Proportional-integral Control Loop Research Articles

Analysis of a Simplified Predictive Function Control Formulation Using First Order Transfer Function for Adaptive Cruise Control

This paper presents a formulation and analysis of a low computation Predictive Functional Control (PFC), which is a simplified version of the more advanced Model Predictive Control (MPC) for an Adaptive Cruise Control (ACC) system by using a representation of first order closed-loop transfer function. In this work, a non-linear mathematical model of vehicle longitudinal dynamics is considered as a control plant. Then, a simple Proportional Integral (PI) controller is employed as an inner loop to identify the first-order relationship between its actual and desired trajectory speed according to the reasonable time constant based on the logical response of pedals pressing. To directly control the whole plant, the PFC is formulated as an outer loop to track the desired speed together with the convergence rate based on a user preference while satisfying constraints related to acceleration and safe distancing. Since PFC is formulated based on the first-order transfer function, the prediction and tuning processes are straightforward and specific to this system. The simulation results confirm that the proposed controller managed to track the desired speed while maintaining a comfortable driving response. Besides, the controller also can retain safe distancing during the car following application, even in the presence of unmeasured disturbance. In summary, this framework can avoid the need to formulate an inverse non-linear model that is typically used when deploying a hierarchical control structure to compute the throttle and brake pedals pressing as it has been replaced with an inner loop PI controller. The performance also is comparable yet more conservative due to the simplification. These findings can become a good reference for designing and improving the ACC controller, as the framework can be easily generalized for any type of vehicle for future work.

Power stabilization of a terahertz-frequency quantum-cascade laser using a photonic-integrated modulator

We demonstrate a technique to stabilize the emission from a 3.4-THz quantum-cascade laser against power drifts, using a recently developed photonic integrated circuit (PIC) structure formed by coupling a racetrack resonator with a ridge waveguide. This structure enables a dynamic power-control range of ±15% and locking over >600 s using a proportional–integral control loop. The resonator yields a 50% weaker perturbation to the laser emission frequency when compared with direct laser modulation, and hence offers the prospect of simultaneous, quasi-independent control of power and frequency. Progress towards integrating the PIC with a precision micromachined rectangular metallic waveguide module has also been demonstrated, with power modulation of the principal laser emission line being observed during pulsed operation.

Analysis of Power-Maximizing Region 2 Controllers for Wind and Marine Turbines

Wind and marine energy are rapidly growing and complementary technologies that share some techniques for simplified modeling and control, particularly in below-rated flow speeds. A turbine operator has several choices of controller for maximizing power in Region 2. The simple and ubiquitous KΩ2 control law is often effective but limited in its flexibility. Alternative controllers use reference tracking to split the control objectives into a low-bandwidth optimal tip-speed ratio tracking loop to maximize steady-state power and a higher-bandwidth proportional-integral control loop to reject inflow turbulence. Several options exist for identifying the slowly varying optimal set point during operation, based on estimating the inflow velocity or filtering the power or torque signals. This study compares the trade-offs between performance and other design priorities for a few choices of reference-tracking controller in the literature for reference wind and marine turbines. Analysis is performed in the frequency domain using the linearization of each controller, and the impact of turbulent disturbances on the closed-loop system is described. The controllers are simulated in OpenFAST to analyze their performance with higher-order nonlinear turbine dynamics.

Control Algorithm of Energy Storage System Based on Virtual Synchronous Generator

Frequency control is one of the most important tasks in electric power systems. However, as a result of the ongoing introduction into modern power systems of inertia-free generating facilities based on power converters, mainly renewable energy sources, this task is becoming more complex. This specificity is especially severe in microgrids, which are characterized by significant frequency changes. An effective way to solve such a problem is the use of energy storage systems (ESS) with grid-forming power converters. For this purpose, the paper develops a new structure of the control algorithm based on a current-controlled virtual synchronous generator (CC-VSG), in which the damping of oscillations is implemented via a feedforward controller. Also, a proportional-integral control loop is added to the structure of the CC-VSG to control the state of charge of the ESS. A methodology based on the separation of bandwidths of different control loops is proposed for tuning the CC-VSG. To confirm the obtained results, time-domain simulation of the microgrid with ESS using the PSCAD software was performed.

GNSS-Denied Semi-Direct Visual Navigation for Autonomous UAVs Aided by PI-Inspired Inertial Priors

This article proposes a method to diminish the horizontal position drift in the absence of GNSS (Global Navigation Satellite System) signals experienced by the VNS (Visual Navigation System) installed onboard a UAV (Unmanned Air Vehicle) by supplementing its pose estimation non-linear optimizations with priors based on the outputs of the INS (Inertial Navigation System). The method is inspired by a PI (Proportional Integral) control loop, in which the attitude and altitude inertial outputs act as targets to ensure that the visual estimations do not deviate past certain thresholds from their inertial counterparts. The resulting IA-VNS (Inertially Assisted Visual Navigation System) achieves major reductions in the horizontal position drift inherent to the GNSS-Denied navigation of autonomous UAVs. Stochastic high-fidelity Monte Carlo simulations of two representative scenarios involving the loss of GNSS signals are employed to evaluate the results and to analyze their sensitivity to the terrain type overflown by the aircraft. The authors release the C++ implementation of both the navigation algorithms and the high-fidelity simulation as open-source software.

Power-Loop-Free Virtual DC Machine Control With Differential Compensation

Conventional virtual dc machine (VDCM) control incorporates the mechanical characteristics of dc machines to emulate necessary system inertia. Utilizing already-existing proportional-integral control loops in the conventional VDCM control, this article eliminates the requirement of calculating torques using power measurements, i.e., power-loop-free VDCM, which greatly simplifies the conventional VDCM and reduces required resources for implementation. Theoretical analysis of the proposed power-loop-free VDCM shows that the controlled steady-state and dynamic characteristics are not aligned and sometimes even conflicting. This work further incorporates a differential compensation in the proposed power-loop-free VDCM to enhance the dynamic performance without affecting its steady-state characteristics. The proposed power-loop-free VDCM control is validated by both numerical simulations and hardware-in-the-loop experiments, and the results of both validations are consistent with the theoretical analysis, which justifies the effectiveness of the proposed VDCM control.

PI Control Loop–Based Frequency Smoothing of a Doubly-Fed Induction Generator

This paper proposes a frequency-smoothing scheme of a doubly-fed induction generator (DFIG) that can significantly eliminate the frequency fluctuations caused by continuously fluctuating wind speeds. To achieve this, a proportional-integral (PI) control loop depending on the frequency deviation instead of a proportional control loop used in conventional schemes is added to the maximum power point tracking loop. The P control loop in the proposed frequency-smoothing scheme eliminates the alternating component in the frequency deviation, whereas the I control loop eliminates the slowly-varying component. The gains for the P control loop and I control loop are suggested for effectively using the rotating masses of a DFIG while avoiding over-deceleration of the rotor speed. The simulation results evidently demonstrate that the proposed scheme nearly removes the frequency deviation under various wind conditions, by using the proposed PI control loop, especially in high penetration levels of wind.

Velocity control of an induction motor fed by an inverter-DC/DC Buck power electronic converter

We present, for the first time, a formal stability proof for velocity control in induction motors fed by three-phase inverter-DC/DC Buck power electronic converters as power amplifier. Although our result is local, we take into account the complete dynamics of the induction motor and the three-phase inverter-DC/DC Buck power electronic converter system. Despite the complexity of the problem, our proposal is based on several proportional-integral control loops. The key to achieve this result is a novel passivity-based approach that we call energy-based control having a number of advantages over previous passivity-based approaches in the literature. An important problem that is considered is that of an unbalanced three-phase voltage source. This condition appears during the transient periods in the inverter-DC/DC Buck power electronic converter system. This is important because the standard models of induction motors are obtained under the assumption of a balanced three-phase voltage source.

An Improved Control Method Based on Source Current Sampled for Shunt Active Power Filters

Active power filters (APFs) are dynamic power electronic devices that suppress harmonics and reactive power. To simplify the detection and extraction of traditional APF harmonics and reactive current, this paper proposes a direct source current control based on a three-phase three-wire shunt APF. The compensation principle and control method of the source current are analyzed systematically. The currents can be controlled without static errors by a proportional-integral (PI) controller in d-q rotating coordinates. Therefore, the compensation accuracy and dynamic performance of the system can be improved by the control strategy. Moreover, considering the grid voltage fluctuations, a droop regulator is proposed to address the impact of DC-link voltages on APF power losses and compensation performance. The regulator is combined with a traditional voltage outer loop PI control to achieve a comprehensive optimization between the power loss and compensation performance of the APF system. Finally, the inner current loop and the outer voltage loop form a double closed-loop cascade PI control structure to achieve the control effect of the APF. Simulation and experimental results verified the validity and feasibility of the APF control approach.

Hybrid BBO-PSO-based extreme learning machine neural network model for mitigation of harmonic distortions in micro grids

Microgrid tends to be the cluster of some of the renewable energy sources. The most important research area in the power distribution system side is the improvement in the quality of power delivered to the end users. This paper focuses on enhancing the power quality of the microgrid system; shunt active power filters (SAPF) is employed at the distribution side and to design an appropriate controller that achieves a better compensation for the considered SAPF. It is to be noted that the compensation methodology is dependent on the regulation process of the DC-link voltage. Traditionally, this regulation process is carried out employing a closed loop proportional-integral controller. In this paper, a hybrid biogeography-based optimisation – particle swarm optimization-based extreme learning machine neural network model is proposed to design the compensation for the SAPF and to mitigate the harmonics so that effective power gets delivered through the grid.

Dynamic performance enhancement for nonlinear stochastic systems using RBF driven nonlinear compensation with extended Kalman filter

In this paper, a novel hybrid control method is proposed to enhance the tracking performance of the Proportional–Integral (PI) based control system for a class of nonlinear and non-Gaussian stochastic dynamic processes with unmeasurable states. The system performance is presented by tracking error entropy as the system is nonlinear and subjected to non-Gaussian noises. The well-known kernel density estimation (KDE) technique is employed to estimate the entropy because the precise statistical property of noises is not available for many industrial processes. Since in many industrial cases gains of PI controllers are fixed, a compensative controller is designed without changing the existing closed loop PI controller. Moreover, the compensative signal is formed using the estimated states from the extended Kalman filter (EKF) and a nonlinear compensation realized by the radial basis function (RBF) neural network. The weights of RBF are trained to minimize the entropy of the closed loop tracking error. The convergence of RBF network is discussed and the stability of the resulting closed-loop control system is analysed in mean square sense. Finally, two numerical examples and a practical system simulation are given to illustrate the effectiveness of the proposed control method.

Robust Adaptive Tracking Control for Quadrotors by Combining PI and Self-Tuning Regulator

This brief is concerned with the robust adaptive tracking control problem of quadrotors. Considering the practicality of control laws to be designed, the self-tuning regulator (STR) for discrete-time systems is employed as our inner loop adaptive tracking mechanism and the classical proportional–integral (PI) control is designed for the outer loop to guarantee the robustness of the whole system. The main contributions of our work include: 1) we design the control laws for the actuator inputs (pulsewidth modulation signals) directly, which removes the need to measure the motor speeds and 2) the proposed PI-STR method can reduce the large overshoot of a single STR and retain the adaptability of the STR and the robustness of the PI control simultaneously. Furthermore, the outer loop PI controller and inner loop STR can easily be implemented in the digital form. The stability analysis is also provided. Simulations indicate that the PI-STR-based control structure can cope with the situations where vehicles are disturbed or have time-varying parameters. Our preliminary experiments show its practicality.

Control allocation based fault-tolerant strategy for a bio-ethanol processor system integrated to a PEM fuel cell

This paper presents a control approach to obtain actuator fault tolerance in a bio-ethanol processor system coupled with a proton exchange membrane fuel cell. The proposed strategy is based on the development of two cascaded modules. First, a high-level controller consisting on single-input single-output conventional proportional-integral control loops is designed for computing virtual actions which represent the overall control effort. Second, a control allocation module is proposed for the on-line redistribution of the virtual commands onto the available healthy actuators. This scheme is able to compensate from actuator position/rate saturations, to severe abnormal events such as loss of effectiveness and lock-in-place actuator faults. Some attractive features of the proposal are: (i) the control structure design is exclusively based on a steady-state model of the process, (ii) different actuator faults can be efficiently handled without the need of reconfiguring the high-level controller, (iii) the control and optimization tasks are efficiently integrated demanding a reduced computation time, (iv) the on-line controller re-allocation allows to manage not predefined actuator faults, (v) a considerable set of disturbances can be rejected with remarkable performance. Dynamic simulations performed on a rigorous nonlinear model of the process show the benefits of the proposed strategy for both fault-free as well as different fault situations comprising partial and total actuator faults.

Dynamic Modularity Approach to Adaptive Control of Robotic Systems With Closed Architecture

Modern applications of robotics typically involve a robot control system with an inner PI (proportional-integral) or PID (proportional-integral-derivative) control loop and an outer user-specified control loop. The existing outer loop controllers, however, do not take into consideration the dynamic effects of robots and their effectiveness relies on the ad hoc assumption that the inner PI or PID control loop is fast enough, and other torque-based control algorithms cannot be implemented in robotics with closed architecture. This paper investigates the adaptive control of robotic systems with an inner/outer loop structure, taking into full account the effects of the dynamics and the system uncertainties, and both the task-space control and joint-space control are considered. We propose a dynamic modularity approach to resolve this issue, and a class of adaptive outer loop control schemes is proposed and their role is to dynamically generate the joint velocity (or position) command for the low-level joint servoing loop. Without relying on the ad hoc assumption that the joint servoing is fast enough or the modification of the low-level joint controller structure, we rigorously show that the proposed outer loop controllers can ensure the stability and convergence of the closed-loop system. We also propose the outer loop versions of several standard joint-space direct/composite adaptive controllers for rigid or flexible-joint robots, and a promising conclusion may be that most torque-based adaptive controllers for robots can be designed to fit the inner/outer loop structure by using the new definition of the joint velocity (or position) command. Simulation results are provided to show the performance of various adaptive outer loop controllers, using a three-DOF (degree-of-freedom) manipulator, and experiment results using the UR10 robotic system are also presented.

A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

Interactive Tuning Tool of Proportional-Integral Controllers for First Order Plus Time Delay Processes

Engineering education and, particularly, control engineering, has shown growth in research and development activities during last years. Currently, proportional–integral (PI) and proportional–integral–derivative (PID) controllers are the most commonly used in industrial process applications. Nonetheless, it is reported that many of them are badly tuned. From an educational perspective, it is crucial for the student to understand the importance of tuning a control loop correctly. This paper presents an interactive tool focused on the study of PI controllers. The tool provides a set of tuning rules for both open-loop stable and unstable first order plus time delay processes. The different tuning rules can be compared interactively by the user, allowing a critical analysis of basic concepts about stability, robustness, and performance in PI control loops. In addition to educational purposes, the tool has been developed, taking into account practical considerations, such as simulation with a controller discrete implementation, process input saturations, and windup effect. We evaluated students’ achievement in the final examination in the Automatic Control course of the Electronics Engineering degree. Students showed significant improvement in their understanding of PI controller design. A survey and a practical case study were performed to evaluate the effectiveness of the proposed tool.

Control of Energy Storage

In the attempt to tackle the issue of climate change, governments across the world have agreed to set global carbon reduction targets. [...]

Multirate Fractional-Order Repetitive Control of Shunt Active Power Filter Suitable for Microgrid Applications

This paper presents a multirate fractional-order repetitive control (MRFORC) of three-phase shunt active power filter (APF) suitable for microgrid applications. The proposed APF control scheme includes an inner proportional-integral control loop with a sampling rate identical to switching frequency and an external plug-in repetitive control (RC) loop with a reduced sampling rate. The MRFORC loop is implemented in the dq-frame with interleaving for the reduction of computational burden in each control cycle. Moreover, in order to deal with the harmonics in the presence of wide grid frequency variations, FORC, which replaces the fractional-order elements with the Lagrange-interpolation-based finite impulse response filter, is adopted instead of the conventional RC. The synthesis, stability analysis, and parameter tuning criteria of the MRFORC system are derived in detail. A step-by-step design example of the proposed controller is also given in this paper. Finally, experiments are performed to validate the feasibility and effectiveness of the proposed scheme.

Simulation and experimental validation of new MPPT algorithm with direct control method for PV application

This paper presents the performance analysis of a new maximum power point tracking (MPPT) algorithm for solar photovoltaic (SPV) system using LUO converter. For effective utilization of the SPV panel, MPPT is essential. Hence, it is significant to simplify the tracking control algorithm with faster response, reduced ripple, higher efficiency, and cost-effective system. The proposed technique performs MPPT using a simple control technique by fine-tuning the duty cycle of the converter so as to make the input resistance of converter equal to the load resistance of the solar panel. Hence, the need for proportional–integral control loop is eliminated. The performance analysis of the proposed MPPT algorithm is compared with an existing perturb-and-observe algorithm in MATLAB simulation and experiment results of the proposed MPPT is implemented with the field programmable gate array controller using LUO converter with 40 W solar panel. From the results, it is proved that the response of the proposed method is faster than the existing perturb-and-observe method under varying solar irradiation conditions for the same step size. The input and output side ripples are considerably low and also the proposed algorithm has higher efficiency and low cost.

An Adaptive Voltage-Sensor-Based MPPT for Photovoltaic Systems With SEPIC Converter Including Steady-State and Drift Analysis

An adaptive voltage-sensor-based maximum power point tracking algorithm employing a variable scaling factor for a single-ended primary-inductance converter is presented. In this method, only a voltage divider circuit is used to sense the photovoltaic (PV) panel voltage. This method can effectively improve both transient and steady-state performance by varying the scaling factor as compared with the fixed step size and adaptive step size with fixed scaling factor. For sudden change in solar insolation or in start-up, this method leads to faster tracking, whereas in steady state, it leads to lower oscillations around maximum power point. The steady-state behavior and drift phenomena are also addressed in this paper to determine the tracking efficiency. The duty cycle is generated directly without using any proportional–integral control loop to simplify the control circuit. MATLAB/Simulink is used for simulation studies, and a microcontroller is used as a digital platform to implement the proposed algorithm for experimental validation. The proposed system is implemented and tested successfully on a PV panel in the laboratory.