linear quadratic
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Hoan Bao Lai ◽  
Anh-Tuan Tran ◽  
Van Huynh ◽  
Emmanuel Nduka Amaefule ◽  
Phong Thanh Tran ◽  

<p>In this paper, load frequency regulator based on linear quadratic Gaussian (LQG) is designed for the MAPS with communication delays. The communication delay is considered to denote the small time delay in a local control area of a wide-area power system. The system is modeled in the state space with inclusion of the delay state matrix parameters. Since some state variables are difficult to measure in a real modern multi-area power system, Kalman filter is used to estimate the unmeasured variables. In addition, the controller with the optimal feedback gain reduces the frequency spikes to zero and keeps the system stable. Lyapunov function based on the LMI technique is used to re-assure the asymptotically stability and the convergence of the estimator error. The designed LQG is simulated in a two area connected power network with considerable time delay. The result from the simulations indicates that the controller performed with expectation in terms of damping the frequency fluctuations and area control errors. It also solved the limitation of other controllers which need to measure all the system state variables.</p>

2022 ◽  
Bradford D. Loucas ◽  
Igor Shuryak ◽  
Stephen R. Kunkel ◽  
Michael N. Cornforth

The relationship between certain chromosomal aberration (CA) types and cell lethality is well established. On that basis we used multi-fluor in situ hybridization (mFISH) to tally the number of mitotic human lymphocytes exposed to graded doses of gamma rays that carried either lethal or nonlethal CA types. Despite the fact that a number of nonlethal complex exchanges were observed, the cells containing them were seldom deemed viable, due to coincident lethal chromosome damage. We considered two model variants for describing the dose responses. The first assumes independent linear-quadratic (LQ) dose response shapes for the yields of both lethal and nonlethal CAs. The second (simplified) variant assumes that the mean number of nonlethal CAs per cell is proportional to the mean number of lethal CAs per cell, meaning that the shapes and magnitudes of both aberration types differ only by a multiplicative proportionality constant. Using these models allowed us to assemble dose response curves for the frequency of aberration-bearing cells that would be expected to survive. This took the form of a joint probability distribution for cells containing ≥1 nonlethal CAs but having zero lethal CAs. The simplified second model variant turned out to be marginally better supported than the first, and the joint probability distribution based on this model yielded a crescent-shaped dose response reminiscent of those observed for mutagenesis and transformation for cells “at risk” (i.e. not corrected for survival). Among the implications of these findings is the suggestion that similarly shaped curves form the basis for deriving metrics associated with radiation risk models.

2022 ◽  
Vol 2 ◽  
Delaney M. Costante ◽  
Aaron M. Haines ◽  
Matthias Leu

Our planet is home to an incredible array of species; however, relatively few studies have compared how anthropogenic threats impact taxonomic groups over time. Our objective was to identify temporal trends in threats facing the four most speciose phyla protected by the United States Endangered Species Act: angiosperms, arthropods, chordates, and mollusks. We determined presence or absence of threats for each species in these phyla by reviewing Final Rule listing decisions. For each phylum, we evaluated whether there was a linear, quadratic, or pseudo-threshold association between year of listing and the presence of 24 anthropogenic threats. We identified temporal trends for 80% of the 96 threat-phylum combinations. We classified threats as topmost (probability of being included in a species' listing decision peaking at ≥ 0.81) and escalating (probability of being included in a listing decision increasing by ≥ 0.81 between a species' first and most recent years of listing). Angiosperms, arthropods, and mollusks each had more topmost and escalating threats than chordates. Percentages of topmost threats were 42.9% (N = 21) for mollusks, 36.4% (N = 22) for angiosperms, and 33.3% (N = 21) for arthropods. Percentages of escalating threats were 22.7% (N = 22) for angiosperms and 14.3% (N = 21) for arthropods and mollusks. In contrast, percentages of topmost and escalating threats were only 4.2% (N = 24) for chordates, this one threat being climate change. Our research suggests potential conservation successes; some overutilization and pollution threats showed only gradually increasing or declining trends for certain phyla. We identified authorized take impacting angiosperms as the sole threat-phylum combination for which the threat had been consistently decreasing since the phylum's first year of listing. Conversely, species interactions, environmental stochasticity, and demographic stochasticity threats have seen drastic increases across all phyla; we suggest conservation efforts focus on these areas of increasing concern. We also recommend that resources be allocated to phyla with numerous topmost and escalating threats, not just to chordates.

J. V. Alamelu ◽  
A. Mythili

In the current scenario, usage of the smart medical pump is predominant in the medical field. The precise drug dosage, flow accuracy should be maintained to increase the performance of an infusion pump. In this work, an attempt has been made to predict and control the speed of the infusion pump for suitable infusion flowrate using machine learning technique and Linear Quadratic Gaussian (LQG) controller. The data for this study is considered from the publicly available online database, electronic Medicines Compendium (eMC). The speed of the infusion pump has been calculated using the drug dosage and flow rate for two different drugs. The prediction of infusion pump speed is achieved using Linear regression with Principal Component analysis (PCR) and Support Vector Machine Regression (SVR). The performance of the prediction schemes is evaluated using standard metrics. To validate the optimal control of the predicted speed, two different medical graded motors are considered. Further, the optimal control of the pump speed is investigated using Proportional–Integral–Derivative (PID), Linear Quadratic Regulator (LQR), and LQG controllers for its stability criteria. The prediction of the pump speed using regression models PCR, SVR has been verified and then the transient response analysis with rise time, settling time for both the motors have been examined. Results demonstrate that the LQG optimal control strategy achieves fast rise time, settling time of motor1 with 0.653s, 1.15s, and 0.22, 0.392s for motor2 respectively.

Energies ◽  
2022 ◽  
Vol 15 (1) ◽  
pp. 365
Wei Hu ◽  
Yu Shen ◽  
Zhichun Yang ◽  
Huaidong Min

The smart transformer has been widely applied for the integration of renewables and loads. For the smart transformer application, the voltage control of low-voltage inverter is important for feeding the load. In this paper, a multi-objective optimization control design approach which comprehensively considers all aspects of indexes, such as linear quadratic (LQ) index, H∞ norm, and closed-loop poles placement, is proposed based on the linear matrix inequality (LMI) solution. The proposed approach is able to alleviate the weight of the designer from the tedious design process of the multiple resonant controllers and the selection of the weighting matrix for the LQ control. Besides that, some excellent performances such as fast recovering time, low total harmonic distortion (THD) and high robustness are achieved by the proposed approach. The THD are 0.5% and 1.7% for linear and non-linear loads, respectively. The voltage drop for linear load step is reduced to 10 V. The proposed approach is applied to a 5 kVA three-phase inverter to yield an optimal control law. Results from the simulation and experiment presented herein will illustrate and validate the proposed approach.

2022 ◽  
Vol 23 (1) ◽  
pp. 129-158
Oktaf Agni Dhewa ◽  
Tri Kuntoro Priyambodo ◽  
Aris Nasuha ◽  
Yasir Mohd Mustofa

The ability of the quadrotor in the waypoint trajectory tracking becomes an essential requirement in the completion of various missions nowadays. However, the magnitude of steady-state errors and multiple overshoots due to environmental disturbances leads to motion instability. These conditions make the quadrotor experience a shift and even change direction from the reference path. As a result, to minimize steady-state error and multiple overshoots, this study employs a Linear Quadratic Regulator control method with the addition of an Integrator. Comparisons between LQR without Integrator and LQR with Integrator were performed. They were implemented on a quadrotor controller to track square and zig-zag waypoint patterns. From experimental results, LQR without Integrator produce of 2 meters steady-state error and -1.04 meters undershoot average with an accuracy of 64.84 % for square pattern, along 3.19 meters steady-state error, and -1.12 meters undershoot average with an accuracy of 46.73 % for a zig-zag way. The LQR method with integrator produce of 1.06 meters steady-state error with accuracy 94.96 % without multiple-overshoot for square pattern, the 1.06 meters steady-state error, and -0.18 meters undershoot average with an accuracy of 86.49 % for the zig-zag way. The results show that the LQR control method with Integrator can minimize and improve steady-state error and multiple overshoots in quadrotor flight. The condition makes the quadrotor able to flying path waypoints with the correct system specification. ABSTRAK: Kemampuan quadrotor dalam pengesanan lintasan waypoint menjadi syarat penting dalam menyelesaikan pelbagai misi pada masa kini. Walau bagaimanapun, besarnya ralat keadaan mantap dan banyak kelebihan kerana gangguan persekitaran menyebabkan ketidakstabilan pergerakan. Keadaan ini menjadikan quadrotor mengalami pergeseran dan bahkan mengubah arah dari jalur rujukan. Oleh itu, kajian ini menggunakan kaedah kawalan Linear Quadratic Regulator dengan penambahan integrator dalam meminimumkan ralat keadaan mantap dan banyak kelebihan. Perbandingan antara LQR tanpa Integrator dan LQR dengan Integrator dilakukan. Mereka dilaksanakan pada pengawal quadrotor untuk mengesan corak titik jalan persegi dan zig-zag. Dari hasil eksperimen, LQR tanpa Integrator menghasilkan ralat keadaan mantap 2 meter dan -1.04 meter rata-rata undur tembak dengan ketepatan 64.84% untuk corak persegi, sepanjang ralat keadaan tetap 3.19 meter, dan -1.12 meter rata-rata undur bawah dengan ketepatan 46.73 % untuk cara zig-zag. Kaedah LQR dengan integrator menghasilkan ralat keadaan mantap 1.06 meter dengan ketepatan 94.96% tanpa tembakan berlebihan untuk corak segi empat sama, ralat keadaan mantap 1.06 meter, dan rata-rata undur tembak -0.18 meter dengan ketepatan 86.49% untuk zig-zag cara. Hasilnya menunjukkan bahawa kaedah kawalan LQR dengan Integrator dapat meminimumkan dan memperbaiki ralat keadaan mantap dan banyak overhoot dalam penerbangan quadrotor. Keadaan tersebut menjadikan quadrotor dapat terbang ke titik jalan dengan spesifikasi sistem yang betul.

Energies ◽  
2022 ◽  
Vol 15 (1) ◽  
pp. 356
Łukasz Nocoń ◽  
Marta Grzyb ◽  
Piotr Szmidt ◽  
Zbigniew Koruba ◽  
Łukasz Nowakowski

This article approaches the issue of the optimal control of a hypothetical anti-tank guided missile (ATGM) with an innovative rocket engine thrust vectorization system. This is a highly non-linear dynamic system; therefore, the linearization of such a mathematical model requires numerous simplifications. For this reason, the application of a classic linear-quadratic regulator (LQR) for controlling such a flying object introduces significant errors, and such a model would diverge significantly from the actual object. This research paper proposes a modified linear-quadratic regulator, which analyzes state and control matrices in flight. The state matrix is replaced by a Jacobian determinant. The ATGM autopilot, through the LQR method, determines the signals that control the control surface deflection angles and the thrust vector via calculated Jacobians. This article supplements and develops the topics addressed in the authors’ previous work. Its added value includes the introduction of control in the flight direction channel and the decimation of the integration step, aimed at speeding up the computational processes of the second control loop, which is the LQR based on a linearized model.

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