a fractional-order sliding mode (FOSM) control scheme combining generalized proportional integral observer (GPIO) is adopted in this paper. A FOSM controller is firstly employed to reduce the negative effects of the load torque and parameter variations in the PMSM system. However, the FOSM control method mostly needs high control gain to moderate the unfavorable effects of the total disturbance, which will inevitably lead to large chattering phenomenon. Therefore, the unknown lumped disturbance is effectively estimated by using a GPIO, and the estimated value is synchronously compensated to the FOSM speed controller. Even if a smaller control gain is chosen, the robustness of the proposed composite GPIO-based FOSM controller is better than that of the FOSM controller. Finally, the effectiveness of the proposed control strategy is verified by comprehensive simulation and experimental results.

Improved Deadbeat Predictive Current Control of Dual Three-Phase Variable-Flux PMSM Drives With Composite Disturbance Observer

The dual three-phase variable-flux permanent-magnet synchronous motors (VF-PMSM) have received more attention in the variable-speed drive applications since they have advantages of high-efficiency in flux-tuning ability, low current stresses in phase legs and high fault-tolerant capability. The magnetization-state of the permanent magnets in VF-PMSM can be manipulated by the larger <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -axis current pulse. However, the accompanied issues of parameter variation and inherent model uncertainty in magnetization manipulation of VF-PMSM increase the difficulty in parameter tuning for conventional proportional-integral controller, which deteriorates the control performance in current loop. To achieve the high performance of current tracking, an improved deadbeat predictive current control (DPCC) with composite disturbance observer has been proposed for dual three-phase VF-PMSM in this article. In the proposed composite disturbance observer, the generalized proportional--integral observer (GPIO) is employed for tracking the time-varying disturbance, and the sliding-mode observer is designed to reduce the settling time caused by the high-order GPIO for the improvement of the system dynamics. The analysis about the bandwidth-parameterized method has been presented for tuning the coefficients of the composite observer. The experimental results are presented to verify the validity of the proposed DPCC with composite disturbance observer for dual three-phase VF-PMSM drives under model uncertainty and different operating conditions.

On the equivalence between Generalized Proportional Integral Observer and Disturbance Observer

This paper presents the equivalence between generalized proportional integral observer (GPIO) and disturbance observer (DOB), which is applicable to reduced-order GPIO (ROGPIO), full-order GPIO (FOGPIO), and extended state observer (ESO). From this equivalence, established in frequency-domain, comprehensive analyses are performed regarding the influence of the system order, the number of extended states, the uncertain control gain, and the tuning method on the robustness and performance of GPIO. In addition, the equivalence allows a detailed comparison between ROGPIO and FOGPIO in the active disturbance rejection control (ADRC) framework. Finally, experimental validation of the main results is presented for the study case of a synchronous buck converter.

Zero-assignment and complex coefficient gain design of generalized proportional-integral observer for robust fault detection

Aiming at early detection of faults in dynamic systems subject to external periodic disturbances, this paper proposes a new generalized proportional-integral observer (GPIO) fault detection scheme with zero-pole joint optimization and novel complex coefficient gain (CCG) of residual evaluation. The focus of the proposed scheme is to reduce the adverse impacts caused by the semi-stationary periodic disturbance whose spectrum is uneven, with most energy being at some dominant frequencies. The proposed GPIO with a complex coefficient gain is designed in a two-stage procedure. In the first stage of zero assignment and pole optimization, the additional zeros introduced by the GPIO’s integration action are allocated to near the disturbance frequency. The gain of the transfer function matrix relating from the disturbances to the fault indicator signals is minimized by pole optimization. In the second stage of designing complex coefficient gain in residual evaluation, the unique feature of rank-deficient caused by the additional zeros assigned in stage one is further exploited to cancel the disturbances in the fault indicator signals (which is also referred to as the fault detection residual in this article). It is proved that, for an arbitrary periodic disturbance with a specific spectrum, the remnant components of the disturbance in the indicator signals generated by the GPIO can cancel each other by a complex gain vector, which can be determined by the zero eigenvalue’s left eigenvector of the rank-deficient of the disturbance transfer function matrix. The sufficient conditions for the convergence of the proposed fault detection filter are also given. Numerical examples illustrate the proposed method’s better performance in detecting minor faults.

Generalized proportional integral observer‐based event‐triggered control for frequency regulation in power systems with wind energy

AbstractThe article addresses a generalized proportional–integral observer (GPIO)‐based event‐triggered control (ETC) for load frequency problems in power systems with wind energy integration. The concept of static event‐triggered mechanism (ETM) with a fixed threshold parameter may be unreasonable in some engineering applications where the transmission rates are time varying as in the case with power systems. Therefore, in this work, a dynamic ETM is designed to dynamically adjust the threshold parameters over time to reflect the time‐varying transmission rates. The unmatched uncertainties are suppressed via high‐gain design while the external disturbance (wind speed) is estimated and attenuated by the GPIO‐based ETC. The proposed design ensures frequency and tie‐line power stabilization and saves the computational and communication resources more effectively than recently reported works in the field. The hybrid closed‐loop system's global bounded stability is theoretically proved and verified by simulation in three‐area interconnected power systems.

Dynamic prescribed performance sliding mode control for DC–DC buck converter system with mismatched time-varying disturbances

A generalized proportional integral observer (GPIO) based dynamic prescribed performance sliding mode control (DPPSMC) method for DC–DC buck converter with mismatched time-varying disturbance is proposed to achieve high output voltage tracking performance. Firstly, because extended state observer (ESO) could only estimate the constant interference, considering the mismatched time-varying interference, GPIO is designed to estimate the lumped disturbance so as to enhance the anti-disturbance performance. Then, for the sake of further improve the transient performance, the prescribed performance algorithm is introduced. However, the traditional prescribed performance adopts static performance function. The dynamic system tracking error is likely to exceed the boundaries set by performance functions due to external disturbance and uncertainty, leading to the failure of the algorithm. On account of this, a dynamic prescribed performance function (PPF) is put forward in this paper to keep the tracking error of the converter system always within the predefined error boundary and the algorithm failure problem is avoided. Finally, combined with disturbance estimation technology and dynamic PPF, DPPSMC method is designed to dispose mismatched time-varying interference and improve the transient performance. The Lyapunov stability theorem is applied to certify that the proposed control algorithm could stabilize the closed-loop system. Simulation and experimental result verify the meliority of the designed controller.

Force Ripple Compensation and Robust Predictive Current Control of PMLSM Using Augmented Generalized Proportional–Integral Observer

In this article, an augmented generalized proportional–integral observer (GPIO) is presented to estimate and then compensate for the disturbance/uncertainty both existing in the electrical and mechanical subsystems of the motion stage driven with an air-bearing permanent-magnet linear synchronous machine (PMLSM). First, a modeling method for the two subsystems, considering the disturbance/uncertainty and the integration of the measured outputs as extended states, is proposed. Second, to reduce the coupling effect of the observer gains and the measurement noises on the disturbance estimation dynamics, an augmented GPIO is designed and its convergence theorem is given. Furthermore, with the extended models, the augmented GPIO is developed for both the compensation of parameter mismatch in the predictive current control (PCC) and the force ripple estimation/suppression of the PMLSM. Finally, with the augmented GPIO, an improved PCC robustness test with time-varying parameter mismatch is conducted both in the single-current closed loop and the double-current closed loop with cascade position-current control. A simple and practical parameter-tuning procedure is also analyzed in detail for both the electrical and mechanical subsystems. The position trajectory tracking error is reduced largely with accurate and real-time force ripple compensation. Experimental setup and results are provided to validate the effectiveness of the proposed design method.

Active disturbance rejection sliding mode control for robot manipulation

PurposeIn recent years, owing to the rapidly increasing labor costs, the demand for robots in daily services and industrial operations has been increased significantly. For further applications and human–robot interaction in an unstructured open environment, fast and accurate tracking and strong disturbance rejection ability are required. However, utilizing a conventional controller can make it difficult for the robot to meet these demands, and when a robot is required to perform at a high-speed and large range of motion, conventional controllers may not perform effectively or even lead to the instability.Design/methodology/approachThe main idea is to develop the control law by combining the SMC feedback with the ADRC control architecture to improve the robustness and control quality of a conventional SMC controller. The problem is formulated and solved in the framework of ADRC. For better estimation and control performance, a generalized proportional integral observer (GPIO) technique is employed to estimate and compensate for unmodeled dynamics and other unknown time-varying disturbances. And benefiting from the usage of GPIO, a new SMC law can be designed by synthesizing the estimation and its history.FindingsThe employed methodology introduced a significant improvement in handling the uncertainties of the system parameters without compromising the nominal system control quality and intuitiveness of the conventional ADRC design. First, the proposed method combines the advantages of the ADRC and SMC method, which achieved the best tracking performance among these controllers. Second, the proposed controller is sufficiently robust to various disturbances and results in smaller tracking errors. Third, the proposed control method is insensitive to control parameters which indicates a good application potential.Originality/valueHigh-performance robot tracking control is the basis for further robot applications in open environments and human–robot interfaces, which require high tracking accuracy and strong disturbance rejection. However, both the varied dynamics of the system and rapidly changing nonlinear coupling characteristic significantly increase the control difficulty. The proposed method gives a new replacement of PID controller in robot systems, which does not require an accurate dynamic system model, is insensitive to control parameters and can perform promisingly for response rapidity and steady-state accuracy, as well as in the presence of strong unknown disturbances.

Output feedback disturbance rejection control for building structure systems subject seismic excitations

In this paper, the output feedback disturbance rejection control (OFDRC) problem is considered for buildings structures subject seismic excitations. First, based on a mild assumption and a linear transformation, the addressed problem of building structure system is translated into the output feedback disturbance rejection control problem large-scale system with disturbances. Then, by utilizing generalized-proportional-integral observer (GPIO) technique and output feedback domination approach, an output feedback decentralized disturbance rejection control law is derived via a systematic design manner. The multi-overlapping output feedback disturbance rejection controller is obtained according to the inverse transformation of a linear transformation. Strict theory analysis demonstrates that the states of the structure system will be stabilized to a small bounded region. Finally, an 8-story structure system is employed to evaluate the effectiveness of the proposed control strategy. Simulation results demonstrate that the proposed OFDRC exhibits better seismic loads attenuation ability and strong robustness against model uncertainties.

Event-triggered output consensus disturbance rejection algorithm for multi-agent systems with time-varying disturbances

This study investigates the problem of event-triggered output consensus disturbance rejection for multi-agent systems subject to time-varying disturbances. By virtue of the reduced-order generalized proportional-integral observer (GPIO) technique, a new output consensus disturbance rejection protocol is developed based on the measurement outputs. Taking the limited communication bandwidth into account, the multi-agent system closes the loop under the proposed consensus protocol only when a distributed event-triggering mechanism decides to transmit agent’s current output to its neighbors. The proposed output consensus protocol can effectively enhance the robustness against the time-varying disturbances and save the communication resource, since the time-varying disturbances are accurately estimated and compensated. Furthermore, the proposed consensus algorithm does not require continuous communication among the neighboring agents and can successfully avoid the Zeno phenomenon. Finally, the numerical simulation results are presented to verify the effectiveness of the proposed output consensus protocol.

GPIO Based Super-Twisting Sliding Mode Control for PMSM

Aiming at optimizing the tracking accuracy of permanent magnet synchronous motor (PMSM) speed regulation system, a super-twisting sliding mode (STSM) control technique combining disturbance observer is investigated in this brief. Since simply increasing the value of the control gain to enhance the robustness of PMSM system will bring unsatisfactory dynamical performance, a generalized proportional integral observer (GPIO) is first introduced to estimate the lumped disturbance. Then, a super-twisting sliding mode (STSM) controller is adopted to combine with the feedforward compensation from the aforementioned GPIO to construct a composite controller, which implies that this composite controller can adopt a smaller switching gain and achieve better tracking precision. Simulation and experimental results are provided to illustrate the proposed control algorithm.

Output feedback based sliding mode control for fuel quantity actuator system using a reduced-order GPIO

In an electronically controlled VE distributive pump, the fuel quantity actuator is a significant component. It is responsible for governing the quantity of fuel being injected into diesel-type engines. The FQA system has nonlinearities and always confronts disturbances caused by the external torque and the input voltage variation in the real working condition, which can be regarded as a lumped disturbance. However, most existing results only focus on dealing with the so called constant disturbance in the FQA system which fail to remove the influence of time-varying disturbances. Therefore, to deal with the nonlinearities and reject the lumped disturbance, a reduced-order generalized proportional integral observer (GPIO) based sliding mode control approach is presented. By using a reduced-order GPIO, time-varying disturbances can be estimated accurately. In addition, a theoretical analysis of the closed-loop system is given. The proposed control scheme exhibits a satisfactory performance in terms of transient behavior and disturbance rejection. Finally, a set of experimental tests are carried out to validate the feasibility as well as efficiency of the proposed control framework.

GPIO-Based Nonlinear Predictive Control for Flux-Weakening Current Control of the IPMSM Servo System

This paper proposes a generalized proportional integral observer (GPIO) based nonlinear predictive control (NPC) for an interior permanent magnet synchronous motor (IPMSM) to improve the flux-weakening (FW) current control performance against the complex nonlinear cross-coupling terms and the IPMSM parameters’ variations. First, the IPMSM is remodeled to further analyze the FW control difficulties caused by such cross-coupling terms and parameters variations. Considering the parameters’ variations as a kind of disturbance, a GPIO is then designed to compensate for such disturbance. A GPIO-based NPC is finally designed to handle the nonlinear cross-coupling terms to obtain an optimized current control performance. Experiments on a digital signal processor (DSP) based IPMSM servo system validate the workability of the proposed control scheme.