Linear Proportional-integral Controller Research Articles

Multiparameter Estimation-Based Sensorless Adaptive Direct Voltage MTPA Control for IPMSM Using Fuzzy Logic MRAS

This paper introduces a parameter-estimation-based sensorless adaptive direct voltage maximum torque per ampere (MTPA) control strategy for interior permanent magnet synchronous machines (IPMSMs). In direct voltage control, the motor’s electrical parameters, speed, and rotor position are of great significance. Thus, any mismatch in these parameters or failure to acquire accurate speed or position information leads to a significant deviation in the MTPA trajectory, causing high current consumption and hence affecting the performance of the entire control system. In view of this problem, a fuzzy logic control-based cascaded model reference adaptive system (FLC-MRAS) is introduced to mitigate the effect of parameter variation on the tracking of the MTPA trajectory and to provide precise information about the rotor speed and position. The cascaded scheme consists of two parallel FLC-MRAS for speed and multiparameter estimation. The first MRAS is utilized to estimate motor speed and rotor position to achieve robust sensorless control. However, the speed estimator is highly dependent on time-varying motor parameters. Therefore, the second MRAS is designed to identify the quadratic inductance and permanent magnet flux and continuously update both the speed estimator and control scheme with the identified values to ensure accurate speed estimation and real-time MTPA trajectory tracking. Unlike conventional MRAS, which uses linear proportional-integral controllers (PI-MRAS), an FLC is adopted to replace the PI controllers, ensuring high estimation accuracy and enhancing the robustness of the control system against sudden changes in working conditions. The effectiveness of the proposed scheme is evaluated under different speed and torque conditions. Furthermore, a comparison against the conventional PI-MRAS is extensively investigated to highlight the superiority of the proposed scheme. The evaluation results and our quantitative assessment show the ability of the designed strategy to achieve high estimation accuracy, less oscillation, and a faster convergence rate under different working conditions. The quantitative assessment reveals that the FLC-MRAS can improve the estimation accuracy of speed, permanent magnet flux, and quadratic inductance by 19%, 55.8% and 44.55%, respectively.

Modeling proportional–integral controllers in tracking and economic model predictive control

In industrial applications, model predictive control (MPC) is typically installed in a hierarchical operational framework above regulatory layer proportional–integral (PI) controllers. Traditional MPC implementations do not include a dynamic model of the regulatory layer PI controller in the MPC optimization problem. This paper presents case studies to illustrate the advantages of modeling the PI controller in the MPC optimization problem. A PI controller implemented with an antiwindup scheme introduces significant nonlinearity into the MPC model that can be challenging to optimize with standard nonlinear solvers. Therefore, an approximate linear PI control law model is proposed for use in the MPC optimization problem. Hard constraints of the plant actuator manipulated by the PI controller are also included in the MPC problem. We illustrate using simulation studies that this PI controller modeling approach in the MPC optimization problem provides the following advantages: (i) systematic constraint handling in the presence of an unmeasured disturbance in the PI feedback loop, (ii) disturbance rejection forecast of the PI controller in the MPC optimization problem for a slow PI feedback loop, and (iii) optimizing plant economics of a cascade control architecture in which the PI controller manipulates a variable that directly influences the economic objective. Case studies on a continuous stirred tank reactor (CSTR) and heating, ventilation, and air-conditioning (HVAC) system are presented to highlight these advantages of modeling the PI controller in the MPC optimization problem.

Linear Quadratic Regulator-Based PI Control of a Non-Ideal Quadratic Boost PFC Converter for Low-Power Wind Energy Conversion Systems Supplying Uninterruptible DC Power

DC–DC converters are efficient in providing a regulated power with power factor control in switch-mode power supplies and also in electric vehicle charging stations. The aim of this research work is to design an efficient DC–DC quadratic boost power factor correction converter for Wind Energy Conversion Systems (WECS) to provide uninterruptible DC power in case of one or two modules loss for low-power applications. The state-space model of the converter is derived using a state-space averaging technique through small signal modeling by considering the non-linearities. The reduced-order model is obtained using Routh-Pade's approximation method to reduce the complexity involved in the design of the controller parameters for the outer and inner loops. The outer voltage is regulated using an Internal Mode Control (IMC)-based proportional integral (PI) controller to overcome the effect of right-half plane zero (RHP) and three-phase currents are shaped by using three PI controllers. The three inner PI controllers for each phase are tuned using three methodologies like Zieglar Nichols, Skogestad and Linear Quadratic Regulator (LQR)-based PI control. The transient and steady-state performances of the closed-loop system are analyzed for variations in the load and set point using extensive computer-based simulation studies. The results reveal that the LQR-based PI controller show considerably better performance in terms of less settling time, overshoot, power factor and %THD, including parasitic parameters of the components.

Evolving Fuzzy Models for Prosthetic Hand Myoelectric-Based Control

This article applies an incremental online identification algorithm to develop a set of evolving fuzzy models (FMs) that characterize the nonlinear finger dynamics of the human hand for the myoelectric (ME)-based control of a prosthetic hand. The FM inputs are the ME signals obtained from eight ME sensors and past inputs and/or outputs. The FM outputs are the finger angles, considered here as the midcarpal joint angles, to ensure their control. The best evolving FMs that characterize each of the five fingers are described with the results validated on real data. Simple second-order linear models are next given to enable the cost-effective controller design. Five separate control loops are proposed, with proportional-integral (PI) controllers separately tuned by a frequency-domain approach. Simple PI-fuzzy controllers are designed starting with the linear PI controllers to ensure the control system performance improvement. The evolving FMs are used to simulate accurately the behavior of the human hand. Digital simulation results are included to show the effectiveness of the PI-fuzzy controllers and the performance improvement in comparison to the initial PI ones.

Robust evaluation of stability regions of oil-well drilling systems with uncertain bit-rock nonlinear interaction

Torsional vibrations due to stick-slip phenomena may yield large variations in the drilling angular velocity which in turn may cause failures in the drilling process such as damage in drill pipes, due to large torsional deformation, and in drill bits, due to large angular velocities. It has been shown that standard linear proportional-integral (PI) control laws, in which the control torque is proportional to the differences between actual and reference drive table angular velocity and displacement, may lead to an oscillating angular velocity at the drill-bit due to stick-slip phenomenon. Aiming at reducing this effect through properly designed control gains, stability regions were defined for these parameters, and for a given drilling condition, using as a criteria the average deviation from expected/target angular velocity. This is done using a finite element model for the drilling system together with a dry friction model for a simplified representation of the interaction between drill-bit and rock formation. In order to provide robustness for the analysis, given the complexity of actual bit-rock interaction, it is proposed to consider uncertain parameters for the dry friction model. This is done using a stochastic model for the bit-rock interaction torque followed by a Monte Carlo simulation, which then leads to stochastic results for the angular velocity response, when subject to a linear PI control, and, thus, for the angular velocity deviation stability regions. Confidence intervals for the control gains, performance and stability regions are presented. Results suggest the use of a more robust criteria for the design of control parameters leading to a substantial increase in the performance robustness while not affecting much the nominal performance.

Supertwisting Sliding-Mode Direct Torque and Flux Control of Induction Machine Drives

A new supertwisting sliding-mode direct torque and flux controller (STSM-DTC) is proposed and investigated for induction motor drives. The supertwisting algorithm is a second-order sliding-mode control (SMC) that operates without high-frequency chattering and preserves the robustness properties of the classical SMC. The new STSM-DTC scheme uses torque and stator flux controllers implemented in the stator flux reference frame and it does not employ current controllers as in the conventional vector control. Both controllers contain a design parameter that allows adjusting their behavior between a linear proportional-integral (PI) like operation and a constant-gain classical sliding-mode behavior. Experimental tests show that STSM-DTC displays a very robust behavior, similar to a conventional SMC, and it works without notable steady-state chattering, as a PI controller. This article presents theoretical aspects for the new STSM-DTC scheme, stability analysis, design and implementation details, and relevant experimental results for a sensorless induction motor drive. The scheme is compared to a second-order sliding-mode controller and a linear PI controller. A robustness assessment against DTC with PI controllers, based on experimental tests, is also included.

Nonlinear PI-Control Approach for Improving the DC-Link Voltage Control Performance of a Power-Factor-Corrected System

When fast voltage control is used in a power factor control, the ripple of the dc link causes current harmonics. This paper proposes a method to reduce the harmonic content of a fast voltage loop in a power factor correction, which can both produce low distortion during steady-state operation and fast recovery from a load transient. The performance is achieved by using a Takagi–Sugeno-type nonlinear controller for dc-link voltage control. The proposed nonlinear control is compared with linear proportional–integral (PI) control, which is tuned to meet the standardized regulations for the harmonic content in a 3-kW single phase power supply. The results show that the presented nonlinear voltage controller can maintain the dynamic performance of the linear control with reduced current harmonics. It is also shown that the used nonlinear control method requires only marginally more complex control algorithm compared to commonly used linear PI control.

Adaptive super‐twisting sliding mode control of three‐phase power rectifiers in active front end applications

A robust control approach for three-phase two-level grid-connected power converters using an adaptive super-twisting algorithm (ASTA) is studied. A cascaded structure of the proposed control method is employed, which consists of two control loops, the dc-link capacitor voltage regulation loop (outer loop) and the grid phase current tracking loop (inner loop). In the outer control loop, a proportional controller using H ∞ technique is considered, which is designed to regulate the dc-link capacitor voltage to some desired value. An extended state observer used to asymptotically estimate the external disturbance is integrated into the outer control loop. For the inner control loop, two ASTA-based controllers are implemented that force the grid phase currents to their desired values in finite time. Lyapunov analysis is provided to show the finite time convergence of the closed-loop system. With the help of ASTA, a priori knowledge of the upper bounds of the derivative of the disturbances is not required. Illustrative simulation results in comparison with the linear proportional-integral control method are provided to demonstrate the effectiveness and robustness of the proposed ASTA, in the presence of load variation and parametric uncertainty.

Smoothing of wind power using flywheel energy storage system

Flywheel systems are quick acting energy storage that enable smoothing of a wind turbine output to ensure a controllable power dispatch. The effectiveness of a flywheel depends on how well it can be controlled to respond to fluctuating power output from intermittent sources. A quadratic Lyapunov function based non-linear controller is proposed which is designed based on an implicit understanding of the system including its inherent nonlinearities. Two different configurations of flywheel designs have been studied. The controller ensures asymptotic stability of the system as well as obtaining a better and more reliable performance than linear proportional–integral controllers in tracking rapid changes in power references. A further benefit is that the tuning of the proposed controller remains unaffected by changes in the system parameter and operating conditions. The efficacy of the algorithm is verified using non-linear time-domain simulation in MATLAB.

Intelligent Ratio Control in Presence of Pneumatic Control Valve Stiction

The presence of hard nonlinearities, such as control valve stiction, may severely degrade the plant profitability by introducing limit cycles in the process variable. This paper presents an innovative use of a recently developed intelligent controller for effective ratio control in the presence of a sticky control valve. The intelligent controller, stiction combating intelligent controller (SCIC), is inherently a fuzzy controller which makes use of Takagi–Sugeno model and changes its gain in run time to deal with stiction nonlinearity. Some of the various advantages which SCIC controller offers are, its simple structure, non-requirement of process parameters’ estimation and its capability to provide standalone solution to stiction nonlinearity. These qualities of SCIC controller make it a front runner among other solutions, for the effective ratio control in the presence of a sticky pneumatic control valve. The efficacy of the SCIC controller in ratio control is experimentally verified on a laboratory scale plant with uncertain parameters. A performance comparison between SCIC and linear proportional integral (PI) controller is also made for their setpoint tracking, disturbance rejection and trajectory tracking capabilities at various operating points. Based on extensive experimental studies, it can be concluded that SCIC controller, undoubtedly, outperformed the linear PI controller for all investigated cases and also efficiently handled uncertainties in the plant parameters.

Nonlinear PI controllers with output transformations

Well‐designed nonlinear proportional‐integral (PI) controllers are successful for nonlinear dynamical processes like linear PI controllers are for linear processes. Two nonlinear blocks representing proportional and integral terms can be designed so that the linearized controllers perform the same as linear PI controllers for linearized processes at the given operating points. For some nonlinear processes, nonlinear blocks for nonlinear PI controllers can be singular at some operating points, and control performances can be poor for set points near those points. To mitigate such disadvantages, new nonlinear PI controllers that introduce output transformations are proposed. Several examples are given, showing the performance of the proposed nonlinear PI controllers. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4264–4269, 2015

DC Bus Stabilization of Li-Ion Battery Based Energy Storage for a Hydrogen/Solar Power Plant for Autonomous Network Applications

This paper presents an energy management approach for a hybrid energy system comprised of a photovoltaic (PV) array and a polymer electrolyte membrane fuel cell (PEMFC). A single storage device, i.e., a Li-ion battery module, is used in the proposed structure. Linear proportional-integral (PI) and nonlinear flatness-based controllers for dc bus stabilization for power plants are compared. To verify the control approaches, a hardware system is realized with analog circuits for the PV, FC, and battery current control loops (inner controller loops) and with numerical calculation (dSPACE) for the external energy control loops. Experimental results with small-scale devices [namely, a PV array (800 W, 31 A), a PEMFC (1200 W, 46 A), and a Li-ion battery module (11.6 Ah, 24 V)] illustrate the excellent energy management scheme during load cycles, and the nonlinear differential flatness-based control was determined to provide improved dc bus regulation relative to a classical linear PI control method.

Controlling roll perturbations in fruit flies.

Owing to aerodynamic instabilities, stable flapping flight requires ever-present fast corrective actions. Here, we investigate how flies control perturbations along their body roll angle, which is unstable and their most sensitive degree of freedom. We glue a magnet to each fly and apply a short magnetic pulse that rolls it in mid-air. Fast video shows flies correct perturbations up to 100° within 30 ± 7 ms by applying a stroke-amplitude asymmetry that is well described by a linear proportional-integral controller. For more aggressive perturbations, we show evidence for nonlinear and hierarchical control mechanisms. Flies respond to roll perturbations within 5 ms, making this correction reflex one of the fastest in the animal kingdom.

Performance investigation of linear and nonlinear controls for a fuel cell/supercapacitor hybrid power plant

In this paper, linear proportional–integral (PI) and nonlinear flatness-based controllers for dc link stabilization for fuel cell/supercapacitor hybrid power plants are compared. For high power applications, 4-phase parallel boost converters are implemented with a switching interleaving technique for a fuel cell (FC) converter, and 4-phase parallel bidirectional converters are implemented with a switching interleaving technique for a supercapacitor converter in the laboratory. As controls, mathematical models (reduced-order models) of the FC converter and the supercapacitor converter are given. The prototype small-scale power plant studied is composed of a PEMFC system (the Nexa Ballard FC power generator: 1.2kW, 46A) and a supercapacitor module (100F, 32V, based on Maxwell Technologies Company). Simulation (by Matlab/Simulink) and experimental results demonstrate that the nonlinear differential flatness-based control provides improved dc bus stabilization relative to a classical linear PI control method.

Moving mass control system in conjunction with brain emotional learning-based intelligent control for rate regulation of suborbital reentry payloads

An adaptive intelligent control strategy based on a brain emotional learning model is investigated in the application of the rate regulation of suborbital reentry payloads. Because of nonlinear time-varying dynamics of these payloads, choosing an appropriate control mechanism and stability strategy can be an engineering challenge. Thus in a new approach, a moving mass control system in conjunction with brain emotional learning-based intelligent control is used to fulfill payload de-tumbling. The contribution of brain emotional learning-based intelligent control in handling the nonlinear time-varying dynamics is shown by comparison with results obtained from a linear proportional–integral controller. The results demonstrate excellent performance of brain emotional learning-based intelligent control in learning dynamic couplings and improvement of behavior without any considerable control system complexity.

A Feedback Linearization Based Unified Power Flow Controller Internal Controller for Power Flow Control

This article presents a feedback linearization based controller design methodology for a unified power flow controller to achieve rapid reference signal tracking in the internal control level. Feedback linearization is a non-linear control technique based on the differential geometry theory and overcomes the drawback of traditional linear proportional-integral control, which is typically tuned for one specific operating condition. In this article, feedback linearization control is developed for the unified power flow controller dynamic model via an appropriate coordinate transformation, and linear quadratic regulator control is then applied on the transformed linear system. The proposed control is validated via a detailed device-level simulation on an 11-bus system and a large scale simulation on the IEEE 118-bus and 300-bus systems. The proposed control is benchmarked against proportional-integral control.

Stochastic inequality constrained closed-loop model-based predictive control of MW-class wind generating system in the electric power supply

Wind turbines have become the most cost-effective renewable energy systems available today and are now completely competitive with essentially all conventional generation systems. However, wind stochasticity results in fluctuations in output power as well as undesirable dynamic loading of the drive train during high turbulence. A model-based predictive control strategy for the field-oriented control of a doubly fed induction generator is presented. The control region is defined over two wind profiles: average wind speeds below and above equipment rating, subject to assigned constraints of the maximum allowable system frequency fluctuations and the power limit of the wind generating system. To meet the control objectives of maximising energy capture and alleviation of drive train fatigue loads, each of the WGS component blocks is modelled separately so as to explore the associated trade-offs. Simulations, carried out under a Matlab ® environment, serve to verify that the proposed paradigm performs better than the classical linear proportional-integral controller in achieving the regulation of torsional dynamics while maintaining optimal operation.

Fuzzy Gain-Scheduling Proportional–Integral Control for Improving Engine Power and Speed Behavior in a Hybrid Electric Vehicle

With the increased emphasis on improving fuel economy and reducing emissions, hybrid electric vehicles (HEVs) have emerged as very strong candidates to achieve these goals. The power-split hybrid system, which is a complex hybrid powertrain, exhibits great potential to improve fuel economy by determining the most efficient regions for engine operation and thereby high-voltage (HV) battery operation to achieve overall vehicle efficiency optimization. To control and maintain the actual HV battery power, a sophisticated control system is essential, which controls engine power and thereby engine speed to achieve the desired HV battery maintenance power. Conventional approaches use proportional-integral (PI) control systems to control the actual HV battery power in power-split HEV, which can sometimes result in either overshoots of engine speed and power or degraded response and settling times due to the nonlinearity of the power-split hybrid system. We have developed a novel approach to intelligently controlling engine power and speed behavior in a power-split HEV using the fuzzy control paradigm for better performances. To the best of our knowledge, this is the first reported use of the fuzzy control method to control engine power and speed of a power-split HEV in the applied automotive field. Our approach uses fuzzy gain scheduling to determine appropriate gains for the PI controller based on the system's operating conditions. The improvements include elimination of the overshoots as well as approximate 50% faster response and settling times in comparison with the conventional linear PI control approach. The improved performances are demonstrated through simulations and field experiments using a ford escape hybrid vehicle.

EQoS: Provisioning of Client-Perceived End-to-End QoS Guarantees in Web Servers

It is important to guarantee client-perceived end-to-end quality of service (QoS) under heavy load conditions. Existing work focuses on network transfer time or server-side request processing time. In this paper, we propose a novel framework, eQoS, to monitor and controll client-perceived response time in heavy loaded Web servers. The response time is measured with respect to Web pages that contain multiple embedded objects. Within the framework, we propose an adaptive fuzzy controller, STFC, to allocate server resources. The controller assumes no knowledge of the pageview traffic model. It deals with the effect of process delay in resource allocation by its two-level self-tuning capabilities. We also prove the stability of the STFC. We implement a prototype of eQoS in Linux and conduct comprehensive experiments across wide-range server workload conditions on PlanetLab and simulated networks. Experimental results demonstrate the effectiveness of the framework: It controls the deviation of client-perceived pageview response time to be within 20 percent of a predefined target with both synthetic and real Web traffics. We also compare the STFC with other controllers, including static fuzzy, linear proportional integral (PI), and adaptive PI controllers. Experimental results show that, although the STFC works slightly worse than the static fuzzy controller in the environment where the static fuzzy controller is best tuned, because of its self-tuning capabilities, it has better performance in all other test cases by around 25 percent on average in terms of the deviation from the target response time. In addition, due to its model independence, the STFC outperforms the linear PI and adaptive PI controllers by 50 percent and 75 percent on average, respectively.

A regulator for a class of unknown continuous-time nonlinear systems

We introduce a control law for a class of unknown nonlinear continuous-time systems in which full state measurements are available. We show that as long as a certain feedback gain parameter is sufficiently large, the closed-loop system is stable. Furthermore, the magnitude of the control is bounded in the limit. As a corollary to the main result, we show that first-order nonlinear systems in the class we consider can be stabilized using linear proportional integral controllers, and we give explicit tuning rules for these controllers.