Fractional order PI control applied to level control in coupled two tank MIMO system with experimental validation

Summary In this paper, a disturbance observer–based adaptive boundary layer sliding mode controller (ABLSMC) is proposed to compensate external disturbance and system uncertainty for a class of output coupled multiple‐input multiple‐output (MIMO) nonlinear systems. To show the effectiveness of the proposed ABLMSC, a traditional adaptive sliding mode controller (ASMC) is also designed. The stability of the closed‐loop system is examined by using the Lyapunov stability approach. The proposed control approach is implemented for a class of nonlinear output coupled MIMO systems. For real‐time validation, a coupled tank system is considered for study. Finally, simulation and real‐time results show that the proposed ABLMSC gives better performance such as reduced chattering and energy efficiency than that of the ASMC and some reported works in the literature.

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“…Disturbance enters through the coupling path. By considering initial conditions zero, the dynamics of the coupling paths are obtained as

{\overset{x}{true}}_{1} ((), t) = - 0.0255 x_{1} ((), t) + 0.0462 u_{2} ((), t),

{\overset{x}{true}}_{2} ((), t) = - 0.0202 x_{2} ((), t) + 0.0499 u_{1} ((), t) .

…”

Section: Resultsmentioning

confidence: 99%

Disturbance observer–based adaptive boundary layer sliding mode controller for a type of nonlinear multiple‐input multiple‐output system

Gurumurthy

Das

2019

Intl J Robust & Nonlinear

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“…The nonlinear differential equations obtained by using Bernoulli's law and mass balance equation for the system are given as follows:

\begin{matrix} lefttrue \\ \frac{{italicdh}_{1} (t)}{italicdt} & = - μ \sqrt{h_{1} (t)} - μ sign (h_{1} (t) - h_{3} (t)) \sqrt{(||, (h_{1} (t) - h_{3} (t)))} + β u_{1} (t) \\ \frac{{italicdh}_{2} (t)}{italicdt} & = μ \sqrt{h_{1} (t)} - μ \sqrt{h_{2} (t)} \\ \frac{{italicdh}_{3} (t)}{italicdt} & = - μ \sqrt{h_{3} (t)} - μ sign (h_{3} (t) - h_{1} (t)) \sqrt{(||, (h_{3} (t) - h_{1} (t)))} + β u_{2} (t) \\ \frac{{italicdh}_{4} (t)}{italicdt} & = μ \sqrt{h_{3} (t)} - μ \sqrt{h_{4} (t)}, \end{matrix}

where

μ = \frac{S_{i}}{A} \sqrt{2 g}

for i = 1, 2,…, 5; S i is the outlet area of the tank i ; S 5 is the cross‐sectional area of the pipe from Tank 1 to Tank 3; A is the cross‐sectional area of the tanks; ...…”

Section: The Tank System and Control Methodsmentioning

confidence: 99%

Sliding mode PI control with backstepping approach for MIMO nonlinear cross‐coupled tank systems

Aksu

Çoban

2019

Intl J Robust & Nonlinear

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Summary The control of tank systems in industrial applications is an important issue for monitoring the chemical processes involved in the manufacture and delivery of product. The most important reason to control the tank systems is to keep the liquid level in the tanks constant and at the desired level for a specified period of time. In this study, the sliding mode control (SMC) with a repetitive approach called backstepping that is insensitive to uncertainties in system parameters and input disturbances is proposed and experimentally applied to a quadruple, cross‐coupled, uncertain, nonlinear, and multiple‐input/multiple‐output tank system. A proportional‐integral (PI) control is used to reduce the steady‐state error caused by the parameter variations and external noises. The traditional way of introducing PI usually leads to sliding surfaces. In this paper, the PI action is introduced to the control signal. The proposed backstepping sliding mode PI control (BSMPIC) is applied to such a complex tank system for the first time. The experimental results are compared with those of the SMC, sliding mode PI control, and backstepping sliding mode control to see the effect of the proposed BSMPIC on the system. As a result of the comparison, it is observed that less overshoot and tracking error, better tracking performance, and faster rise time in the transient regime is obtained by the BSMPIC.

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“…As given in (Podlubny, 1999b;Roy and Roy, 2016), with regard to the general characteristics of Bode's ideal transfer function, the desired phase margin is can be obtained for the considered system. With these situation, we obtain fractional I λ D μ controllers, which is a particular case of the PI λ D μ controllers for the tank 1 and tank 2 control as follow;…”

Section: Fractional Controller Designmentioning

confidence: 99%

Real time fractional-order control technique for coupled tank liquid level control process

Dumlu¹,

Ayten

2017

Int. j. adv. appl. sci.

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This paper presents real time fractional-order control technique for a coupled tank liquid level system that often used in industry. First of all system dynamic model has been presented. And then two different control approaches such as the classical proportional-integral-derivative (PID) and fractional-order PI λ D μ control are used to improve the tracking performance of the coupled tank liquid level system. Design procedures for both controllers are given in detail. Additionally, to verify the effectiveness of the fractional-order PID controller, detailed experimental comparisons with a feedforward proportional integral controller has been realized. It is observed that not only transient but also steady-state error values have been reduced with the aid of the PI λ D μ controller for tracking control purpose.

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Fractional order PI control applied to level control in coupled two tank MIMO system with experimental validation

Cited by 74 publications

References 30 publications

Disturbance observer–based adaptive boundary layer sliding mode controller for a type of nonlinear multiple‐input multiple‐output system

Disturbance observer–based adaptive boundary layer sliding mode controller for a type of nonlinear multiple‐input multiple‐output system

Sliding mode PI control with backstepping approach for MIMO nonlinear cross‐coupled tank systems

Real time fractional-order control technique for coupled tank liquid level control process

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