Evaluation of Block-Oriented Models Use for the Purpose of Robust Controllers Synthesis

Evaluation of Block-Oriented Models Use for the Purpose of Robust Controllers Synthesis

Jhonathan C. Resende Márcio F. S. Barroso  Valter Jr. de Souza Leite 

Postgraduate Master’s Program in Electrical Engineering – Federal University of São João Del-Rei/ Federal Center for Technological Education of Minas Gerais, 170 Frei Orlando Square, 36307-352, São João Del-Rei, Minas Gerais, Brazil

Electrical Engineering Department, Federal University of São João Del-Rei, 170 Frei Orlando Square, 36307-352, São João Del-Rei, Minas Gerais, Brazil

Mechatronic Engineering Department, Federal Center for Technological Education of Minas Gerais / Campus Divinópolis, 400 Álvares Azevedo Street, 35503-882, Divinópolis, Minas Gerais, Brazil

Corresponding Author Email: 
jhonathanresende@outlook.com
Page: 
22-31
|
DOI: 
https://doi.org/10.18280/mmc_a.910104
Received: 
7 January 2018
|
Accepted: 
17 April 2018
|
Published: 
31 March 2018
| Citation

OPEN ACCESS

Abstract: 

A comparative study of the use of block-oriented and autoregressive with exogenous inputs (ARX) models in the context of robust controller synthesis is presented in this paper. Parameters uncertainties of the identified models are taken into account in the synthesis of the controllers by state feedback, which aim to assure the maximum attenuation of H2 and H costs. The study consists in evaluating the effects of the variation in the models order and respective estimated deviation in their parameters in the synthesis of robust controllers. The models were obtained from an air heating system with nonlinear dynamics and controllers were designed by means of convex optimization procedures in the form of linear matrix inequalities. The results obtained point to the preferential use of low order Wiener or Hammerstein models, even if they have RMSE and correlation coefficient between simulation error and simulated output indexes worse than higher order models.

Keywords: 

system identification, Hammerstein model, Wiener model, block-oriented models, robust control, linear matrix inequalities

1. Introduction
2. Preliminaries
3. System Description
4. Methodology
5. Results and Discussion
6. Conclusion
  References

[1] Aguirre LA. (2007). Introduction to system identification: linear and non-linear techniques applied to real systems. 3. ed. Belo Horizonte: UFMG. p. 730.

[2] Barroso MFS. (2006). Bi-objective optimization applied to estimation of polynomial NARX model parameters: characterization and decision-making. Belo Horizonte: Federal University of Minas Gerais. (Doctoral thesis, Postgraduate Program in Electrical Engineering).

[3] Biagiola SI, Figueroa JL. (2011). Robust model predictive control of Wiener systems. International Journal of Control 84(3): 432–444.

[4] Bloemen HHJ, Van Den Boom TJJ. (1999). MPC for Wiener systems. Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona, USA 7-10: 4595–4600.

[5] Boyd S, El Ghaoui L, Feron E, Balakrishnan V. (1994). Linear matrix inequalities in system and control theory. Philadelphia: Society for Industrial and Applied Mathematics 193.

[6] de Oliveira PJ, Oliveira RCLF, Leite VJS, Montagner VF, Peres PLD. (2004). H_∞ guaranteed cost computation by means of parameter-dependent Lyapunov functions. Automatica 40: 1053-1061.

[7] de Oliveira PJ, Oliveira RCLF, Leite VJS, Montagner VF, Peres PLD. (2004). H_2 guaranteed cost computation by means of parameter-dependent Lyapunov functions. International Journal of Systems Science 35(5): 305-315. 

[8] Dorf RC, Bishop RH. (2009). Modern Control Systems. 11. ed. Rio de Janeiro: LTC p. 724.

[9] Fernando TL, Phat VN, Trinh HM. (2013). Output feedback guaranteed cost control of uncertain linear discrete systems with interval time-varying delays. Applied Mathematical Modelling 37: 1580–1589.

[10] Franco AEO. (2013). Automatic control of a thermal process with multiple inputs and multiple outputs using modern control techniques. Divinópolis: Federal Center for Technological Education of Minas Gerais. (Undergraduate thesis, Mechatronic Engineering).

[11] Khani F, Haeri M. (2015). Robust model predictive control of nonlinear processes represented by Wiener or Hammerstein models. Chemical Engineering Science 129: 223–231.

[12] Ribeiro AH, Aguirre LA. (2014). Static relationships of NARX MISO models and their Hammerstein representation. In: Brazilian Congress of Automation, Belo Horizonte. Proceedings of the 20th Brazilian Congress of Automation. 

[13] Silva LFP. (2011). Study on the inclusion of performance in the synthesis of controllers for discrete time systems with delayed states. Belo Horizonte: Federal Center for Technological Education of Minas Gerais. (Master’s dissertation, Postgraduate Program in Electrical Engineering).

[14] Söderström T, Stoica P. (1989). System Identification. Prentice Hall International (UK) Ltd.

[15] Takahashi RHC, Dutra DA, Palhares RM, Peres PLD. (2000). On robust non-fragile static state-feedback controller synthesis. Conference on Decision and Control. Sydney, Australia.

[16] Teixeira MH, Leite VJS, Silva LFP, Gonçalves EN. (2013). Revisiting the problem of robust H_∞ control with regional pole location of uncertain discrete-time systems with delayed states. 52nd IEEE Conference on Decision and Control. Florence, Italy.

[17] Wang Z, Xi J, Yao Z, Liu G. (2015). Guaranteed cost consensus for multi-agent systems with fixed topologies. Asian Journal of Control 17(2): 729-735.

[18] Zhang B, Mao Z. (2017). A robust adaptive control method for Wiener nonlinear systems. International Journal of Robust and Nonlinear Control 27:434–460. 

[19] Zhou K, Doyle JC. (1998). Essentials of robust control. Upper Saddle River: Prentice Hall 411.