Analytical Design of PID Controllers

Díaz-Rodríguez, Iván D.; Han, Sangjin; Bhattacharyya, S.P.

doi:10.1007/978-3-030-18228-1

Cited by 36 publications

(23 citation statements)

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“…On the other hand, the controller with a too short time constant can force the wheel to slip in the fixture and therefore cause misalignment in relation to the rotation axis of the shaft. Therefore, the controller should be tuned as overdamped (see for reference [ 26 ]) and according to parameters calculated by Formulas (2)–(4).

where: e —control error, e static —the static part of control error, e dynamic —the dynamic part of control error, m —mass of wheel, I —moment of inertia of wheel, g —gravity constant, d —diameter of contact plane between wheel and fixture, ω —angular speed, n —number of samples around circumference, t s —time between sample acquisition of B .…”

Section: Methodsmentioning

confidence: 99%

Application of Magnetic Sensor for Magnetic Profile (1D) and Surface (2D) Measurement of Automotive Wheels

Brol

2021

Sensors

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This paper shows a report of over three years of intensive work on application of a 3-axis anisotropic magnetoresistive sensor with I2C interface for measurement of magnetic flux density distribution of automotive wheels. The work was undertaken to answer the question of whether is a possibility to effectively apply low-cost magnetic sensors with serial interface to measure the magnetic field surrounding the automotive wheel or tire. Two measurement techniques were discussed: Magnetic profile (1D) and magnetic surface measurement (2D) over tread, and also gear associated with the sensor, as well as its design, layout, operation, and control technique during (1D) and (2D) measurements. Three experiments were performed to asses accuracy and repeatability concerning component and resultant magnetic circumferential profiles and also magnetic surface. Differences between measurement outcomes in experiment were assessed. The results show that accuracy and repeatability lays below maximum admissible uncertainty declared by the producer. This proves directly that there is no measurable influence of motors, gear, operation, or measurement procedure on results obtained by magnetic sensors, and indirectly, that the assumed requirements regarding gear design and parameters are correct, and measurement of magnetic flux density distribution of automotive wheels and tires using (1D) and (2D) techniques is possible using a 3-axis anisotropic magnetoresistive sensor with I2C interface.

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Section: Methodsmentioning

confidence: 99%

Application of Magnetic Sensor for Magnetic Profile (1D) and Surface (2D) Measurement of Automotive Wheels

Brol

2021

Sensors

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“…In this paper, we use the stabilising set for PID controllers [5, 19] and results to synthesise a PI/PID controller with an

H_{\infty}

norm [25] to design a PI/PID controller which tracks step reference signals and mitigates selective harmonics disturbances present in DC microgrids systems. Preliminary results for a PI controller with a single disturbance signal were presented in [26] and summarised in [27]. In this paper, we extended the results of [26] for a PID case with multiple disturbance signals by using matrix representation of conic sections to describe the upper bound on the sensibility function and considered a DC–DC converter application which was validated by simulation and experimental results.…”

Section: Introductionmentioning

confidence: 94%

“…The gains indicated by filled square and filled lozenge in the stabilising set shown in Table 1 were selected to be tested. In order to show the effectiveness of the proposed method, we performed a classic tuning based on the concepts of bandwidth and phase margin [27]. As

ω_{1_{d_{1}}} = 5

rad/s, for a fair comparison, we selected the bandwidth as half of this value and we obtained the controller (filled triangle) of Table 1 with the same phase margin of filled lozenge using the tuning strategy of [18].…”

Section: Examplesmentioning

confidence: 99%

Geometric‐based PID control design with selective harmonic mitigation for DC–DC converters by imposing a norm bound on the sensitivity function

Magossi

Han

Machado

et al. 2020

IET Control Theory & Appl

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The DC-DC converters usually interfaces renewable energy sources in DC microgrids which may be contaminated by harmonic perturbations that adversely affect performance, creates stability and protection problems in a DC grid system. In this paper, the authors propose the use of the popular proportional-integral-derivative (PID) controller to mitigate selected harmonics. The solution is obtained by computing the complete set of stabilising controllers and imposing a bound on the sensitivity function. Using matrix representation of conic sections, the geometric-based PID controller is derived in the controller parameter space. The main result finds a subset of the stabilising set in which the controller mitigate harmonics with prescribed levels of attenuation which are constructively determined for each frequency of the selected harmonics. Simulation and experimental results using a boost converter are provided for validation.

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“…PID regulators are the most commonly used regulators in industrial practice [22,23]. In this paper, the temperature of the water in the storage tank is regulated using a digital PID controller (Figure 3).…”

Section: Pid Controllermentioning

confidence: 99%

Influence of the Thermometer Inertia on the Quality of Temperature Control in a Hot Liquid Tank Heated with Electric Energy

et al. 2020

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This paper presents the medium temperature monitoring system based on digital proportional–integral–derivative (PID) control. For industrial thermometers with a complex structure used for measuring the temperature of the fluid under high pressure, the accuracy of the first-order model is inadequate. A second-order differential equation was applied to describe a dynamic response of a temperature sensor placed in a heavy thermowell (industrial thermometer). The quality of the water temperature control system in the tank was assessed when measuring the water temperature with a jacketed thermocouple and a thermometer in an industrial casing. A thermometer of a new design with a small time constant was also used to measure temperature. The quality of water temperature control in the hot water storage tank was evaluated using a classic industrial thermometer and a new design thermometer. In both cases, there was a K-type sheathed thermocouple inside the thermowell. Reductions in the time constant of the new thermometer are achieved by means of a steel casing with a small diameter hole inside which the thermocouple is precisely fitted. The time constants of the thermometers were determined experimentally with a jump in water temperature. A digital controller was designed to maintain the preset temperature in an electrically heated hot water tank. The function of the regulator was to adjust the power of the electrical heater to maintain a constant temperature of the liquid in the tank.

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Analytical Design of PID Controllers

Cited by 36 publications

References 0 publications

Application of Magnetic Sensor for Magnetic Profile (1D) and Surface (2D) Measurement of Automotive Wheels

Application of Magnetic Sensor for Magnetic Profile (1D) and Surface (2D) Measurement of Automotive Wheels

Geometric‐based PID control design with selective harmonic mitigation for DC–DC converters by imposing a norm bound on the sensitivity function

Influence of the Thermometer Inertia on the Quality of Temperature Control in a Hot Liquid Tank Heated with Electric Energy

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