Linear Quadratic Integral Research Articles

A Novel LQI Control Technique for Interleaved-Boost Converters

Hybrid electric vehicles (HEVs) and fuel cell electric vehicles (FCEVs) utilize boost converters to gain a higher voltage than the battery. Interleaved boost converters are suitable for low input voltage, large input current, miniaturization, and high-efficiency applications. This paper proposes a novel linear quadratic integral (LQI) control for the interleaved boost converters. First, the small-signal model of the interleaved-boost converter is derived. In the proposed method, an output voltage and a current signal error between two-phase input currents are selected to control not only the output voltage but also a balance between two-phase input currents. Furthermore, steady-state characteristics in terms of the output voltage and the input current are demonstrated by experiments and simulations using an experimental apparatus with a rated power of 700 W. The validity of the proposed method’s tracking performance and load response is demonstrated by comparing it with that of the conventional PI control. The tracking performance of the LQI control for the 40 V step response has a ten times faster response than that of the PI control. Also, the experimental results demonstrate that the proposed method maintains a constant output voltage for a 300 W load step while the PI control varies by 10 V during 70 ms. Additionally, the proposed method has an excellent disturbance rejection.

Improvement of the linear quadratic regulator control applied to a DC-DC boost converter driving a permanent magnet direct current motor

This article discusses a new robust control technique that enables the DC-DC boost converter driving a permanent magnet direct current (PMDC) motor to operate in high static and dynamic performances. The new technique is based on the design of a both linear quadratic regulator (LQR) and linear quadratic regulator-proportional integral (LQR-PI) type controllers, which have the advantage of eliminating oscillations, overshoots and fluctuations on different characteristics in steady-state system operation. In order to increase the output voltage, the LQR regulator is combined with a first-order system represented in the form of a closed-loop transfer function, the latter raising the output voltage to 24 volts, this voltage is enough to drive the permanent magnet direct current motor. The contribution of this paper is the creation of a robust control system represented in the form of a hybrid corrector able to regulate steady-state and transient disturbances and oscillations as well as to increase DC-DC boost converter output voltage for the PMDC motor to operate at rated voltage. The results of the three control techniques are validated by MATLAB Simulink.

A Linear Quadratic Integral Controller for PV-Module Voltage Regulation for the Purpose of Enhancing the Classical Incremental Conductance Algorithm

As a result of the exhaustion of fossil energy sources and the corresponding increase of their negative environmental impact, recent research has intensively focused on regions of alternative energy resources and, especially, on solar energy. Slow tracking of the maximum power point (MPP) and fluctuations around the MPP reduce the efficiency of photovoltaic power generation systems (PV). This study offers a novel design for the MPPT controller, which we refer to as the “hybrid IC-LQI approach”, which combines the incremental conductance (IC) technique and the linear quadratic integral (LQI) controller based on the boost converter’s small signal model. We conduct a comparative study of the proposed hybrid IC-LQI, and the classical one-stage IC technique in order to show the effectiveness of our proposal under three different scenarios of weather conditions and load. According to simulation findings, the proposed hybrid IC-LQI approach has a high tracking efficiency of up to 98.92%, owing to faster tracking of MPP with very large reduction of oscillations. On the other hand, the IC technique provides less efficiency, up to 96.1%, showing very slow tracking and high oscillations. The presented analysis of the results confirms the superior performance of the developed hybrid IC-LQI technique to the classical IC technique.

Model-based linear–quadratic–integral controller for simultaneous regulation of the current profile and normalized beta in NSTX-U

Achieving advanced scenarios that are characterized by steady-state operation, stable plasma confinement, and high-performance plasmas is one of the primary objectives of the National Spherical Tokamak eXperiment-Upgrade (NSTX-U). Active control of the plasma may be necessary to achieve these conditions. In particular, control algorithms that can simultaneously optimize the shapes and values of plasma profiles and scalars, respectively, may play a critical role in robustly achieving and sustaining these advanced scenarios. In this work, a model-based optimal control algorithm is developed for feedback control of the current profile in NSTX-U. The linear, finite-dimensional, control model is derived by discretizing and linearizing the magnetic diffusion equation in combination with empirical correlations for electron density, electron temperature, and noninductive current drives. The linear, time-variant model is then used for designing a linear–quadratic–integral (LQI) controller that is capable of regulating both the safety factor and the normalized beta around desired targets. The controller determines the neutral beam injection powers and the overall plasma current that are needed to achieve the desired current profile and normalized beta. The proposed controller is tested in higher-fidelity nonlinear simulations that employ 1D models for the evolutions of both current and temperature profiles using the Control Oriented Transport SIMulator (COTSIM). The closed-loop simulations show the effectiveness of the controller at shaping the safety factor in NSTX-U while achieving the desired normalized beta.

A robust variable-structure LQI controller for under-actuated systems via flexible online adaptation of performance-index weights.

This article presents flexible online adaptation strategies for the performance-index weights to constitute a variable structure Linear-Quadratic-Integral (LQI) controller for an under-actuated rotary pendulum system. The proposed control procedure undertakes to improve the controller's adaptability, allowing it to flexibly manipulate the control stiffness which aids in efficiently rejecting the bounded exogenous disturbances while preserving the system's closed-loop stability and economizing the overall control energy expenditure. The proposed scheme is realized by augmenting the ubiquitous LQI controller with an innovative online weight adaptation law that adaptively modulates the state-weighting factors of the internal performance index. The weight adaptation law is formulated as a pre-calibrated function of dissipative terms, anti-dissipative terms, and model-reference tracking terms to achieve the desired flexibility in the controller design. The adjusted state weighting factors are used by the Riccati equation to yield the time-varying state-compensator gains.

Avoiding contingent incidents by quadrotors due to one or two propellers failure.

With the increasing impact of drones in our daily lives, safety issues have become a primary concern. In this study, a novel supervisor-based active fault-tolerant (FT) control system is presented for a rotary-wing quadrotor to maintain its pose in 3D space upon losing one or two propellers. Our approach allows the quadrotor to make controlled movements about a primary axis attached to the body-fixed frame. A multi-loop cascaded control architecture is designed to ensure robustness, stability, reference tracking, and safe landing. The altitude control is performed using a proportional-integral-derivative (PID) controller, whereas linear-quadratic-integral (LQI) and model-predictive-control (MPC) have been investigated for reduced attitude control and their performance is compared based on absolute and mean-squared error. The simulation results affirm that the quadrotor remains in a stable region, successfully performs the reference tracking, and ensures a safe landing while counteracting the effects of propeller(s) failures.

Experimental Validation of Adaptive Augmented LQI Control for a 2 DoF Helicopter

This paper presents a novel adaptive augmented linear quadratic integral (LQI) controller for a 2 degrees of freedom (DoF) helicopter to improve the closed-loop performance of the baseline controller even when the system contains unmodeled dynamics and exogenous disturbances. Although the LQI controller is widely used in aircraft control applications for its excellent reference-tracking capability and inherent robustness, the performance of the baseline LQI controller degrades when the aircraft model has unmodeled dynamics and external disturbances, which are inevitable in aircraft applications. Hence, to deal with the parameter uncertainty and unmeasured disturbances, we present an adaptive control framework using a model reference adaptive control (MRAC) scheme combined with the baseline LQI controller. The key aspect of the proposed control scheme is that the robustness of the closed-loop control system to deal with the matched uncertainty is enhanced by tracking error augmentation with the control law. Moreover, this work proves the asymptotic stability of the closed-loop system using the inverse Lyapunov function and Barbalat’s lemma. The efficacy of the adaptive augmented LQI is experimentally validated through hardware in loop (HIL) implementation on a laboratory scale 2 DoF helicopter workstation for several real-time test cases. Experimental results accentuate that the adaptive augmented control scheme can significantly improve not only the reference-tracking capability but also the robustness of the closed-loop system.

Robust Aircraft Performance using Hypersurface Gain Scheduling LQI Controller for Supermaneuverable Aircraft

A new approach to cater abrupt gain switching at boundaries of steady-state trim points in Conventional Gain Scheduling (CGS) applied to aircraft flight control applications. The primary purpose of this research is to improve the stability properties of a supermaneuverable aircraft during different mission task of flight envelope, controlled using a gain scheduled approach. An output feedback based on Linear Quadratic Integral (LQI) controller is proposed which is able to guarantee stability and performance of the required task of the entire flight envelope. The results are demonstrated using comparison of pilot control maneuvers using CGS with proposed scheduling scheme for angular rates control by keeping states and control input contraints under consideration.

A Control-Theoretical System for Modulating Hippocampal Gamma Oscillations Using Stimulation of the Posterior Cingulate Cortex.

Closed-loop stimulation for targeted modulation of brain signals has emerged as a promising strategy for episodic memory restoration. In parallel, closed-loop neuromodulation strategies have been applied to treat brain conditions including drug-resistant depression, Parkinson’s Disease, and epilepsy. In this study, we seek to apply control theoretical principles to achieve closed loop modulation of hippocampal oscillatory activity. We focus on hippocampal gamma power, a signal with an established association for episodic memory processing, which may be a promising ‘biomarker’ for the modulation of memory performance. To develop a closed-loop stimulation paradigm that effectively modulates hippocampal gamma power, we use a novel data-set in which open-loop stimulation was applied to the posterior cingulate cortex and hippocampal gamma power was recorded during the encoding of episodic memories. The dataset was used to design and evaluate a linear quadratic integral (LQI) servo-controller in order to determine its viability for in-vivo use. In our simulation framework, we demonstrate that applying an LQI servo controller based on an autoregressive with exogenous input (ARX) plant model achieves effective control of hippocampal gamma power in 15 out of 17 experimental subjects. We demonstrate that we are able to modulate gamma power using stimulation thresholds that are physiologically safe and on time scales that are reasonable for application in a clinical system. We outline further experimentation to test our proposed system and compare our findings to emerging closed-loop neuromodulation strategies.

Sag feedback based multi-roll coordinating optimal control of a low-tension roll-to-roll system

The roll-to-roll (R2R) system is crucial for manufacturing low-strength sheets. And the speed control of rolls in this multi-roll system has a significant influence on the quality of the fragile sheets. However, the previous system with tension-based feedback control methods might crack the low-tension sheets during transportation. And few studies have carried out other effective control strategies for the R2R system. In this paper, the sag of sheets between rolls is chosen to be the feedback quantity, which provides a low-tension condition. A multi-roll coordinating optimal control method for the R2R system is introduced to keep sags stable by adjusting rolls’ speeds when the linear velocity of the upstream roll changes. A multiple-input multiple-output (MIMO) linear-quadratic-integral (LQI) controller is designed for the system. Several simulations and experiments are performed to confirm its validity. The effects of the hyperparameters in the proposed controller are also investigated. Compared with the series single-input single-output (SISO) PID control method, the proposed control method does better in reducing the speed fluctuation and eliminating error propagation and amplification in the low-tension R2R system. This control method and controller meet the needs of manufacturing low-strength sheets and show potential in enhancing the performance of the R2R system.

A robust LQR-FOPIλDµ controller design for output voltage regulation of stand-alone self-excited induction generator

This paper presents several optimal controllers compared with a robust control method for the terminal voltage regulation of a stand-alone self-excited induction generator (SEIG) with fixed capacitor and thyristor controlled reactor (FC-TCR). The major challenge of designing process of the controllers is the nonexistence of perfect model of SEIG. Therefore, small-signal based models for the output voltage and frequency are carried out using real input-output data. Accordingly, Linear Quadratic Regulator (LQR), Linear Quadratic Integral (LQI) and Linear Quadratic Fractional Order Integral (LQFOIλ) controllers are designed to regulate output voltage. Moreover, novelty and main contribution of the paper is to design a hybrid controller which combines LQR and Fractional Order Proportional Integral Derivative (LQR-FOPIλDµ) controller to ensure the best tracking dynamics, robustness against disturbances and sensor noise suppression. The proposed hybrid LQR-FOPIλDµ controller is obtained by solving H∞ weighted mixed sensitivity problem. Optimization process of the controller parameters is implemented by using particle swarm optimization (PSO) algorithm. Matlab/Simulink program is used to compare the effectiveness of the proposed controllers. Furthermore, the experimental results show that robust LQR-FOPIλDµ controller has the best tracking dynamics among them with less overshoot, settling time as well as the robust structure against external disturbances and sensor noises.

A Scalable 128-Channel, Time-Multiplexed Potentiostat for Parallel Electrochemical Experiments

Electrochemical experiments like chronoamperometry or cyclic voltammetry (CV) are essential in the research for novel bioelectrochemical systems. These experiments, executed by a potentiostat, are time-consuming which hinders research progression. To speed up those experiments, this work presents a potentiostat with 128 individual parallel stimulation and sensing channels. A channel architecture exploiting time division multiplexing is developed to minimize the hardware cost and area. Potential control is done in the digital domain using 128 individual Linear Quadratic Integral (LQI) controllers. The 128-channel potentiostat is implemented with Printed Circuit Board (PCB) technology and has $16 {\times }$ more channels than the state of the art low-cost potentiostats with a $4 {\times }$ lower cost-per-channel (5 $) and a $4 {\times }$ lower area-per-channel (${93}\,mm^{2}$ ). Using parallelism, chronoamperometry experiments can be done ${128\times }$ faster, while a conventional ${1}\, mV\,s^{-1}$ -CV can be done $72\,\, {\times }$ faster by sampling instead of voltage sweeping.

Robust design of high performance controller for transient stability enhancement of a single machine infinite bus power system

The control of damping torque of the synchronous machine in the power system is an important factor that may be affected by any transmission line fault, unknown loads or uncertainties and hampers the power system by increasing oscillation of the speed, rotor angle and terminal voltage of the synchronous machine. This paper proposes a high-performance controller to damp out the oscillation of the power system by integrating the linear quadratic Gaussian (LQG) and the integral controller together that ensures high bandwidth and robust performance over the uncertainties. The performance of the proposed controller is compared with the linear quadratic regulator (LQR), LQG, and linear-quadratic-integral (LQI) controller to ensure the effectiveness of the proposed controller. Besides, a level of uncertainty is intentionally added to the system dynamics to check the robust performance of the proposed controller.

Turbojet direct-thrust control scheme for full-envelope fuel consumption minimization

Purpose Reducing fuel consumption of unmanned aerial vehicles (UAVs) during transient operation is a cornerstone to achieve environment-friendly operations. The purpose of this paper is to develop a control scheme that improves the fuel economy of a turbojet in its full operating envelope. Design/methodology/approach A novel direct-thrust linear quadratic integral (LQI) approach, comprised by an optimal observer/controller satisfying specified performance parameters, is presented. The thrust estimator, based in a Wiener model, is validated with the experimental data of a micro-turbojet. Model uncertainty is characterized by analyzing variations between the identified model and measured data. The resulting uncertainty range is used to verify closed-loop stability with the circle criterion. The proposed controller provides stable responses with the specified performance in the whole operating range, even with after considering plant nonlinearities. Finally, the direct-thrust LQI is compared with a standard thrust controller to assess fuel economy and performance. Findings The direct-thrust LQI approach reduced the fuel consumption by 2.1090% in the most realistic scenario. The controllers were also evaluated using the environmental effect parameter (EEP) and transient-thrust-specific fuel consumption (T-TSFC). These novel metrics are proposed to evaluate the environmental impact during transient-thrust operations. The direct-thrust LQI approach has a more efficient fuel consumption according to these metrics. The results also show that isolating the thrust dynamics within the feedback loop has an important impact in fuel economy. Controllers were also evaluated using the EEP and T-TSFC. These novel metrics are proposed to evaluate the environmental impact during transient-thrust operations. The direct-thrust LQI approach has a more efficient fuel consumption according to these metrics. The results also show that isolating the thrust dynamics within the feedback loop has an important impact in fuel economy. Originality/value This study shows the design of an effective direct-thrust control approach that minimizes fuel consumption, ensures stable responses for the full operation range, allows isolating the thrust dynamics when designing the controller and is compatible with classical robustness and performance metrics. Finally, the study shows that a simple controller can reduce the fuel consumption of the turbojet during transient operation in scenarios that approximate realistic operating conditions.

Fuzzy Fault Tolerant Control of a Bacterial Growth Process Using a Multiple Lyapunov Function

Abstract This paper presents the problem of actuator fault estimation and fault-tolerant control (FTC) of a biological process using Takagi–Sugeno fuzzy formulation. The goal is to ensure the desired outputs tracking even if the time-varying actuator faults occur. We propose to use a proportional multi-integral (PMI) observer to estimate both the time-varying actuator faults and the state of system. The reconstructed faults are used to reconfigure the nominal controller. As a nominal control, we use a fuzzy linear quadratic integral (LQI) law. To ensure the global asymptotic convergence of the PMI observer and to improve the compensation speed of faults, we propose to use the multiple Lyapunov function by introducing a convergence rate. Sufficient conditions in terms of linear matrix inequalities (LMIs) are developed. The obtained results show that, the proposed approach is successfully applied to the problem of actuator fault-tolerant control of a bacterial growth process.

Optimal Robust LQI Controller Design for Z-Source Inverters

This paper investigates the linear quadratic integral (LQI)-based control of Z-source inverters in the presence of uncertainties such as parameter perturbation, unmodeled dynamics, and load disturbances. These uncertainties, which are naturally available in any power system, have a profound impact on the performance of power inverters and may lead to a performance degradation or even an instability of the system. A novel robust LQI-based design procedure is presented to preserve the performance of the inverter against uncertainties while a proper level of disturbance rejection is satisfied. The stability robustness of the system is also studied on the basis of the maximum sensitivity specification. Moreover, the bat algorithm is adopted to optimize the weighting matrices. Simulation results confirm the effectiveness of the proposed controller in terms of performance and robustness.

Performance enhancement of multivariable model reference optimal adaptive motor speed controller using error-dependent hyperbolic gain functions

The main contribution of this paper is to formulate a robust-adaptive and stable state-space speed control strategy for DC motors. The linear-quadratic-integral (LQI) controller is utilized as the baseline controller for optimal speed-regulation, accurate reference-tracking and elimination of steady-state fluctuations in the motor’s response. To reject the influence of modelling errors, the LQI controller is augmented with a Lyapunov-based model reference adaptation system (MRAS) that adaptively modulates the controller gains while maintaining the asymptotic stability of the controller. To further enhance the system’s robustness against parametric uncertainties, the adaptation gains of MRAS online gain-adjustment law are dynamically adjusted, after every sampling interval, using smooth hyperbolic functions of motor’s speed-error. This modification significantly improves the system’s response-speed and damping against oscillations, while ensuring its stability under all operating conditions. It dynamically re-configures the control-input trajectory to enhance the system’s immunity against the detrimental effects of random faults occurring in practical motorized systems such as bounded impulsive-disturbances, modelling errors, and abrupt load–torque variations. The efficacy of the proposed control strategy is validated by conducting credible hardware-in-the-loop experiments on QNET 2.0 DC Motor Board. The experimental results successfully validate the superior tracking accuracy and disturbance-rejection capability of the proposed control strategy as compared to other controller variants benchmarked in this article.

Design and Simulation of an LQR-PI Control Algorithm for Medium Wind Turbine

In this paper, a new linear quadratic regulator (LQR) and proportional integral (PI) hybrid control algorithm for a permanent-magnet synchronous-generator (PMSG) horizontal-axis wind turbine was developed and simulated. The new algorithm incorporates LQR control into existing PI control structures as a feed-forward term to improve the performance of a conventional PI control. A numerical model based on MATLAB/Simulink and a commercial aero-elastic code were constructed for the target wind turbine, and the new control technique was applied to the numerical model to verify the effect through simulation. For the simulation, the performance data were compared after applying the PI, LQR, and LQR-PI control algorithms to the same wind speed conditions with and without noise in the generator speed. Also, the simulations were performed in both the transition region and the rated power region. The LQR-PI algorithm was found to reduce the standard deviation of the generator speed by more than 20% in all cases regardless of the noise compared with the PI algorithm. As a result, the proposed LQR-PI control increased the stability of the wind turbine in comparison with the conventional PI control.

Fuel cell and ultracapacitor energy system control using linear quadratic regulator proportional integral controller

Application of fuel cell (FC) in power generation requires efficient power converters and controllers for hybridization of energy storage devices. This paper presents the control technique in a fuel cell and ultracapacitor hybrid system to eliminate the slow dynamic problem of FC. The control technique involves a linear quadratic regulator and proportional integral (LQR–PI) controller, where the FC boost converter and the UC bidirectional converter are controlled using a double-loop PI controller and a voltage-mode LQR controller, respectively. The simulation with different types of load was performed to compare the performance of the proposed controller with both PI and LQR controllers. The results revealed that the LQR–PI controller had better overshoot and undershoot responses (7.37% and 6.43%, respectively) than the proportional integral controller (11.47% and 11.42%, respectively) and linear quadratic regulator (23.87% and 21.5%, respectively). The energy sharing performance was verified through variation in load resistance and disturbances in bus voltage. The voltage recovery time of LQR–PI controller was slightly higher (200 ms) than that of the LQR controller (23.8 ms) and, however, lower than that of the PI controller (300 ms). The results revealed that the proposed controller is efficient for load voltage as well as load current fluctuations.

Modelling, design and analysis of three controllers based on LQR formulation for a non-linear hydraulic uniaxial seismic shake table

This study presents the modelling, design and analysis of three controllers applied to the non-linear model of a hydraulic uniaxial seismic shake table. Firstly, the system’s non-linear model is constructed based on the dynamic and mathematical analysis of the hydraulic actuator and the servo valve. Then, three control systems based on the LQR formulation are designed for the acceleration tracking: Linear quadratic integral (LQI), linear quadratic tracking (LQT) and a variation of LQT. Lastly, simulations are carried out using the non-linear model as the plant and the results showed that the variation of the LQT control exhibited the best acceleration tracking performance.