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steady-state error analysis and modeling of water-cooled shielded multi-probe thermocouples

INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER 2025年 165卷

作者： Zhao, Antao Zhang, Weihao He, Tingyu Li, Zhen Beihang Univ Sch Energy & Power Engn Beijing 100191 Peoples R China Natl Key Lab Sci & Technol Aeroengine Aerothermody Beijing 100191 Peoples R China Taihnag Lab Chengdu 610200 Peoples R China

Water-cooled probes resolve operational issues in high-temperature environments but increase steady-state errors, reducing the accuracy of existing models. Therefore, a new steady-state error prediction model incorporating the effects of water cooling is essential. This study employs numerical simulation to analyze the steadystate error magnitude and variation of Water-Cooled Shielded Multi-Probe Thermocouples (WSMTC) at Mach numbers of 0.2 to 0.5. The results indicate that water cooling can increase the probe's steady-state error by a factor of three. To address this issue, we analyzed the probe's flow and heat transfer characteristics. The WSMTC configuration parameters were integrated into the steady-state error prediction model. Additionally, the radiation error prediction model was improved to account for radiative heat transfer between the thermocouple junction, shield, turbine engine casing walls, and surrounding fluid, considering their significant temperature differences. Finally, a steady-state error prediction model for various measurement probes was developed using a multi-fin parallel approach. The constructed model exhibits a maximum error of less than 5 K (0.3% of the total temperature), demonstrating high precision.

关键词： Conjugate heat transfer (CHT) Shielded multiple-probes thermocouples with water-cooled steady-state error Prediction model

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steady-state error Compensation for Reinforcement Learning-Based Control of Power Electronic Systems

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IEEE ACCESS 2023年 11卷 76524-76536页

作者： Weber, Daniel Schenke, Maximilian Wallscheid, Oliver Paderborn Univ Dept Power Elect & Elect Drives D-33098 Paderborn Germany

Data-driven approaches like reinforcement learning (RL) allow a model-free, self-adaptive controller design that enables a fast and largely automatic controller development process with minimum human effort. While it was already shown in various power electronic applications that the transient control behavior for complex systems can be sufficiently handled by RL, the challenge of non-vanishing steady-state control errors remains, which arises from the usage of control policy approximations and finite training times. This is a crucial problem in power electronic applications which require steady-state control accuracy, e.g., voltage control of grid-forming inverters or accurate current control in motor drives. To overcome this issue, an integral action state augmentation for RL controllers is introduced that mimics an integrating feedback and does not require any expert knowledge, leaving the approach model free. Therefore, the RL controller learns how to suppress steady-state control deviations more effectively. The benefit of the developed method both for reference tracking and disturbance rejection is validated for two voltage source inverter control tasks targeting islanded microgrid as well as traction drive applications. In comparison to a standard RL setup, the suggested extension allows to reduce the steady-state error by up to 52% within the considered validation scenarios.

关键词： ~Control disturbance rejection power electronic systems reference tracking reinforcement learning steady-state error

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steady-state error estimation and calibration of a shielded total temperature probe for turbomachinery

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INTERNATIONAL JOURNAL OF THERMAL SCIENCES 2023年第1期190卷

作者： Wang, Zhihui Ji, Nian Ma, Chaochen Jinzhong Univ Sch Mech Jinzhong 030619 Peoples R China Beijing Inst Technol Sch Mech Engn Beijing 100081 Peoples R China

Accurate measurement of the total gas temperature plays a vital role in the performance research of turbomachinery. The total temperature thermocouple (TC) used in the measurement often needs to be specially designed and calibrated. In the past, the calibration was usually completed by a complex and highly costly experiment. The present work developed a new shielded total temperature probe (NTTP) for relatively low-temperature gas measurement. Meantime, this new design's characteristics and different error sources are analyzed based on the Conjugate Heat Transfer (CHT) simulation method. The CHT results show that the thermal conduction error is kept at a small value in the range of Mach number from 0.2 to 0.6;The velocity error contributes more than 90% of the total error. Four standard temperature probes are selected for the comparison. The maximum measurement error is 1.13 K, which is 331.62%, 119.4%, 61.6% and 59.5% lower than the standard type-A, B, C and D, respectively. Moreover, the detailed flow field and the influence of TC junction position on measurement accuracy are discussed. With the increases of the junction away from the supporting, the total measurement error of the NTTP increases first and then decreases. To vindicate the applicability of the proposed design, the measurement error of the NTTP is verified by a new experimental method with the relatively static fluid as the gas flow source. The testing results show that when the inflow's Mach number is 0.52, the measurement error of the NTTP is about 40% lower than that of the type-C total temperature probe.

关键词： Shielded total temperature probe Thermocouple Conjugate heat transfer steady-state error Calibration experiment

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Conjugate heat transfer analysis and steady-state error model for shielded thermocouples with multi-probes

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INTERNATIONAL JOURNAL OF THERMAL SCIENCES 2025年 211卷

作者： He, Tingyu Zhang, Weihao Li, Zhen Zhang, Zhibo Gao, Feilong Beihang Univ Sch Energy & Power Engn Beijing 100191 Peoples R China Natl Key Lab Sci & Technol Aeroengine Aerothermody Beijing 100191 Peoples R China AECC Shenyang Engine Res Inst Shenyang 110015 Peoples R China

The steady-state error of the shielded thermocouple (TC) is a key factor limiting its application in the field of aero-engines. The work presented in this paper involves analyzing the flow structure and heat transfer of a shielded thermocouple with three probes (STCP) to find methods for predicting this error. To achieve this goal, the paper uses numerical simulation to study the magnitude and composition of the steady-state error of the STCP working at Mach number (Ma) from 0.2 to 0.5. It provides insights into how velocity error, conduction error, and radiation error change with Mach number. By analyzing the characteristics of the flow structure and heat transfer around the STCP, three steady-state error prediction models are constructed based on physical heat transfer mechanism. These three models can not only predict the magnitude and variation of the three steadystate errors with high precision in a wide range of working conditions, but also accurately reflect the differences of the conduction error and radiation error among the probes.

关键词： Shielded thermocouples with multi-probes steady-state error Conjugate heat transfer (CHT) Prediction model Total temperature correction

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steady-state error Compensation for Reinforcement Learning with Quadratic Rewards 14

Steady-State Error Compensation for Reinforcement Learning w...

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14th Asian Control Conference (ASCC)

作者： Wang, Liyao Zheng, Zishun Lin, Yuan South China Univ Technol Shien Ming Wu Sch Intelligent Engn Guangzhou Peoples R China

ISBN: (纸本)9798331540845;9789887581598

Quadratic reward functions in Reinforcement Learning (RL) lead to steady-state errors, while absolute value reward functions, although alleviating this issue, induce substantial fluctuations in specific system states, causing abrupt changes. In response to this challenge, this study proposed an approach that integrates an integral term into quadratic type reward functions. Through experiments and performance evaluations on the Adaptive Cruise Control (ACC) and lane change models, we validate that the proposed method effectively diminishes steady-state errors and does not cause significant spikes in some system states.

关键词： Reinforcement Learning Quadratic Reward Function steady-state error PID

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A physics-information-enabled self-updating method to monitor steady-state error of capacitor voltage transformers

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MEASUREMENT 2023年第1期220卷

作者： Zhang, Yuxuan Zhang, Chuanji He, Cheng Li, Hongbin Chen, Qing Guo, PanPan Cheng, Cheng Huazhong Univ Sci & Technol SEEE Wuhan 430074 Peoples R China State Key Lab Adv Electromagnet Engn & Technol Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol AIA Wuhan 430074 Peoples R China

Understanding long-term monitoring steady-state errors of capacitor voltage transformers (CVTs) is critical for acquiring accurate and continuous voltage signals from the power grid. However, existing methods cannot maintain good performance over the long term because they cannot update the initial model while primary voltages fluctuate nor maintain stability while steady-state error deteriorates. To remedy this problem, this paper proposes a physics-information-enabled self-updating method. Differences in fluctuations between primary voltages and steady-state error are illustrated based on the physical structure of CVTs. This information is then used to select samples that only contain fluctuations from primary voltages and update the model. At the same time, the mapping relationship between statistics and errors is derived, which makes the evaluation of error possible. Simulations on data from real substations show that its recognition accuracy reaches 97%, and the evaluation deviations of ratio error and phase displacement are within & PLUSMN;0.085% and & PLUSMN;2.5 & PRIME;.

关键词： Capacitor voltage transformer steady-state error On-line detection method Self-updated method

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Dead-Time Effect Analysis and Compensation for Deadbeat-Direct Torque and Flux Control of PMSMs to Eliminate steady-state error 25

Dead-Time Effect Analysis and Compensation for Deadbeat-Dire...

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25th International Conference on Electrical Machines and Systems (ICEMS)

作者： Lang, Jiewen Tong, Chengde Zheng, Ping Liang, Xiaoyu Yuan, Xuejin Ren, Wu Harbin Inst Technol Sch Elect Engn & Automat Harbin Peoples R China Beijing Inst Aerosp Control Devices Beijing Peoples R China

ISBN: (纸本)9781665493024

Although deadbeat-direct torque and flux control (DB-DTFC) can realize excellent dynamic responses for permanent magnet synchronous machine (PMSM) drives, it suffers from problems of steady-state error and transient oscillation due to dead-time effect. To solve these problems, this paper proposes a dead-time compensation scheme. In order to investigate the effect of dead-time on DB-DTFC, the voltage distortion is derived and analyzed. Then, by both mathematical and graphical methods, it is originally verified that dead-time would lead to steady-state error in DB-DTFC. Therefore, a zero time delay compensation method which could overcome the weakness of the sampling and calculation time delay and eliminate steady-state error and undesired transient oscillation is proposed. Hence, the degradation caused by dead-time could be virtually mitigated and thus deadbeat responses are guaranteed. Finally, the proposed compensation scheme is experimentally validated on a 10.2kW PMSM drive platform.

关键词： dead-time compensation DB-DTFC steady-state error

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Enhanced Model Predictive Control Using state Variable Feedback for steady-state error Cancellation

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SENSORS 2024年第18期24卷 5869页

作者： Andreu, Marcos Rohten, Jaime Espinoza, Jose Silva, Jose Pulido, Esteban Leon, Lesyani Univ Arizona Dept Min & Geol Engn Tucson AZ 85719 USA Univ Bio Bio Dept Elect & Elect Engn Concepcion 4051381 Chile Univ Concepcion Dept Elect Engn Concepcion 4070386 Chile Univ Tecn Federico Santa Maria Dept Elect Engn Valparaiso 2390123 Chile

The rapid dynamic responses of predictive control algorithms are widely acknowledged. However, achieving accurate steady-state reference tracking hinges not just on a precise mathematical model of the system but also on its parameters. This document presents a predictive control scheme augmented with integral state feedback tailored to a photovoltaic (PV) application. In scenarios with uncertain system parameters, steady-state errors can particularly impact reactive power regulation, where the absence of an integral term in the loop exacerbates this issue. The robustness and sensitivity of both predictive control and the proposed enhanced predictive controller are thoroughly examined. Simulation and experimental results are included to validate the effectiveness of this approach.

关键词： predictive control voltage-source converters optimal control steady-state error

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PID auto-tuning for simultaneously fulfilling the requirements of relative stability and steady-state error

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ARTIFICIAL LIFE AND ROBOTICS 2021年第2期26卷 162-168页

作者： Lu, Yu-Sheng Tsai, Tsang-Shiuan Huang, Chien-Chih Cheng, Chung-Hsin Natl Taiwan Normal Univ Taipei Taiwan Natl Yunlin Univ Sci & Technol Touliu Yunlin Taiwan

Proportional-integral-derivative (PID) control is commonly used in industrial automatic control systems. However, it is not straightforward to determine control gains in a PID controller for satisfactory closed-loop performance. Many research works have been devoted to the auto-tuning of PID control gains. In contrast to previous studies, this paper develops an auto-tuning rule for PID controllers to simultaneously satisfy specifications of both steady-state error and relative stability, in which stability is specified in terms of phase margin. To illustrate the proposed auto-tuning rule, a focus servo of an optical disk drive is used, in which a voice coil motor drives a lens to focus a laser beam on a data layer of an optical disk. Experimental results show the effectiveness of the proposed PID auto-tuning process.

关键词： Auto-tuning PID control Relative stability Phase margin Low-frequency gain steady-state error

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steady-state error's Suppression Strategy for Continuously Frequency-Adjustment Inverter 22

Steady-state Error's Suppression Strategy for Continuously F...

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22nd International Conference on Electrical Machines and Systems (ICEMS)

作者： Yao, Zhiyuan Ben, Hongqi Meng, Tao Ning, Jichao Tu, Jiaming Harbin Inst Technol Sch Elect Engineer & Automat Harbin Peoples R China

ISBN: (纸本)9781728133980

In the conventional PI controllers, the output can't track the sinusoidal signal with zero steady-state error, and the output can only track the single frequency sinusoidal signal with zero steady-state error using PR controllers. Therefore, in order to suppress the steady-state error of the output voltage under continuous frequency conversion, a variable parameters quasi-PR control strategy is proposed in this paper. It can be found that the proposed control method can suppress the output steady-state error effectively by comparing the output steady-state error rates under conventional PI control and variable parameters quasi-PR control. Finally, the effectiveness of the proposed control strategy is verified by simulation results.

关键词： steady-state error variable parameters quasi-PR control continuous frequency adjustment

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