Sliding Mode Controllers and Sliding Mode Control for ... · PDF fileSliding Mode Controllers and Sliding Mode Control for ... multi-input nonlinear uncertain systems, ... Simplexmethods

Osaka University

June 7, 2017

Sliding Mode Controllers and Sliding Mode Control for

Multi-input Nonlinear Uncertain Systems

Elisabetta Punta

CNR-IEIIT, Italy

Outline

Osaka University, June 7, 2017

Main Concepts of Sliding Mode

First Order Sliding Mode

Second Order Sliding Mode

Multi-input First Order Sliding Mode

Component-Wise Sliding Mode

Simplex-Based Sliding Mode

Research Results and Applications

2

Sliding Surface

Uncertain Nonlinear Systems

Discontinuous Control

Sliding Mode: a Simple Example


perturbation

control

sliding motion

The right-hand side is discontinuous,Finite time convergence toDifferential inclusion:

3

Sliding Mode: a Second Simple Example


perturbation

control

sliding motion

The right-hand side is discontinuous,Finite time convergence to

4

Osaka University, June 7, 2017 5


Filippov's Solution of an ODE with Discontinuous r.h.s. (Filippov, 1960)


Filippov’s Solutions

Filippov's definition of solution, 1960


A sliding motion exists if the projections of f + and f – on grad(s) haveopposite sign.

The sliding motion on

The sliding surface

defines the equivalent dynamics

7




Filippov’s SolutionsDiscontinuous Control

Sliding Surface

Chattering PhenomenonEquivalent Control (Utkin, 1972)

8

Sliding Surface




Sliding Surface

Finite Time Convergence to 𝜎 = 0

9

The sliding surface defines the desired system’s dynamics.The sliding mode control objective is to reach in finite time. Once on the control must keep the trajectories sliding on thesurface: sliding mode.

Equivalent Control (Utkin, 1972)



Discontinuous ControlSliding Surface

10

To find the value of the control on the sliding surface :

If is non singular , then the Equivalent Control is defined as:

The sliding mode dynamics:

Equivalent Control (Utkin, 1972)

Problem Formulation


Uncertain Systems

Design such that and :

with bounded uncertainty (modeling errors and external perturbations)

Control Problem

Sliding Surface



Invariance of Sliding Mode (Drazenovic, 1969)


Matched Perturbations

First Order Sliding Mode(Emelyanov, 1967), (Utkin, 1971)


are the states. is the control.

14

Uncertain Systems

Sliding Surface


First Order Sliding Mode(Precision)



15

Uncertain Systems

Sliding Surface




Second Order Sliding ModeTwisting Algorithm (Emelyanov et al., 1986)



17

Uncertain Systems

Sliding Surface


Second Order Sliding ModeTwisting Algorithm (Precision)



18

Uncertain Systems

Sliding Surface


Comparison First vs Second Order Sliding Mode(Twisting Algorithm)


Uncertain SystemsSliding Surface


Second Order Sliding ModeSuper Twisting Algorithm (Levant, 1993)



Lipschitz Condition

20

Uncertain Systems

Sliding Surface

Continuous Control

Second Order Sliding ModeSuper Twisting Algorithm (Precision)



21

Uncertain Systems

Sliding Surface

Continuous Control

Comparison First vs Second Order Sliding Mode(Twisting and Super Twisting Algorithms)


Comparison First vs Second Order Sliding Mode(Twisting and Super Twisting Algorithms)


Second Order Sliding ModeSub-Optimal Algorithm (Bartolini et al., 1997)



24

Uncertain Systems

Sliding Surface



Multi-Input First Order Sliding Mode

Multi-Input First Order Sliding Mode(Component-Wise and Simplex-Based)


26

Uncertain Systems

Sliding Surface

Component-WiseDiscontinuous Control

Simplex-BasedDiscontinuous Control

is non singular

Multi-Input First Order Sliding Mode(Convergence Conditions)


27

Uncertain Systems

Sliding Surface

Lyapunov Function Candidate

Asymptotic Convergence Finite Time Convergence

Simplex of Vectors


Multi-Input Sliding Mode Control: Switching Logics


Component-WiseSwitching Logic

Simplex-BasedSwitching Logic

29


Research Activity on Sliding Mode: Results, Projects and Publications

Research Activity on Sliding Mode: Results, Projects and Publications


2017 Sliding Mode

Second Order Sliding ModeSimplex Sliding Mode

ApproximabilityNonlinear Observers

Chattering ReductionMechanical Systems

Publications

Projects

Applications

years

Cooperative Control for Energy Management SystemsJoint International Lab COOPS


Principal Investigators Roberto TempoCNR-IEIIT, Italy

Yasumasa FujisakiOsaka University, Japan

Italian Research UnitE. Punta, CNR-IEIITC. Ravazzi, CNR-IEIITE. Capello, Politecnico di TorinoG. Como, Politecnico di TorinoP. Frasca, CNRS GrenobleP. Bolzern, Politecnico di MilanoP. Colaneri, Politecnico di MilanoR. Scattolini, Politecnico di Milano

Novel Tools and Algorithms

Computational Efficiency

Robustness

Heterogeneous Devices

Reliability

National Research Council of Italy &Japan Science and Technology Agency

(2015-17)

Fabrizio DabbeneCNR-IEIIT, Italy

Sliding Mode Control for Wind Energy Conversion Optimization


Aerospace Applications(E. Capello, F. Dabbene, G. Guglieri, E. Punta, R. Tempo)


[1] E. Capello, F. Dabbene, G. Guglieri, E. Punta, R. Tempo, “Rendez-Vous and Docking Position Trackingvia Sliding Mode Control,” American Control Conference-ACC 2015, Chicago, IL, USA, July 1–3, 2015.

[2] E. Capello, F. Dabbene, G. Guglieri, E. Punta, R. Tempo, “Rendez-Vous and Docking Maneuvers viaSliding Mode Controllers,” Journal of Guidance, Control, and Dynamics, vol. 40, no. 6, 2017.

Rendez-Vous and Docking Maneuvers via Sliding Mode Controllers

Fault Detection and Monitoring via Sliding Mode Techniques

Bilateral Project – CNR (Italy) and CoNaCyT (Mexico)


Principal Investigators Elisabetta PuntaCNR-IEIIT, Turin, Italy

Leonid FridmanUNAM, Mexico City

Fault Detection and Isolation Novel Tools and Algorithms

Second Order Sliding Mode Sliding Mode Differentiators

Nonlinear Observers

National Research Council of Italy &National Council of Science and Technology of Mexico (2013-15)

[1] G. Bartolini, A. Estrada, E. Punta, “Output regulation of some classes of SISO non-minimum phase non-affine systems,” the 52nd IEEEConference on Decision and Control - CDC 2013, Florence, Italy, December 10-13, 2013.[2] A. Ferreira de Loza, E. Punta, L. Fridman, G. Bartolini, S. Delprat, “Nested backward compensation of unmatched perturbations viaHOSM observation,” Journal of the Franklin Institute, vol. 351, no. 5, pp. 2397–2410, 2014.[3] H. Rios, E. Punta, L. Fridman, “Fault detection for nonlinear non-affine systems via sliding-mode output-feedback and HOSMdifferentiator,” the 13th IEEE International Workshop on Variable Structure Systems - VSS 2014, Nantes, France, June 29-July 2, 2014.[4] H. Rios, E. Punta, L. Fridman, "Fault Detection and Isolation for Nonlinear Non-Affine Uncertain Systems via Sliding-Mode Techniques,"International Journal of Control, submitted, 2015.[5] G. Bartolini, A. Estrada, E. Punta, “Adaptive tracking of sinusoids with unknown frequencies for some classes of SISO non-minimumphase systems,” International Journal of Adaptive Control and Signal Processing, submitted, 2015.[6] G. Bartolini, A. Estrada, E. Punta, “Observation and output adaptive tracking for a class of nonlinear nonminimum phase systems,”International Journal of Control, submitted, 2015.

Simplex Sliding Mode Methods(G. Bartolini, E. Punta, T. Zolezzi)


Multi-Input Nonlinear Systems Mono-directional InputsSimplex of Vectors

[1] G. Bartolini, E. Punta, “Multi-input sliding mode control of nonlinear uncertain non-affine systems withmono-directional actuation,” IEEE Transactions on Automatic Control, vol. 60, no. 2, pp. 393–403, 2015.[2] G. Bartolini, E. Punta, T. Zolezzi, “Simplex sliding mode control of multi-input systems with chatteringreduction and mono-directional actuators,” Automatica, vol. 47, no. 11, pp. 2433–2437, 2011.[3] G. Bartolini, E. Punta, T. Zolezzi, “Simplex sliding mode methods for the chattering reduction control ofmulti-input nonlinear uncertain systems,” Automatica, vol. 45, no. 8, pp. 1923–1928, 2009.[4] G. Bartolini, E. Punta, T. Zolezzi, “Simplex methods for nonlinear uncertain sliding mode control,” IEEETransactions on Automatic Control, vol. 49, no. 6, pp. 922–933, 2004.[5] G. Bartolini, F. Parodi, E. Punta, T. Zolezzi, “On sliding mode control of mechanical systems,” ComptesRendus de l’Académie des Sciences - Série IIb - Mécanique, vol. 329, no. 12, pp. 835–842, 2001.[6] G. Bartolini, M. Coccoli, E. Punta, “Simplex Based Sliding Mode Control of an Underwater Gripper,”ASME Journal of Dynamic Systems, Measurement and Control, vol. 122, no. 4, pp. 604–610, 2000.

Sliding Mode Output-Feedback(G. Bartolini, E. Punta)


Multi-Input Multi-Output Nonlinear Systems Nonlinear Observers

[1] G. Bartolini, E. Punta, “Sliding mode output-feedback stabilization of uncertain nonlinear nonaffinesystems,” Automatica, vol. 48, no. 12, pp. 3106–3113, 2012.[2] G. Bartolini, E. Punta, “Reduced-Order Observer in the Sliding Mode Control of Nonlinear Non-AffineSystems,” IEEE Transactions on Automatic Control, vol. 55, no. 10, pp. 2368–2373, 2010.[3] G. Bartolini, E. Punta, “Reduced order observers for the sliding mode control of mechanical systems withelastic joints,” International Journal of Control, vol. 83, no. 7, pp. 1364–1373, 2010.[4] E. Punta, “Observers with Discrete-Time Measurements in the Sliding Mode Output- FeedbackStabilization of Nonlinear Systems (Invited Chapter),” B. Bandyopadhyay, S. Janardhanan, S. Spurgeon, Eds.,in Advances in Sliding Mode Control. Concept, Theory and Implementation. Springer Verlag, 2013.

Multi-Input Sliding Mode Control with Uncertain Control Matrix(G. Bartolini, E. Punta)


Multi-Input Multi-Output Nonlinear Systems

Integral Sliding Mode Control

[1] G. Bartolini, E. Punta, T. Zolezzi, “Multi-input sliding mode control of nonlinear uncertain affine systems,”International Journal of Control, vol. 84, no. 5, pp. 867–875, 2011.[2] G. Bartolini, E. Punta, “Integral Sliding Mode Control of Multi-input Nonlinear Uncertain Non-affineSystems (Invited Chapter),” Xinghuo Yu, Mehmet Onder Efe, Eds., in Recent Advances in Sliding Modes:From Control to Intelligent Mechatronics. Springer Verlag, 2015.

Uncertain Control Matrix

Mechanical Systems(G. Bartolini, M. Coccoli, A. Ferrara, A. Pisano, E. Punta, E. Usai, T. Zolezzi)


Water-Jet Systems Underwater Gripper BipedGantry Crane[1] G. Bartolini, E. Punta, “Reduced order observers for the sliding mode control of mechanical systems with elastic joints,” InternationalJournal of Control, vol. 83, no. 7, pp. 1364–1373, 2010.[2] G. Bartolini, N. Orani, A. Pisano, E. Punta, E. Usai, “A combined first-/second-order sliding-mode technique in the control of a jet-propelledvehicle,” International Journal of Robust and Nonlinear Control, vol. 18, no. 4–5, pp. 570–585, 2008.[3] G. Bartolini, A. Pisano, E. Punta, E. Usai, “A survey of applications of second-order sliding mode control to mechanical systems,”International Journal of Control, vol. 76, no. 9–10, pp. 875–892, 2003.[4] G. Bartolini, F. Parodi, E. Punta, T. Zolezzi, “On sliding mode control of mechanical systems,” Comptes Rendus de l’Académie des Sciences- Série IIb - Mécanique, vol. 329, no. 12, pp. 835–842, 2001.[5] G. Bartolini, M. Coccoli, E. Punta, “Simplex Based Sliding Mode Control of an Underwater Gripper,” ASME Journal of Dynamic Systems,Measurement and Control, vol. 122, no. 4, pp. 604–610, 2000.[6] G. Bartolini, E. Punta, “Chattering elimination with second order sliding modes robust to Coulomb friction,” ASME Journal of DynamicSystems, Measurement and Control, vol. 122, no. 4, pp. 679–686, 2000.[7] G. Bartolini, A. Ferrara, E. Punta, “Multi-input second-order sliding-mode hybrid control of constrained manipulators,” Dynamics andControl, vol. 10, no. 3, pp. 277–296, 2000.[8] G. Bartolini, A. Ferrara, E. Punta, E. Usai, “Chattering elimination in the hybrid control of constrained manipulators via first/second ordersliding mode control,” Dynamics and Control, vol. 9, no. 2, pp. 99–124, 1999.

Water-Jet Propulsion System


variable-area nozzles spear valves directly-coupled linear electric motors

Water-Jet Actuated

Italian Patent: Dynamic Positioning of Objects

Gantry Crane Model


dimensions: 1.4 x 1 x 1.2 m (LxWxH) hoisting capability: 2kg hoisting speed: 0.15 m/s trolley speed: 0.1 m/s

Dexterous Underwater Gripper(AMADEUS 1-2, EU-Mast II-III, 1994-96, 1997-99)


Direct-Electric-Drive Hydraulic Actuation System Bellows Cardan (universal) joints Linear electric motors (voice coil type) Position sensors

ElectrohydraulicActuation

Dexterity

Pressure Compensated

Biped Robot (PFR Robotic Project -CNR, 1993-94)


8 DOF (3 rotational, 5 linear) walk speed up to 0.15 m/s (flat surface) climb step up to 0.15 m high change direction of motion

BipedRobot

Approximability for Sliding Mode Systems(G. Bartolini, E. Punta, T. Zolezzi)


Approximability Properties Second Order Sliding Mode

[1] G. Bartolini, E. Punta, T. Zolezzi, “Approximability Properties for Second-Order Sliding Mode ControlSystems,” IEEE Transactions on Automatic Control, vol. 52, no. 10, pp. 1813–1825, 2007.


Conclusions

Conclusions





Multi-input First Order Sliding Mode

Component-Wise Sliding Mode

Simplex-Based Sliding Mode

Research Results and Applications

Documents

Sliding Mode Controllers and Sliding Mode Control for ... · PDF fileSliding Mode Controllers and Sliding Mode Control for ... multi-input nonlinear uncertain systems, ... Simplexmethods