Abstract
The presented work envisaged to explore the possibility of implementing a repetitive control strategy along with a proportional (P) controller for a liquid level system (LLS) in real time to track a periodic reference command. The objective of this paper is to validate the servo mechanism (accurate tracking) and periodic disturbance attenuating property of repetitive control (RC) along with P control system. The whole effort is divided in to two distinct parts. In the first part, the controller and plant are modeled, developed and experimented in software. The tracking performance and stability measure of the plant has been studied with inclusion of repetitive controller (RC) in presence of P controller and compared with conventional P and PI controller in both time and frequency domain subjected to periodic command to establish the usefulness of the RC-P control using simulation. The limitation of the first part is due to the consideration of all ideal condition of experimentation like ideal source, ideal plant etc. In the second part of this work the limitation of the first part of taking all ideal condition is avoided through the development of a real time experimentation setup. In this section, software model of LLS is replaced by its analogous electrical circuit. Emulation of the actual hardware plant is carried out interfaced through DAC NI6221 with PC using LabVIEW for better and flexible experimenting environment. The deployment of RC in Controller In Loop is done to conduct all experiments with actual source of reference and actual hardware plant. The effectiveness of RC with P controller for periodic reference input is shown through simulation and validated through real time experimentation.
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Abbreviations
- \(H(s)\) :
-
Head of water level
- \(Q_i (s)\) :
-
liquid in flow rate in Laplace domain
- \(G_{lls} \) :
-
Transfer function of LLS
- R:
-
Resistance of output valve of the process
- C:
-
Capacitance of tank \(=\) cross section area of tank
- \(\tau =\) RC:
-
time constant of the system
- \(Y(s)\) :
-
Output in Laplace domain
- \(U(s)\) :
-
Input in Laplace domain
- \(T_d\) :
-
Associated time delay
- \(k_P \) :
-
System gain
- \(u(t)=A\sin (\omega t)\) :
-
Sinusoidal input
- \(y(t)=B\sin (\omega t+\phi )\) :
-
Output
- \(A\) :
-
Amplitude of the input sinusoid
- \(B\) :
-
Amplitude of the output sinusoid
- \(\omega \) :
-
Frequency of the reference input
- \(\phi \) :
-
Phase shift of input signal due to plant without delay
- \(\phi ^{\prime }\) :
-
Phase shift of input signal for delay
- \(K_P \) :
-
Proportional gain
- \(K_I\) :
-
Integral gain
- \(G_{RC} \) :
-
Transfer function of the repetitive controller
- \(L\) :
-
Period of reference input \(=\) Delay of the RC
- \(C1,\,C2,\,b\) and \(c\) :
-
Residues
- \(p_1 \) and \(p_2\) :
-
Poles
- \(S_d \) :
-
Sensitivity of the system
- \(E(s)\) :
-
Error in Laplace domain
- \(D(s)\) :
-
Disturbance in Laplace domain
- DAC:
-
Data acquisition card
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Mondal, U., Sengupta, A. & Roy, A. Repetitive controller: an advanced servomechanism for periodic reference input. Int. J. Dynam. Control 4, 428–437 (2016). https://doi.org/10.1007/s40435-014-0144-z
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DOI: https://doi.org/10.1007/s40435-014-0144-z