Abstract
This paper describes the design and successful implementation of a constrained model predictive controller with integral action for the control of a Twin Rotor MIMO System (TRMS). The integral action guarantees zero steady-state error in set-point tracking with robustness toward perturbations of the nominal system parameters. In addition to saturation constraints on the input variables, hard constraints are imposed on the controlled output variables, i.e., on pitch and yaw angular positions, to avoid collisions with obstacles. The model predictive controller was designed using a high-fidelity nonlinear model of the TRMS developed in previous work. As an intermediate step, exact linearized models of the TRMS are obtained and their closed-form expressions are reported. The controller was tested experimentally, also showing its effectiveness in ensuring actual collision avoidance by the TRMS when physical obstacles were present.
Issue Section:
Research Papers
References
1.
López-Martínez
,
M.
,
Ortega
,
M. G.
,
Vivas
,
C.
, and
Rubio
,
F. R.
, 2007
, “
Nonlinear l2 Control of a Laboratory Helicopter With Variable Speed Rotors
,” Automatica
,
43
(4
), pp. 655
–661
.10.1016/j.automatica.2006.10.0132.
Wen
,
P.
, and
Lu
,
T. W.
, 2008
, “
Decoupling Control of a Twin Rotor MIMO System Using Robust Deadbeat Control Technique
,” IET Control Theory Appl.
,
2
(11
), pp. 999
–1007
.10.1049/iet-cta:200703353.
Mullhaupt
,
P.
,
Srinivasan
,
B.
,
Lévine
,
J.
, and
Bonvin
,
D.
, 2008
, “
Control of the Toycopter Using a Flat Approximation
,” IEEE Trans. Control Syst. Technol.
,
16
(5
), pp. 882
–896
.10.1109/TCST.2007.9163334.
Mondal
,
S.
, and
Mahanta
,
C.
, 2012
, “
Adaptive Second-Order Sliding Mode Controller for a Twin Rotor Multi-Input–Multi-Output System
,” IET Control Theory Appl.
,
6
(14
), pp. 2157
–2167
.10.1049/iet-cta.2011.04785.
Rotondo
,
D.
,
Nejjari
,
F.
, and
Puig
,
V.
, 2013
, “
Quasi–LPV Modeling, Identification and Control of a Twin Rotor MIMO System
,” Control Eng. Pract.
,
21
(6
), pp. 829
–846
.10.1016/j.conengprac.2013.02.0046.
Belmonte
,
L.
,
Morales
,
R.
,
Fernández-Caballero
,
A.
, and
Somolinos
,
J.
, 2016
, “
Robust Decentralized Nonlinear Control for a Twin Rotor MIMO System
,” Sensors
,
16
(8
), p. 1160
.10.3390/s160811607.
Roman
,
R. C.
,
Radac
,
M. B.
, and
Precup
,
R. E.
, 2016
, “
Multi-Input-Multi-Output System Experimental Validation of Model-Free Control and Virtual Reference Feedback Tuning Techniques
,” IET Control Theory Appl.
,
10
(12
), pp. 1395
–1403
.10.1049/iet-cta.2016.00288.
Pandey
,
S. K.
,
Dey
,
J.
, and
Banerjee
,
S.
, 2018
, “
Design of Robust Proportional-Integral-Derivative Controller for Generalized Decoupled Twin Rotor Multi-Input-Multi-Output System With Actuator Non-Linearity
,” Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng.
,
232
(8
), pp. 971
–982
.10.1177/09596518187714879.
Grüne
,
L.
, and
Pannek
,
J.
, 2017
, Nonlinear Model Predictive Control: Theory and Algorithms
,
Springer International Publishing, Cham, Switzerland.10.
Rawlings
,
J. B.
,
Mayne
,
D. Q.
, and
Diehl
,
M.
, 2017
, Model Predictive Control: Theory, Computation, and Design
,
Nob Hill Publishing
,
Madison, WI
.11.
Propoi
,
A. I.
, 1963
, “
Application of Linear Programming Methods for the Synthesis of Automatic Sampled-Data Systems
,” Avtomat. i Telemekh
,
24
(7
), pp. 912
–920
.http://mi.mathnet.ru/at1190512.
Richalet
,
J.
,
Rault
,
A.
,
Testud
,
J.
, and
Papon
,
J.
, 1978
, “
Model Predictive Heuristic Control: Applications to Industrial Processes
,” Automatica
,
14
(5
), pp. 413
–428
.10.1016/0005-1098(78)90001-813.
Qin
,
S. J.
, and
Badgwell
,
T. A.
, 2003
, “
A Survey of Industrial Model Predictive Control Technology
,” Control Eng. Pract.
,
11
(7
), pp. 733
–764
.10.1016/S0967-0661(02)00186-714.
Lee
,
J. H.
, 2011
, “
Model Predictive Control: Review of the Three Decades of Development
,” Int. J. Control, Autom. Syst.
,
9
(3
), pp. 415
–424
.10.1007/s12555-011-0300-615.
Di Cairano
,
S.
,
Bernardini
,
D.
,
Bemporad
,
A.
, and
Kolmanovsky
,
I. V.
, 2014
, “
Stochastic MPC With Learning for Driver-Predictive Vehicle Control and Its Application to Hev Energy Management
,” IEEE Trans. Control Syst. Technol.
,
22
(3
), pp. 1018
–1031
.10.1109/TCST.2013.227217916.
Oleinikov
,
A.
,
Kusdavletov
,
S.
,
Shintemirov
,
A.
, and
Rubagotti
,
M.
, 2021
, “
Safety-Aware Nonlinear Model Predictive Control for Physical Human-Robot Interaction
,” IEEE Rob. Autom. Lett.
,
6
(3
), pp. 5665
–5672
.10.1109/LRA.2021.308358117.
Bordons
,
C.
, and
Montero
,
C.
, 2015
, “
Basic Principles of MPC for Power Converters: Bridging the Gap Between Theory and Practice
,” IEEE Ind. Electron. Mag.
,
9
(3
), pp. 31
–43
.10.1109/MIE.2014.235660018.
Oldewurtel
,
F.
,
Parisio
,
A.
,
Jones
,
C. N.
,
Gyalistras
,
D.
,
Gwerder
,
M.
,
Stauch
,
V.
,
Lehmann
,
B.
, and
Morari
,
M.
, 2012
, “
Use of Model Predictive Control and Weather Forecasts for Energy Efficient Building Climate Control
,” Energy Build.
,
45
, pp. 15
–27
.10.1016/j.enbuild.2011.09.02219.
Mayne
,
D. Q.
, 2014
, “
Model Predictive Control: Recent Developments and Future Promise
,” Automatica
,
50
(12
), pp. 2967
–2986
.10.1016/j.automatica.2014.10.12820.
Camacho
,
E. F.
,
Ramírez
,
D. R.
,
Limón
,
D.
,
De La Peña
,
D. M.
, and
Alamo
,
T.
, 2010
, “
Model Predictive Control Techniques for Hybrid Systems
,” Annu. Reviews Control
,
34
(1
), pp. 21
–31
.10.1016/j.arcontrol.2010.02.00221.
Allan
,
D. A.
,
Bates
,
C. N.
,
Risbeck
,
M. J.
, and
Rawlings
,
J. B.
, 2017
, “
On the Inherent Robustness of Optimal and Suboptimal Nonlinear MPC
,” Syst. Control Lett.
,
106
, pp. 68
–78
.10.1016/j.sysconle.2017.03.00522.
Mayne
,
D. Q.
,
Rawlings
,
J. B.
,
Rao
,
C. V.
, and
Scokaert
,
P. O.
, 2000
, “
Constrained Model Predictive Control: Stability and Optimality
,” Automatica
,
36
(6
), pp. 789
–814
.10.1016/S0005-1098(99)00214-923.
Kantas
,
N.
,
Maciejowski
,
J. M.
, and
Lecchini-Visintini
,
A.
, 2009
, “
Sequential Monte Carlo for Model Predictive Control
,” Nonlinear Model Predictive Control: Towards New Challenging Applications
,
Springer-Verlag, Berlin Heidelber, pp. 263
–273
.24.
Mesbah
,
A.
, 2016
, “
Stochastic Model Predictive Control: An Overview and Perspectives for Future Research
,” IEEE Control Syst. Mag.
,
36
(6
), pp. 30
–44
.10.1109/MCS.2016.260208725.
Rubagotti
,
M.
,
Patrinos
,
P.
, and
Bemporad
,
A.
, 2014
, “
Stabilizing Linear Model Predictive Control Under Inexact Numerical Optimization
,” IEEE Trans. Autom. Control
,
59
(6
), pp. 1660
–1666
.10.1109/TAC.2013.229345126.
Berberich
,
J.
,
Köhler
,
J.
,
Müller
,
M. A.
, and
Allgöwer
,
F.
, 2021
, “
Data-Driven Model Predictive Control With Stability and Robustness Guarantees
,” IEEE Trans. Autom. Control
,
66
(4
), pp. 1702
–1717
.10.1109/TAC.2020.300018227.
Viswanathan
,
S. P.
,
Sanyal
,
A. K.
, and
Samiei
,
E.
, 2018
, “
Integrated Guidance and Feedback Control of Underactuated Robotics System in SE (3)
,” J. Intell. Rob. Syst.
,
89
(1–2
), pp. 251
–263
.10.1007/s10846-017-0547-028.
Chen
,
T.
,
Babanin
,
A.
,
Muhammad
,
A.
,
Chapron
,
B.
, and
Chen
,
C.
, 2020
, “
Modified Evolved Bat Algorithm of Fuzzy Optimal Control for Complex Nonlinear Systems
,” Rom. J. Inf. Sci. Technol
,
T
(23
), pp. T28
–T40
.https://www.romjist.ro/full-texts/paper672.pdf29.
Precup
,
R.-E.
,
Roman
,
R.-C.
, and
Safaei
,
A.
, 2022
, Data-Driven Model-Free Controllers
,
CRC Press
, Boca Raton, FL.30.
Bemporad
,
A.
,
Morari
,
M.
,
Dua
,
V.
, and
Pistikopoulos
,
E. N.
, 2002
, “
The Explicit Linear Quadratic Regulator for Constrained Systems
,” Automatica
,
38
(1
), pp. 3
–20
.10.1016/S0005-1098(01)00174-131.
Oliveri
,
A.
,
Barcelli
,
D.
,
Bemporad
,
A.
,
Genuit
,
B.
,
Heemels
,
M.
,
Poggi
,
T.
,
Rubagotti
,
M.
, and
Storace
,
M.
, 2012
, “
MOBY-DIC: A MATLAB Toolbox for Circuit-Oriented Design of Explicit MPC
,” Proceedings of IFAC Conference on Nonlinear Model Predictive Control,
August 23–27, Noordwijkerhout, The Netherlands, pp. 218
–225
.10.3182/20120823-5-NL-3013.0003432.
Rubagotti
,
M.
,
Barcelli
,
D.
, and
Bemporad
,
A.
, 2014
, “
Robust Explicit Model Predictive Control Via Regular Piecewise-Affine Approximation
,” Int. J. Control
,
87
(12
), pp. 2583
–2593
.10.1080/00207179.2014.93595833.
Rahideh
,
A.
, and
Shaheed
,
M. H.
, 2011
, “
Stable Model Predictive Control for a Nonlinear System
,” J. Franklin Inst.
,
348
(8
), pp. 1983
–2004
.10.1016/j.jfranklin.2011.05.01534.
Rahideh
,
A.
, and
Shaheed
,
M. H.
, 2012
, “
Constrained Output Feedback Model Predictive Control for Nonlinear Systems
,” Control Eng. Pract.
,
20
(4
), pp. 431
–443
.10.1016/j.conengprac.2011.12.00335.
Duţescu
,
D. A.
,
Radac
,
M. B.
, and
Precup
,
R. E.
, 2017
, “
Model Predictive Control of a Nonlinear Laboratory Twin Rotor Aero-Dynamical System
,” IEEE International Symposium on Applied Machine Intelligence and Informatics,
Herl’any, Slovakia, Jan. 26–28, pp. 37
–42
.10.1109/SAMI.2017.788033936.
Raghavan
,
R.
, and
Thomas
,
S.
, 2017
, “
Practically Implementable Model Predictive Controller for a Twin Rotor Multi-Input Multi-Output System
,” J. Control, Autom. Electr. Syst.
,
28
(3
), pp. 358
–370
.10.1007/s40313-017-0311-537.
Tahir
,
F.
,
Ahmed
,
Q.
, and
Bhatti
,
A. I.
, 2013
, “
Real-Time Switched Model Predictive Control of a Twin Rotor System
,” IEEE Conference on Decision and Control
, Florence, Italy, Dec. 10–13, pp. 4847
–4852
.10.1109/CDC.2013.676064938.
Pannocchia
,
G.
, 2015
, “
Offset–Free Tracking MPC: A Tutorial Review and Comparison of Different Formulations
,” European Control Conference (ECC
), Linz, Austria, July 15–17, pp. 527
–532
.10.1109/ECC.2015.733059739.
Ferramosca
,
A.
,
González
,
A. H.
, and
Limon
,
D.
, 2017
, “
Offset–Free Multi-Model Economic Model Predictive Control for Changing Economic Criterion
,” J. Process Control
,
54
, pp. 1
–13
.10.1016/j.jprocont.2017.02.01440.
Incremona
,
G. P.
,
Messori
,
M.
,
Toffanin
,
C.
,
Cobelli
,
C.
, and
Magni
,
L.
, 2018
, “
Model Predictive Control With Integral Action for Artificial Pancreas
,” Control Eng. Pract.
,
77
, pp. 86
–94
.10.1016/j.conengprac.2018.05.00641.
Abdelrahem
,
M.
,
Hackl
,
C. M.
,
Kennel
,
R.
, and
Rodriguez
,
J.
, 2019
, “
Efficient Direct-Model Predictive Control With Discrete-Time Integral Action for PMSGs
,” IEEE Trans. Energy Convers.
,
34
(2
), pp. 1063
–1072
.10.1109/TEC.2018.287262642.
Ramírez
,
R. O.
,
Espinoza
,
J. R.
,
Baier
,
C. R.
,
Rivera
,
M.
,
Villarroel
,
F.
,
Guzman
,
J. I.
, and
Melín
,
P. E.
, 2019
, “
Finite-State Model Predictive Control With Integral Action Applied to a Single-Phase z–Source Inverter
,” IEEE J. Emerging Sel. Top. Power Electron.
,
7
(1
), pp. 228
–239
.10.1109/JESTPE.2018.287098543.
Tastemirov
,
A.
,
Lecchini-Visintini
,
A.
, and
Morales-Viviescas
,
R. M.
, 2017
, “
Complete Dynamic Model of the Twin Rotor MIMO System (TRMS) With Experimental Validation
,” Control Eng. Pract.
,
66
, pp. 89
–98
.10.1016/j.conengprac.2017.06.00944.
Prempain
,
E.
, and
Lecchini-Visintini
,
A.
, 2018
, “
Dynamic Analysis of a Twin Rotor MIMO System and Control Design
,” UKACC International Conference,
Sheffield, UK, Sept. 5–7, pp. 87
–92
.10.1109/CONT ROL.2018.851672745.
Mattingley
,
J.
,
Wang
,
Y.
, and
Boyd
,
S.
, 2010
, “
Code Generation for Receding Horizon Control
,” IEEE International Symposium on Computer-Aided Control System Design
, Yokohama, Japan, Sept. 8–10, pp. 985
–992
.10.1109/CACSD.2010.561266546.
Mattingley
,
J.
, and
Boyd
,
S.
, 2012
, “
CVXGEN: A Code Generator for Embedded Convex Optimization
,” Optim. Eng.
,
13
(1
), pp. 1
–27
.10.1007/s11081-011-9176-947.
Mattingley
,
J.
, and
Boyd
,
S.
, “
CVXGEN: Code Generation for Convex Optimization
,” accessed June 21, 2023, https://cvxgen.com48.
Bryson
,
A. E.
, and
Ho
,
Y. C.
, 1975
, Applied Optimal Control (Revised Printing)
,
Hemisphere
,
New York
.Copyright © 2023 by ASME
You do not currently have access to this content.
