Steady-state Control Research Articles

Investigation of Disturbance Observers for Model Predictive Current Control in Electric Drives

Model predictive control (MPC) of power electronic converters has obtained much attention in many applications and especially in electric motor control. As the control loop is closed by predicting the future plant behavior by means of a mathematical model, disturbances and uncertainties are important aspects when using any MPC strategy. The plant model may be inaccurate due to plenty of reasons, such as parameter mismatches or the inverter nonlinearity. If these disturbances are not properly addressed during the MPC design process, the control performance is deteriorated. Hence, a suitable disturbance observer (DOB) is required to compensate for model inaccuracies. This contribution is comparing different lumped-DOB designs in the context of a continuous-control set MPC for induction motor current control. As a baseline for comparison, a field-oriented proportional-integral (PI)-type regulator is utilized which does not require a DOB due to its integral feedback.Comprehensive experimental results prove the necessity of a proper DOB; however, it is also shown that the overall transient and steady-state control improvement due to MPC has to be bought at a high price since the computational burden is at least doubled compared to the PI-baseline.

Performance seeking control of minimum infrared characteristic on double bypass variable cycle engine

Abstract In order to study the performance seeking control of double bypass variable cycle engine, a Feasible Sequential Quadratic Programming (FSQP) algorithm with global and local superlinear convergence characteristics is adopted. The engine model established a backward infrared radiation intensity prediction method for exhaust system, which could calculate the infrared radiation intensity of the high temperature components and nozzle stream in the system. The infrared radiation absorption effect of the nozzle stream on the high temperature components is considered in the method. According to the above model, a minimum infrared characteristic performance seeking control based on infrared prediction model is proposed. The optimal control simulations of the maximum thrust, minimum specific fuel consumption and minimum infrared characteristic mode on the double bypass variable cycle engine are carried out. Finally, the simulation results show that the algorithm could obtain the optimal operating conditions of double bypass variable cycle engine in different working conditions, which achieves the steady-state performance seeking control of the engine.

Dynamic Droop Control in Low-Inertia Power Systems

A widely embraced approach to mitigate the dynamic degradation in low-inertia power systems is to mimic generation response using grid-connected inverters to restore the stiffness of the grid. In this article, we seek to challenge this approach and advocate for a principled design based on a systematic analysis of the performance trade-offs of inverter-based frequency control. With this aim, we perform a qualitative and quantitative study comparing the effect of conventional control strategies-droop control (DC) and virtual inertia (VI)-on several performance metrics induced by <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> signal norms. By extending a recently proposed modal decomposition method, we capture the effect of step and stochastic power disturbances, and frequency measurement noise, on the overall transient and steady-state behavior of the system. Our analysis unveils several limitations of these solutions, such as the inability of DC to improve dynamic frequency response without increasing steady-state control effort, or the large frequency variance that VI introduces in the presence of measurement noise. We further propose a novel dynam-i-c droop controller (iDroop) that overcomes the limitations of DC and VI. More precisely, we show that iDroop can be tuned to achieve high noise rejection, fast system-wide synchronization, or frequency overshoot (Nadir) elimination without affecting the steady-state control effort share, and propose a tuning recommendation that strikes a balance among these objectives. Extensive numerical experimentation shows that the proposed tuning is effective even when our proportionality assumption is not valid, and that the particular tuning used for Nadir elimination strikes a good trade-off among various performance metrics.

Predictive Control of Five-leg Inverter-Double Permanent Magnet Synchronous Motor System with Error Feedback Model

In this paper, the five-leg inverter-dual permanent magnet synchronous motor system is taken as the research object. To solve the problem of large steady-state speed fluctuation when applying the traditional model predictive control strategy, based on the mathematical models of the five-leg inverter and the dual permanent magnet synchronous motor, the causes of the fluctuation are analyzed, and then an improved model predictive control algorithm with error feedback is proposed. The algorithm makes full use of the high-speed operation ability of modern digital processor, and introduces the prediction value of error feedback correction model, so that the rolling optimization is not only based on the model, but also makes full use of the actual value of the feedback state variables. At the same time, the second-order Euler discrete method is used to further improve the model progress. Simulation and experimental results show that the model predictive control strategy with error feedback can effectively improve the steady-state speed control performance of the system while maintaining the dynamic performance of the original system and the decoupling control effect of the two motors.

Fast Resource Scheduling for Distribution Systems Enabled With Discrete Control Devices

This article proposes a framework for fast short-term scheduling and steady-state voltage control in distribution systems enabled with both continuous control devices, e.g., inverter interfaced distributed generators (DGs) and discrete control devices (DCDs), e.g., on-load tap changers. The voltage-dependent nature of loads is taken into account to further reduce the operating cost by managing the voltage levels. Branch and cut method is applied to handle the integrality constraints associated with the operation of DCDs. A globally convergent trust region algorithm (TRA) is applied to solve the integer-relaxed problems at each node during the branching process. The TRA subproblems are solved using interior point method. To reduce the branching burden of branch and cut algorithm, before applying TRA at each node, a simplified optimization problem is first solved. Using the convergence status and value of objective function of this problem, a faster decision is made on stopping the regarding branch. Solving the simplified problem obviates the application of TRA at most nodes. It is shown that the method converges to the optimal solution with a considerable saving in computation time according to the numerical studies.

Load mitigation and wind power maximization of a HESG-based wind conversion system

This article discusses the control optimization of a hybrid generator-based wind conversion system (WCS). The optimization issues consider the maximization of the extracted wind power for the below-rated wind speeds and the load mitigation for high wind speeds. To do so, a DC/DC converter is used to realize the steady-state control of the generator's velocity through the adjustment of the excitation current, leading to maximization in the wind extracted power. As for the high wind speeds, a H∞ regulator implemented for the pitch control and a filter smoothing for the pitch angle reference are used to mitigate the load. Thanks to the implemented control strategy, the amplitude of the fluctuation of the bending moment was reduced by about 20% and the turbine torque vibration was reduced by 66% in comparison with other existing works from the literature conducted on the same wind turbine. The velocity controller is three times faster than the baseline controller and allows for increasing the wind extracted power by 6%. In this research, an integrated simulation platform, combining the electrical, mechanical, and aerodynamic aspects of a WCS, is set up. The space harmonics of the generator, the commutation effects of the power converters, the flexible coupling between the wind turbine's mechanical elements, and the aerodynamic interactions are taken into account. Finally, the control of the WCS in its full operating range is considered. The mechanical and aerodynamic data from the 1.5 MW WindPACT turbine available in the Fatigue, Aerodynamics, Structures, and Turbulence simulator are used for the simulations.

An overview of prescribed performance control and its application to spacecraft attitude system

High-quality control method is of great importance for the attitude determination and maneuvering of spacecraft in the on-orbit servicing technology. Prescribed performance control methodology, as a potential way, has gained considerable attention due to its quantitative description for the transient and steady-state control performance in recent years. Thus, this article constructs a survey for the prescribed performance control methodology along with the detailed analysis of the attitude control methods in the existing reported works. Then, the basic structure of prescribed performance control methodology is discussed in theory, and application to the attitude control of postcapture spacecraft works as an example to further explain the procedure of prescribed performance control methodology. Finally, with consideration of some vital aerospace applications, potential open issues of the prescribed performance control methodology are analyzed.

Schrödinger Approach to Optimal Control of Large-Size Populations

Large-size populations consisting of a continuum of identical and non-cooperative agents with stochastic dynamics are useful in modeling various biological and engineered systems. This paper addresses the stochastic control problem of designing optimal state-feedback controllers which guarantee the closed-loop stability of the stationary density of such agents with nonlinear Langevin dynamics, under the action of their individual steady state controls. We represent the corresponding coupled forward-backward PDEs as decoupled Schr\"odinger equations, by applying two variable transforms. Spectral properties of the linear Schr\"odinger operator which underlie the stability analysis are used to obtain explicit control design constraints. Our interpretation of the Schr\"odinger potential as the cost function of a closely related optimal control problem motivates a quadrature based algorithm to compute the finite-time optimal control.

Model predictive current control method for PMSM drives based on an improved prediction model

In motor drive systems based on model predictive control, a mathematic model of the motor is used to predict the future behavior of the system. However, the parameters in the motor model may not match their real values since these parameters may vary under different operation conditions. All parameter variations result in inaccurate predictions, and influence the steady-state control performance of the whole control system. In this paper, an improved model predictive control method is presented. Firstly, when parameter mismatches exist, the sources of the current prediction error are analyzed. It is revealed that current prediction error is directly affected by a prediction model with parameter mismatches and inaccurate one-step delay compensation. In particular, the influence form one-step delay compensation is discussed in this paper. Then a reaching-law-based sliding mode discrete observer is introduced to implement accurate one-step delay compensation and to observe all parameter variations. Finally, a predictive control method combined with sliding-mode discrete observation is presented to reduce parameter sensitivity. Simulation and experimental results show that the proposed method can increase the robustness of model predictive control systems.

Analysis of an efficient interleaved ultra‐large gain DC–DC converter for DC microgrid applications

This study deals with steady-state analysis and control of a step-up interleaved winding cross-coupled inductor DC–DC converter with high voltage gain and reduced voltage stress across semiconductors using voltage multiplier cells (VMCs). Because of the interleaved scheme, the thermal stress is reduced and the input current ripple is minimised. The leakage energy is recycled by passive lossless clamp circuit to the output. Meanwhile, the voltage stress across the semiconductors is substantially low. Hence, MOSFETs with less ON-state resistances and diodes with a less forward voltage drop can be utilised that improves the circuit performance. The operation principle and the steady state are discussed. Small-signal modelling of the proposed converter is derived via state-space averaging technique and a dual loop controller for output voltage regulation is designed. The adopted strategy utilises a fast dynamical inner loop to control the input current and an outer loop for the output voltage regulation. Finally, a 1 kW prototype with 60 V–1 kV voltage conversion is fabricated and tested to probe the carried analysis.

Optimized Model Predictive Control With Dead-Time Voltage Vector for PMSM Drives

In order to improve the current steady-state control performance of the model predictive control (MPC), a dead-time voltage-vector based MPC method is proposed in this article. First, the effect of the dead-time on MPC is introduced, and the formation process of the dead-time voltage vector existed in MPC is analyzed. Furthermore, the beneficial dead-time voltage vector and nonbeneficial dead-time voltage vector for the current steady-state control performance of MPC is distinguished, and the advantage of the beneficial dead-time voltage vector is analyzed. Then, the MPC method based on dead-time voltage vector is presented, which optimizes the action time of dead-time. Finally, the experimental results prove that the current steady-state control performance of the proposed MPC method is better than the conventional MPC method without increasing the switching frequency.

Learning impedance control of robots with enhanced transient and steady-state control performances

This study proposes a learning impedance controller comprising a proportional feedback control term, a composite-learning-based uncertainty estimation term, and a robot-environment interaction control term. The impedance control problem is converted into a particular reference-trajectory tracking problem based on a generated reference trajectory. The proposed controller ensures the exponential convergence of the auxiliary tracking error and the uncertainty estimation error. The interaction control term improves the transient control performance through suppression/encouragement of the incorrect/correct robot movements. The composite-learning update law enhances the transient and steady-state control performances based on the exponential convergence of the uncertainty estimation error and auxiliary tracking error. Finally, the effectiveness and advantages of the proposed impedance controller are validated by theoretical analysis and simulations on a parallel robot.

A Mechatronic Brake Booster for Electric Vehicles: Design, Control, and Experiment

The electro-mechanical brake booster (EMBB) is a kind of mechatronic actuator, which is developed to suit the brake assist requirement of electric vehicles. In this paper, we report on the design of an EMBB system consisting of a dc motor, a two-state reduction of a gear and ball screw, a servo body, and a reaction disk. Considering the inconvenience of installation and high price of the pedal force sensor, we translate the control problem of brake power assist control to position tracking control. Meanwhile, a nonlinear control method for position tracking is presented to solve the problem of power assist braking, which is formalized as three parts: the steady-state control, feed-forward control based on reference dynamics, and state-dependent feedback control. The benefit of the nonlinear control method is that it offers a concise control law and performs well in engineering implementations. In addition, a second-order filter was designed to do the signal processing and obtain a higher-order derivative. Finally, the bench tests based on rapid control prototyping environment were designed and implemented to verify the performance of the controller. Test results show that both the position tracking performance and response time of the EMBB system performed well.

Optimal Setting and Control for Iron Removal Process Based on Adaptive Neural Network Soft-Sensor

Satisfying the process technical requirements while optimizing the control of oxygen and zinc oxide is the main task for optimal operation of the iron removal process. However, due to the complicated mechanism and varied production conditions, the process is difficult to achieve optimal operation with the simple controller. The manual control, as a result, is extensively used in practice. In this paper, we develop an optimal setting and control (OSC) system for the iron removal process to achieve its technical requirements with minimal process consumptions. The OSC system is composed of a neural network soft-sensor, an optimal setting module, an optimal controller, and a fuzzy-logic-based compensator. First, we define the oxygen reaction efficiency (ORE) to measure the difference between the theoretical oxygen amount and its actual amount. Due to the ORE cannot be measured online and it varies with the production conditions, an adaptive weight radial basis function neural network soft-sensor is designed to estimate it. The adaptive weight adjusting method contributes to improve the adaptability of the soft-sensor, and its convergence is discussed. The optimal setting module provides the set-point of outlet ferrous ion concentration for the optimal operation of every reactor. The steady-state optimal control of oxygen and zinc oxide is then established, and the compensator compensates the control inputs utilizing the feedforward and feedback information. Finally, simulations validate that the ORE is important for the optimal control of the process. Furthermore, industrial experiments are presented to verify the effectiveness and potential of the proposed strategy.

Data-driven model-free adaptive damping control with unknown control direction for wind farms

Abstract The wide-area damping control (WADC) designed by conventional model-based methods faces the challenge from the strong nonlinearity, time-varying structure, and disturbances from complex operating conditions of the interconnected multi-machine power systems. In this paper, as one of the data-driven methods, the model-free adaptive control (MFAC), which employs the pseudo-partial derivative (PPD) to linearize the nonlinear power system dynamically, is adopted to design WADC for its advantages of the low cost, simple structure & low calculation burden, and the analyzable stability. However, when applied to the WADC design, the prototype MFAC is infeasible due to the assumed known control direction, the non-zero steady-state controller output, and unconsidered disturbances. To solve these problems, a novel data-driven adaptive WADC, consisting of control direction correction, PPD updating, one-step-ahead weighted predictive control, is proposed, moreover, the stability of the closed-loop system considering disturbances is thoroughly analyzed. Finally, case studies with various disturbances are conducted to validate the proposed control strategy.

Adaptive Robust Control and Optimal Design for Fuzzy Unmanned Helicopter Tail Reduction

This paper develops an adaptive robust control scheme combined with optimal design for the unmanned helicopter tail reduction (UHTR) system. The dynamical model of the UHTR system with uncertainties is established. The uncertainties are assumed to be bounded and expressed by fuzzy set theory. With this prerequisite, an adaptive robust controller is proposed to drive the system to meet the trajectory requirements approximately. The adaptive law with leakage and dead zone is performance based and flexibly adjustable. By means of Lyapunov stability theorem, the UHTR system is both uniform bounded and uniform ultimate bounded with the proposed controller. The control scheme is deterministic rather than fuzzy if-then rules-based control. Moreover, the fuzzy performance index which contains the steady-state system performance and control cost is presented. In this way, the optimal design problem can be replaced by minimizing the performance index. Overall, the resulting control scheme can guarantee deterministic performance of the UHTR system and minimize the fuzzy performance index simultaneously.

Design and control of economically attractive side-stream extractive distillation process

Abstract The performance and effectiveness of the conventional and heat-integrated side-stream extractive distillation arrangements are explored with the simultaneous consideration of the steady-state economics, thermodynamics and dynamic controllability aspects of the process. The overall performance of simple stream-to-stream heat-integrated F-S-E configuration (serially preheating column inlet feeds by solvent stream) is superior to others because of the least total annual cost (TAC), CO2 emissions and highest second-law efficiency among these side-stream cases. It can further reduce 8.16% in TAC compared to the conventional extractive distillation configuration. Exergy and entropy generation analyses are employed in these heat-integrated side-stream extractive distillation arrangements to thorough evaluate the energy degeneration in each component. Furthermore, dynamic control analyses for conventional and heat-integrated side-stream extractive distillation processes are also explored. Two novel compromised tactics are proposed to make the economically optimal heat-integrated arrangement more stable at rejecting large feed disturbances according to the physical implemented issues of economizers. Both effective and robust dual-product quality controls are provided for tackling the large (20%) throughput and feed composition perturbations. Furthermore, a new developed control scheme with parallel arrangement works better than that with series exchangers’ arrangement by comprehensively weighing results of steady-state economic design and dynamic controllability.

Steady-State Predictive Optimal Control of Integrated Building Energy Systems Using a Mixed Economic and Occupant Comfort Focused Objective Function

Control of energy systems in buildings is an area of expanding interest as the importance of energy efficiency, occupant health, and comfort increases. The objective of this study was to demonstrate the effectiveness of a novel predictive steady-state optimal control method in minimizing the economic costs associated with operating a building. Specifically, the cost of utility consumption and the cost of loss productivity due to occupant discomfort were minimized. This optimization was achieved through the use of steady-state predictions and component level economic objective functions. Specific objective functions were developed and linear models were identified from data collected from a building on Texas A&amp;M University’s campus. The building consists of multiple zones and is serviced by a variable air volume, chilled water air handling unit. The proposed control method was then co-simulated with MATLAB and EnergyPlus to capture effects across multiple time-scales. Simulation results show improved comfort performance and decreased economic cost over the currently implemented building control, minimizing productivity loss and utility consumption. The potential for more serious consideration of the economic cost of occupant discomfort in building control design is also discussed.

Linear–quadratic optimal steady state controllers for engineering students and practicing engineers

This paper is an overview of fundamental linear–quadratic optimal control techniques used for linear dynamic systems. The presentation is suitable for undergraduate and graduate students and practicing engineers. The paper can be used by class instructors as supplemental material for undergraduate and graduate control system courses. The paper shows how to find the solution to a dynamic optimization problem: optimize an integral quadratic performance criterion along trajectories of a linear dynamic system over an infinite time period (steady-state linear–quadratic optimal control problem). The solution is obtained by solving a static optimization problem. All derivations done in the paper require only elementary knowledge of linear algebra and state space linear system analysis. The results are presented also for the observer-driven linear–quadratic steady-state optimal controller, output feedback-based linear–quadratic optimal controller, and the Kalman filter-driven linear–quadratic stochastic optimal controller. Having full understanding of derivations of the linear–quadratic optimal controller, observer-driven linear–quadratic optimal controller, optimal linear–quadratic output feedback controller, and optimal linear–quadratic stochastic controller, students and engineers will feel confident to use these controllers in numerous engineering and scientific applications. Several optimal linear–quadratic control case studies involving models of real physical systems, with the corresponding Simulink block diagrams and MATLAB codes, are included in the paper.

Design, implementation and experimental verification of a compensator-based triple-step model reference controller for an automotive electronic throttle

The electronic throttle of a gasoline vehicle controls the air inflow into the cylinders of the engine to ensure the desired power output. Therefore, a well-established electronic throttle control (ETC) system is fundamental and necessary to obtain fast transient engine torque responses without overshoot and with high static precision. To achieve highly precise servo control of the throttle in an environment with system nonlinearity, model uncertainties and external disturbances, a discrete-time triple-step model reference controller (DT-TSMRC) with an adaptive compensator is proposed for an ETC system. In contrast to previously investigated systems, the proposed controller consists of steady-state control, reference feedforward control, proportional-derivative (PD)-type feedback control, and an online updating compensation law. Experimental results show that the proposed control algorithm can not only ensure fast transient performance in the control response without overshoot but also guarantee accurate servo tracking of the valve plate angle. • Novel DT-TSMRC method is proposed for the electronic throttle control problem. • The proposed adaptive compensator accounts for all system mismatch and disturbances. • The proposed error feedback controller is extended to the classic PD structure. • Experimental tests validate the performance of the proposed control system.