Skip to main content
SpringerLink
Log in

Design of Full-Order Neural Observer with Nonlinear Filter Techniques for State Estimation of a Three-Tank Process Control System

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Electrical Engineering Aims and scope Submit manuscript

Abstract

A novel model-based approach to design a full-order state observer for estimating the states of a three-tank process has been attempted in this research study. State estimation has been a methodology that integrates the prediction from exact models pertaining to the system and achieves consistent estimation of the non-measurable variables. This study has attempted to develop a full-order observer for estimation of non-measurable variables of the considered three-tank process control system. Neural observer is designed with the nonlinear state update equation that is structured as the neural network employing radial basis function (RBF) model. Also, nonlinear full-order state observer is designed based on a new recursive likelihood synthesizer (RLS) of the extended Kalman filter (EKF) and classic unscented Kalman filter (UKF) and finally the states are estimated. The likelihood synthesizer determines the covariance and Kalman gains so as to match the real-time process measurements. Three-tank process system (TTPS) is represented by its mathematical model and the developed state estimation techniques are applied for estimating the non-measurable variables. Likelihood synthesizer tends to evaluate the covariance of the initial states and simulation tests confirm the attainment of better results using the new nonlinear filtering techniques. RBF neural observer has resulted in an ARMSE of 4.1629 × 10–3, 0.3963 × 10–3 and 0.1085 × 10–3 for the measured heights h1, h2 and h3, respectively. The new RLS-EKF observer with its recursive determination of the maximum likelihood has attained ARMSE of 2.1982 × 10–6, 0.1512 × 10–6 and 0.0261 × 10–7 for the measured heights h1, h2 and h3, respectively. This novel RLS-EKF has proved to be highly robust and has higher precision than the RBF neural observer and UKF technique as applied for the TTPS model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  • AbouOmar MS, Su Y, Zhang H, Shi B, Wan L (2022) Observer-based interval type-2 fuzzy PID controller for PEMFC air feeding system using novel hybrid neural network algorithm-differential evolution optimizer. Alex Eng J 61(9):7353–7375

    Article  Google Scholar 

  • Adil A, Hamaz A, N’Doye I, Zemouche A, Laleg-Kirati TM, Bedouhene F (2022) On high-gain observer design for nonlinear systems with delayed output measurements. Automatica 141:110281

    Article  MathSciNet  MATH  Google Scholar 

  • Ahmed H, Biricik S, Benbouzid M (2021) Linear Kalman filter-based grid synchronization technique: an alternative implementation. IEEE Trans Industr Inf 17(6):3847–3856

    Article  Google Scholar 

  • Aucoin R, Chee SA, Forbes JR (2019) Linear-and linear-matrix-inequality-constrained state estimation for nonlinear systems. IEEE Trans Aerosp Electron Syst 55(6):3153–3167

    Article  Google Scholar 

  • Avilés JD, Torres-Zúñiga I, Villa-Leyva A, Vargas A, Buitrón G (2022) Experimental validation of an interval observer-based sensor fault detection strategy applied to a biohydrogen production dark fermenter. J Process Control 114:131–142

    Article  Google Scholar 

  • Bernard P, Sanfelice RG (2022) Observer design for hybrid dynamical systems with approximately known jump times. Automatica 141:110225

    Article  MathSciNet  MATH  Google Scholar 

  • Bian M, Wang J, Liu W, Qiu K (2017) Robust and reliable estimation via recursive nonlinear dynamic data reconciliation based on cubature Kalman filter. Clust Comput 20(4):2919–2929

    Article  Google Scholar 

  • Briers M, Doucet A, Maskell S (2010) Smoothing algorithms for state–space models. Ann Inst Stat Math 62(1):61

    Article  MathSciNet  MATH  Google Scholar 

  • Bušek J, Zítek P, Vyhlídal T (2022) Observer based anti-windup compensator with functional state feedback for time delay controllers—design and case study application. IET Control Theory Appl 16(9):861–871

    Article  Google Scholar 

  • Bzioui S, Channa R (2021) An adaptive observer design for nonlinear systems affected by unknown disturbance with simultaneous actuator and sensor faults. Appl CSTR 12(4):4847–4856

    Google Scholar 

  • Catlin DE (2012) Estimation, control, and the discrete Kalman filter, vol 71. Springer

  • Chairez I, Andrianova O, Poznyak T, Poznyak A (2022) Adaptive modeling of nonnegative environmental systems based on projectional Differential Neural Networks observer. Neural Netw 151:156–167

    Article  Google Scholar 

  • Chan JCL, Lee TH (2022) Observer-based fault-tolerant control for non-infinitely observable descriptor systems with unknown time-varying state and input delays. Appl Math Comput 430:127230

    MathSciNet  MATH  Google Scholar 

  • Chen Z, Duan Y, Zhang Y (2021) Automated vehicle path planning and trajectory tracking control based on unscented Kalman filter vehicle state observer. SAE Technical Paper, No. 2021-01-0337

  • Cheng Z, Ren H, Zhang B, Lu R (2021) Distributed Kalman filter for large-scale power systems with state inequality constraints. IEEE Trans Industr Electron 68(7):6238–6247

    Article  Google Scholar 

  • Cumbo R, Mazzanti L, Tamarozzi T, Jiranek P, Desmet W, Naets F (2021) Advanced optimal sensor placement for Kalman-based multiple-input estimation. Mech Syst Signal Process 160:107830

    Article  Google Scholar 

  • Dalwadi N, Deb D, Muyeen SM (2022) Observer based rotor failure compensation for biplane quadrotor with slung load. Ain Shams Eng J 13(6):101748

    Article  Google Scholar 

  • Dang L, Chen B, Wang S, Ma W, Ren P (2020) Robust power system state estimation with minimum error entropy unscented Kalman filter. IEEE Trans Instrum Meas 69(11):8797–8808

    Article  Google Scholar 

  • Das L, Kumar G, Rengaswamy R, Srinivasan B (2018) A novel approach for benchmarking and assessing the performance of state estimators. ISA Trans 80:137–145

    Article  Google Scholar 

  • Deisenroth MP, Turner RD, Huber MF, Hanebeck UD, Rasmussen CE (2011) Robust filtering and smoothing with Gaussian processes. IEEE Trans Autom Control 57(7):1865–1871

    Article  MathSciNet  MATH  Google Scholar 

  • Del Rosario MB, Khamis H, Ngo P, Lovell NH, Redmond SJ (2018) Computationally efficient adaptive error-state Kalman filter for attitude estimation. IEEE Sens J 18(22):9332–9342

    Article  Google Scholar 

  • Gao Z (2018) Reduced order Kalman filter for a continuous-time fractional-order system using fractional-order average derivative. Appl Math Comput 338:72–86

    MathSciNet  MATH  Google Scholar 

  • Garcia RV, Kuga HK, Silva WR, Zanardi MC (2018) Unscented Kalman filter and smoothing applied to attitude estimation of artificial satellites. Comput Appl Math 37(1):55–64

    Article  MathSciNet  MATH  Google Scholar 

  • Geetha M, Jerome J, Kumar A (2014) Critical evaluation of non-linear filter configurations for the state estimation of Continuous Stirred Tank Reactor. Appl Soft Comput 25:452–460

    Article  Google Scholar 

  • Ghaderi N (2022) A novel observer-based approach for the exponential stabilization of the string PDE with cubic nonlinearities. Syst Control Lett 165:105273

    Article  MathSciNet  MATH  Google Scholar 

  • Guo X, Albalawi F, N’Doye I, Laleg-Kirati TM (2019) State estimation in direct contact membrane distillation based desalination using nonlinear observer. IFAC-PapersOnLine 52(23):61–66

    Article  Google Scholar 

  • Gutmann HM (2001) A radial basis function method for global optimization. J Global Optim 19(3):201–227

    Article  MathSciNet  MATH  Google Scholar 

  • Haring M, Johansen TA (2020) On the stability bounds of Kalman filters for linear deterministic discrete-time systems. IEEE Trans Autom Control 65(10):4434–4439

    Article  MathSciNet  MATH  Google Scholar 

  • He Z, Yang Z, Cui X, Li E (2020) A method of state-of-charge estimation for EV power lithium-ion battery using a novel adaptive extended Kalman filter. IEEE Trans Veh Technol 69(12):14618–14630

    Article  Google Scholar 

  • Hou M, Xiong YS, Patton RJ (2005) Observing a three-tank system. IEEE Trans Control Syst Technol 13(3):478–484

    Article  Google Scholar 

  • Janjanam L, Saha SK, Kar R, Mandal D (2021) Global gravitational search algorithm-aided Kalman filter design for volterra-based nonlinear system identification. Circuits Syst Signal Process 40(5):2302–2334

    Article  Google Scholar 

  • Jiang B, Wu Z, Karimi HR (2022) A distributed dynamic event-triggered mechanism to HMM-based observer design for H∞ sliding mode control of Markov jump systems. Automatica 142:110357

    Article  MathSciNet  MATH  Google Scholar 

  • Kaur H, Khosla M, Sarin RK (2018) Interval type-2 fuzzy Kalman filter aided individual channel estimation in MIMO relay systems. Int J Commun Syst 31(17):e3792

    Article  Google Scholar 

  • Kulikova MV, Tsyganova JV, Kulikov GY (2019) SVD-based state and parameter estimation approach for generalized Kalman filtering with application to GARCH-in-Mean estimation. J Comput Appl Math 387:112487

    Article  MathSciNet  MATH  Google Scholar 

  • Lamouchi R, Raissi T, Amairi M, Aoun M (2022) On interval observer design for active Fault Tolerant Control of Linear Parameter-Varying systems. Syst Control Lett 164:105218

    Article  MathSciNet  MATH  Google Scholar 

  • Le BK (2022) Sliding mode observers for time-dependent set-valued Lur’e systems subject to uncertainties. J Optim Theory Appl 194(1):290–305

    Article  MathSciNet  MATH  Google Scholar 

  • Li Y, Wang C, Gong J (2017) A multi-model probability SOC fusion estimation approach using an improved adaptive unscented Kalman filter technique. Energy 141:1402–1415

    Article  Google Scholar 

  • Li S, Li Z, Li J, Fernando T, Iu H, Wang Q, Liu X (2021a) Application of event-triggered cubature Kalman filter for remote nonlinear state estimation in wireless sensor network. IEEE Trans Industr Electron 68(6):5133–5145

    Article  Google Scholar 

  • Li X, Meng Q, Liu M, Guo Y (2021b) A fast robust Kalman filter for initial alignment of strapdown inertial navigation system. Optik 237:166541

    Article  Google Scholar 

  • Li X, Zhang W, Lu D, Yang G (2022) A novel robust fault estimation observer design for semi-Markovian jump systems with partially bounded transition rate. Int J Robust Nonlinear Control 32(9):5398–5419

    Article  MathSciNet  Google Scholar 

  • Lio WH, Li A, Meng F (2021) Real-time rotor effective wind speed estimation using Gaussian process regression and Kalman filtering. Renew Energy 169:670–686

    Article  Google Scholar 

  • Liu YJ, Dou CH, Shen F, Sun QY (2021) Vehicle state estimation based on unscented Kalman filtering and a genetic-particle swarm algorithm. J Inst Eng (india): Ser C 102(2):447–469

    Google Scholar 

  • Luo Z, Fu Z, Xu Q (2020) An adaptive multi-dimensional vehicle driving state observer based on modified Sage-Husa UKF algorithm. Sensors 20(23):6889

    Article  Google Scholar 

  • Mathiyalagan K, Nidhi AS, Su H, Renugadevi T (2022) Observer and boundary output feedback control for coupled ODE-transport PDE. Appl Math Comput 426:127096

    MathSciNet  MATH  Google Scholar 

  • Mehralian MA, Soryani M (2020) EKFPnP: extended Kalman filter for camera pose estimation in a sequence of images. IET Image Proc 14(15):3774–3780

    Article  Google Scholar 

  • Meyer L, Ichalal D, Vigneron V (2020) An unknown input extended Kalman filter for nonlinear stochastic systems. Eur J Control 56:51–61

    Article  MathSciNet  MATH  Google Scholar 

  • Mondal P, Malakar MK, Tripathy P, Krishnaswamy S, Saha UK (2021) Robust observer design for sensorless voltage and frequency control of a doubly fed induction generator in standalone mode. IEEE Trans Energy Convers 37(2):844–854

    Article  Google Scholar 

  • Murata M, Kawano I, Inoue K (2020) Extended, unscented Kalman, and sigma point multiple distribution estimation filters for nonlinear discrete state-space models. IEEE Control Syst Lett 4(4):982–987

    Article  MathSciNet  Google Scholar 

  • Mussot V, Mercère G, Dairay T, Arvis V, Vayssettes J (2021) Noise covariance matrix estimation with subspace model identification for Kalman filtering. Int J Adapt Control Signal Process 35(4):591–611

    Article  MathSciNet  Google Scholar 

  • Musunuri YR, Kwon OS (2021) State estimation using a randomized unscented Kalman filter for 3D skeleton posture. Electronics 10(8):971

    Article  Google Scholar 

  • N’Doye I, Zhang D, Adil A, Zemouche A, Rajamani R, Laleg-Kirati TM (2022) An LMI-based discrete time nonlinear observer for Light-Emitting Diode optical communication. Automatica 141:110309

    Article  MathSciNet  MATH  Google Scholar 

  • Orr MJ (1995) Regularization in the selection of radial basis function centers. Neural Comput 7(3):606–623

    Article  Google Scholar 

  • Pan Q, Yang F, Ye L, Liang Y, Cheng YM (2005) Survey of a kind of nonlinear filters-UKF. Control Decis 20(5):481

    Google Scholar 

  • Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257

    Article  Google Scholar 

  • Patel Z, Boje E (2020) A hybrid, coupled approach to the continuous-discrete Kalman filter. IEEE Control Syst Lett 5(3):827–832

    Article  MathSciNet  Google Scholar 

  • Rajaei A, Raeiszadeh M, Azimi V, Sharifi M (2021) State estimation-based control of COVID-19 epidemic before and after vaccine development. J Process Control 102:1–14

  • Rathnayake B, Diagne M, Espitia N, Karafyllis I (2022) Observer-based event-triggered boundary control of a class of reaction-diffusion PDEs. IEEE Trans Autom Control 67(6):2905–2917

    Article  MathSciNet  MATH  Google Scholar 

  • Rios JD, Alanis AY, Arana-Daniel N, Lopez-Franco C (2020) Real-time neural observer-based controller for unknown nonlinear discrete delayed systems. Int J Robust Nonlinear Control 30(18):8402–8429

    Article  MathSciNet  Google Scholar 

  • Rodríguez AJ, Sanjurjo E, Pastorino R, Naya MÁ (2021) State, parameter and input observers based on multibody models and Kalman filters for vehicle dynamics. Mech Syst Signal Process 155:107544

    Article  Google Scholar 

  • Rúa S, Vásquez RE, Crasta N, Zuluaga CA (2020) Observability analysis and observer design for a nonlinear three-tank system: theory and experiments. Sensors 20(23):6738

    Article  Google Scholar 

  • Sanchez B, Ordaz P, Poznyak A (2022) Model based reduced-order observers for a class of mechatronic systems with mitigation of disturbances effects using the Attractive Ellipsoid Method. Mechatronics 84:102778

    Article  Google Scholar 

  • Sassi HB, Errahimi F, Najia ES (2020) State of charge estimation by multi-innovation unscented Kalman filter for vehicular applications. J Energy Storage 32:101978

    Article  Google Scholar 

  • Self R, Coleman K, Bai H, Kamalapurkar R (2021) Online observer-based inverse reinforcement learning. IEEE Control Syst Lett 5(6):1922–1927

    Article  MathSciNet  Google Scholar 

  • Shi S, Fei Z, Zhao X (2022) Time-scheduled observer design for switched linear systems with unknown inputs. Sci China Inf Sci 65(7):1–12

    Article  MathSciNet  Google Scholar 

  • Siket M, Eigner G, Drexler DA, Rudas I, Kovács L (2020) State and parameter estimation of the mathematical carcinoma model under chemotherapeutic treatment. Appl Sci 10(24):9046

    Article  Google Scholar 

  • Simon D (2010) Kalman filtering with state constraints: a survey of linear and nonlinear algorithms. IET Control Theory Appl 4(8):1303–1318

    Article  MathSciNet  Google Scholar 

  • Singh B, Xiong X, Dinh TN, Kamal S, Ghosh S (2021) Interval observer design for nonlinear systems using simplified contraction theory. IET Control Theory Appl 16(10):935–944

    Article  Google Scholar 

  • Sneha K, Vaishnavi P, Ganesh M, Jagadeesh C, Hariharan A (2020). Detection of soft sensor fault using EKF algorithm for two tank interacting system. In: IOP conference series: materials science and engineering, vol 995, no 1. IOP Publishing, , p 012011

  • Souaihia M, Belmadani B, Taleb R (2019) Performance of state of charge estimation model-based via adaptive extended Kalman filter. J Electr Syst 15(4):553–567

    Google Scholar 

  • Su H, Zhang W (2022) Observer-based adaptive neural quantized control for nonlinear systems with asymmetric fuzzy dead zones and unknown control directions. Nonlinear Dyn 108(4):3643–3656

    Article  Google Scholar 

  • Sun D, Yu X, Zhang C, Wang C, Huang R (2020) State of charge estimation for lithium-ion battery based on an intelligent adaptive unscented Kalman filter. Int J Energy Res 44(14):11199–11218

    Article  Google Scholar 

  • Suresh M, Srinivasan JG, Hemamalini RR (2009) Integrated fuzzy logic based intelligent control of three tank system. Serb J Electr Eng 6(1):1–14

    Article  Google Scholar 

  • Surwase SK, Varshney D, Patel NV, Bhushan M (2017). Nonlinear state estimation for three tank experimental setup: a comparative evaluation. In: 2017 6th international conference on computer applications in electrical engineering-recent advances (CERA). IEEE, pp 485–490

  • Vahidpour V, Rastegarnia A, Khalili A, Sanei S (2019) Partial diffusion Kalman filtering for distributed state estimation in multiagent networks. IEEE Trans Neural Netw Learn Syst 30(12):3839–3846

    Article  MathSciNet  Google Scholar 

  • Wan M, Huang S, Wang G, Zhang Q (2022) Observer-based adaptive neural network control for stabilized platform in rotary steerable system with unknown input dead-zone. Trans Inst Meas Control 44(11):2152–2165

    Article  Google Scholar 

  • Wang X, Yaz EE (2019) Second-order fault tolerant extended Kalman filter for discrete time nonlinear systems. IEEE Trans Autom Control 64(12):5086–5093

    Article  MathSciNet  MATH  Google Scholar 

  • Wang H, Meng A, Liu Y, Fu X, Cao G (2019) Unscented Kalman Filter based interval state estimation of cyber physical energy system for detection of dynamic attack. Energy 188:116036

    Article  Google Scholar 

  • Wang M, An A, Zhao Y (2021a). Model predictive control of microbial fuel cell based on Kalman state estimation. In: Journal of physics: conference series, vol 1848, no 1. IOP Publishing, p 012063

  • Wang C, Wang Z, Zhang L, Cao D, Dorrell DG (2021b) A vehicle rollover evaluation system based on enabling state and parameter estimation. IEEE Trans Industr Inf 17(6):4003–4013

    Article  Google Scholar 

  • Wen P, Dong H, Huo F, Li J, Lu X (2022) Observer-based PID control for actuator-saturated systems under binary encoding scheme. Neurocomputing 499:54–62

    Article  Google Scholar 

  • Xiao M, Zhang Y, Fu H (2017) Three-stage unscented Kalman filter for state and fault estimation of nonlinear system with unknown input. J Frankl Inst 354(18):8421–8443

    Article  MathSciNet  MATH  Google Scholar 

  • Yang S, Zhou S, Hua Y, Zhou X, Liu X, Pan Y, Ling H, Wu B (2021) A parameter adaptive method for state of charge estimation of lithium-ion batteries with an improved extended Kalman filter. Sci Rep 11(1):1–15

    Google Scholar 

  • Yang H, Wang X, Zhong S, Shu L (2022) Observer-based asynchronous event-triggered control for interval type-2 fuzzy systems with cyber-attacks. Inf Sci 606:805–818

    Article  Google Scholar 

  • Yildiz R, Barut M, Zerdali E (2020) A comprehensive comparison of extended and unscented Kalman filters for speed-sensorless control applications of induction motors. IEEE Trans Industr Inf 16(10):6423–6432

    Article  Google Scholar 

  • Yu H, Juniper MP, Magri L (2019) Combined state and parameter estimation in level-set methods. J Comput Phys 399:108950

    Article  MathSciNet  MATH  Google Scholar 

  • Yuan H, Dai H, Wei X, Ming P (2020) A novel model-based internal state observer of a fuel cell system for electric vehicles using improved Kalman filter approach. Appl Energy 268:115009

    Article  Google Scholar 

  • Zhang Z, Jiang L, Zhang L, Huang C (2021) State-of-charge estimation of lithium-ion battery pack by using an adaptive extended Kalman filter for electric vehicles. J Energy Storage 37:102457

    Article  Google Scholar 

  • Zhou DH, He X, Wang Z, Liu GP, Ji YD (2011) Leakage fault diagnosis for an internet-based three-tank system: an experimental study. IEEE Trans Control Syst Technol 20(4):857–870

    Article  Google Scholar 

  • Zhou C, Wang C, Yao W, Lin H (2022) Observer-based synchronization of memristive neural networks under DoS attacks and actuator saturation and its application to image encryption. Appl Math Comput 425:127080

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electronics and Instrumentation Engineering, Government College of Technology, Coimbatore, 641 013, India

    A. Suguna

  2. Deptarment of Electrical and Electronics Engineering, Dr. NGP Institute of Technology, Coimbatore, 641 048, India

    V. Ranganayaki

  3. Department of Electrical Engineering, National Institute of Technology Arunachal Pradesh, Jote, 791113, India

    S. N. Deepa

Authors
  1. A. Suguna
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. Ranganayaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. N. Deepa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Suguna.

Ethics declarations

Conflict of interest

The authors confirm no conflict of interest in the research study made and its publishing.

Appendix

Appendix

1.1 Abbreviations

RBF :

Radial basis function

RLS :

Recursive likelihood synthesizer

EKF :

Extended Kalman filter

UKF :

Unscented Kalman filter

TTPS :

Three-tank process system

UI :

Unknown inputs

IAUKF :

Intelligent adaptive unscented Kalman filter

EM :

Expected maximum

ARMSE :

Average root mean square error

1.2 List of symbols

h :

Height of liquid/fluid level in the tank

fw :

Flow rate within and from the three tanks

R :

Resistance of the flow

g :

Gravitational force

a :

Area of connecting pipes

A :

Area of cylindrical tanks

D :

Inner diameter of the tanks

h 1 :

Steady-state fluid level of tank 1

h 2 :

Steady-state fluid level of tank 2

h 3 :

Steady-state fluid level of tank 3

C 1 :

Discharge of inlet orifice

C 2 :

Discharge of interconnecting orifice—coupler

C 3 :

Discharge of outlet orifice

x(q):

System’s unobserved state

y(q):

Observed state

u(q):

Input signal

v(q) and z(q):

Gaussian white noise

L and M:

Covariance matrices

G and H:

Functional vectors

δ(q):

Past and present observations

ψ RBF :

Nonlinear function

α y :

Number of past output corresponding to the measured state

α e :

Number of past output corresponding to the observed state

e(q):

Error term used in RBF full-order neural observer

χ 0 :

Initial covariance

x q |Q :

Smoothing estimate state value

J q :

Jacobian matrix of the measured vector

C q :

Conditional covariance of xq

C q|Q :

Covariance estimate

w :

Dimensions

V(j):

Linked weights

σ :

Spread of the mean of the sigma point

Q :

Secondary scaling coefficient

ζ :

Prior knowledge of the probability distribution

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Suguna, A., Ranganayaki, V. & Deepa, S.N. Design of Full-Order Neural Observer with Nonlinear Filter Techniques for State Estimation of a Three-Tank Process Control System. Iran J Sci Technol Trans Electr Eng 46, 1057–1087 (2022). https://doi.org/10.1007/s40998-022-00528-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40998-022-00528-y

Keywords

Search

Navigation