Dual mode adaptive fractional order PI controller with feedforward controller based on variable parameter model for quadruple tank process

Roy, Prasanta; Roy, Binoy Krishna

doi:10.1016/j.isatra.2016.03.010

Cited by 25 publications

(16 citation statements)

References 20 publications

(63 reference statements)

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“…The water tank system is a nonlinear plant with strong coupling and large time delay. To get the theoretical model, some assumptions have to be given as follows , and then a simplified model of the water tank system can be obtained.Assumptions. The time‐lag of the electric control valves is ignored. The coupling between the inlet flows of Tank I and Tank II is ignored. α 1 and α 2 in (2) are simplified as constants. β 1 and β 2 in (3) are also simplified as constants. First, considering the mass balance , the dynamic equation of each tank can be given as

({,, \begin{array}{c} center & \frac{d y_{1}}{dt} = \frac{1}{S_{1}} ((),, Q_{i 1} - Q_{o 1}) \\ center & \frac{d y_{2}}{dt} = \frac{1}{S_{2}} ((),, Q_{i 2} + Q_{o 1} - Q_{o 2}) \end{array})

Section: Modeling Of Water Tank Systemmentioning

confidence: 99%

“…To get the theoretical model, some assumptions have to be given as follows , and then a simplified model of the water tank system can be obtained.Assumptions. The time‐lag of the electric control valves is ignored. The coupling between the inlet flows of Tank I and Tank II is ignored. α 1 and α 2 in (2) are simplified as constants. β 1 and β 2 in (3) are also simplified as constants. First, considering the mass balance , the dynamic equation of each tank can be given as

({,, \begin{array}{c} center & \frac{d y_{1}}{dt} = \frac{1}{S_{1}} ((),, Q_{i 1} - Q_{o 1}) \\ center & \frac{d y_{2}}{dt} = \frac{1}{S_{2}} ((),, Q_{i 2} + Q_{o 1} - Q_{o 2}) \end{array})

where y 1 and y 2 are the liquid levels, S 1 and S 2 are the cross‐sectional areas, Q i 1 and Q i 2 are the inlet liquid flow rates, Q o 1 and Q o 2 are the outlet liquid flow rates of Tank I and Tank II, respectively. According to Bernoulli's law for a non‐viscous, incompressible fluid in steady flow, the following simplified equations can be obtained under the assumptions above

({,, \begin{array}{c} center & Q_{i 1} = α_{1} u_{1} \\ center & Q_{i 2} = α_{2} u_{2} \end{array})

where u 1 (0% ~ 100%) and u 2 (0% ~ 100%) are the opening of the electric valves Ev I and Ev II, respectively; α 1 , α 2 are proportionality factors that depend on the coefficients of the electric control valves Ev I and Ev II, the pumping frequency, and the liquid level in Tank III, etc; and

({,, \begin{array}{c} center & Q_{o 1} = k_{1} s_{1} \sqrt{2 g} \sqrt{y_{1}} = β... \end{array})

…”

Section: Modeling Of Water Tank Systemmentioning

confidence: 99%

“…The water tank system is a nonlinear plant with strong coupling and large time delay. To get the theoretical model, some assumptions have to be given as follows [2,3], and then a simplified model of the water tank system can be obtained. Assumptions.…”

Section: Theoretical Modelmentioning

confidence: 99%

“…where y 1 and y 2 are the liquid levels, S 1 and S 2 are the crosssectional areas, Q i1 and Q i2 are the inlet liquid flow rates, Q o1 and Q o2 are the outlet liquid flow rates of Tank I and Tank II, respectively. According to Bernoulli's law for a non-viscous, incompressible fluid in steady flow, the following simplified equations can be obtained [2,3] under the assumptions above…”

Section: Theoretical Modelmentioning

confidence: 99%

“…Model (4) is just an approximate model under Assumptions (1)(2)(3)(4). In fact, factors α 1 and α 2 in model (2) are not constants in the water tank system.…”

Section: Theoretical Modelmentioning

confidence: 99%

See 4 more Smart Citations

Modeling and Control Approach to Coupled Tanks Liquid Level System Based on Function‐Type Weight RBF‐ARX Model

Feng

Peng

Zeng

et al. 2016

Asian Journal of Control

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A multi‐input multi‐output (MIMO) FWRBF‐ARX model, which adopts radial basis function (RBF) neural networks with function‐type weights (FWRBF) to approximate the coefficients of the state‐dependent AutoRegressive model with eXogenous input variables (SD‐ARX), is utilized for describing the dynamics of a coupled tanks liquid system. Based on local linearization information of the MIMO FWRBF‐ARX model, a predictive control strategy is proposed. In the algorithm, the control actions of the model predictive control (MPC) are calculated based on the local linearization of the MIMO FWRBF‐ARX model at current working point. Real‐time control experiments are carried out on the coupled tanks liquid system. The detailed comparative experiments demonstrate the feasibility and effectiveness of the proposed modeling and model‐based control strategy for the coupled tanks plant.

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({,, \begin{array}{c} center & \frac{d y_{1}}{dt} = \frac{1}{S_{1}} ((),, Q_{i 1} - Q_{o 1}) \\ center & \frac{d y_{2}}{dt} = \frac{1}{S_{2}} ((),, Q_{i 2} + Q_{o 1} - Q_{o 2}) \end{array})

Section: Modeling Of Water Tank Systemmentioning

confidence: 99%

({,, \begin{array}{c} center & \frac{d y_{1}}{dt} = \frac{1}{S_{1}} ((),, Q_{i 1} - Q_{o 1}) \\ center & \frac{d y_{2}}{dt} = \frac{1}{S_{2}} ((),, Q_{i 2} + Q_{o 1} - Q_{o 2}) \end{array})

({,, \begin{array}{c} center & Q_{i 1} = α_{1} u_{1} \\ center & Q_{i 2} = α_{2} u_{2} \end{array})

({,, \begin{array}{c} center & Q_{o 1} = k_{1} s_{1} \sqrt{2 g} \sqrt{y_{1}} = β... \end{array})

…”

Section: Modeling Of Water Tank Systemmentioning

confidence: 99%

Section: Theoretical Modelmentioning

confidence: 99%

Section: Theoretical Modelmentioning

confidence: 99%

“…Model (4) is just an approximate model under Assumptions (1)(2)(3)(4). In fact, factors α 1 and α 2 in model (2) are not constants in the water tank system.…”

Section: Theoretical Modelmentioning

confidence: 99%

See 3 more Smart Citations

Modeling and Control Approach to Coupled Tanks Liquid Level System Based on Function‐Type Weight RBF‐ARX Model

Feng

Peng

Zeng

et al. 2016

Asian Journal of Control

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An adaptive fractional order optimizer based optimal tilted controller design for artificial ventilator

Acharya,

Das

2024

Optim Control Appl Methods

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Artificial ventilators are vital respiratory support systems in the field of medical care, especially for patients in critical condition. It is crucial to make sure the ventilator keeps the intended airway pressure because variations might be harmful to the brain and lungs. Thus, achieving accurate pressure tracking is a primary objective in designing optimal controllers for pressure‐controlled ventilators (PCVs). To address this need, a novel approach is proposed: a mixed integer tilted fractional order integral and integer order derivation controller tailored for PCV systems. The gains of different parameters of the proposed controller are optimized using an adaptive chaotic search fractional order class topper optimization algorithm, augmented with a Gaussian‐based mutation operator. Moreover, the controller is designed to minimize oscillations in its output signal, thereby mitigating physical risks and reducing the size of actuators required. The efficacy of the optimized controller is further examined across various scenarios, including different lung resistances and compliances across different age groups of patients. Additionally, the impact of endotracheal tube resistance on air pressure is assessed as a potential disturbance in the PCV system. Through comprehensive testing, the proposed controller demonstrates superior performance in accurately tracking airway pressure to the desired levels. Across all evaluated cases, the proposed controller structure and accompanying algorithm outperform existing solutions. Notably, improvements are observed in system response time, overshoot, and settling time. This underscores the significance of employing advanced control strategies to enhancing the functionality and safety of PCV systems in medical settings.

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PSO Tuned Cascade of Fractional Order PI - Fractional Order PD for Pneumatic Positioning System

Muftah

Shouran

Faudzi

et al. 2022

Lecture Notes in Electrical Engineering

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Dual mode adaptive fractional order PI controller with feedforward controller based on variable parameter model for quadruple tank process

Cited by 25 publications

References 20 publications

Modeling and Control Approach to Coupled Tanks Liquid Level System Based on Function‐Type Weight RBF‐ARX Model

Modeling and Control Approach to Coupled Tanks Liquid Level System Based on Function‐Type Weight RBF‐ARX Model

An adaptive fractional order optimizer based optimal tilted controller design for artificial ventilator

PSO Tuned Cascade of Fractional Order PI - Fractional Order PD for Pneumatic Positioning System

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