Fault-Tolerant Sliding Mode Control Of A Quadrotor UAV .
International Journal of Mechanical Engineering and Robotics Research Vol. 9, No. 1, January 2020Fault-Tolerant Sliding Mode Control of aQuadrotor UAV with Delayed FeedbackSafi Ullah and Kamran IqbalUniversity of Arkansas at Little Rock, Little Rock, Arkansas, USAEmail: sxullah@ualr.edu, kxiqbal@ualr.eduFahad Mumtaz MalikCollege of Electrical and Mechanical Engineering, NUST, Islamabad, PakistanEmail: malikfahadmumtaz@ceme.nust.edu.pkAbstractβA quadrotor unmanned aerial vehicle (UAV)controller distributes the pitch, roll and yaw commands toindividual propellers. This paper explores fault-tolerantcontrol of a quadrotor UAV using delayed feedback andDivided State Feedback Control (DSFC). Initially, a SlidingMode Controller (SMC) for the quadrotor UAV is designedto obtain sustained performance in the presence of actuatorfaults. The SMC performance deteriorates considerably inthe presence of delayed sensory feedback from the UAV. ADSFC is then used to restore effectiveness of the devicecontroller. The proposed control structure deliversimproved stabilization, robustness and transient response inthe presence of actuator faults. Computer simulations arepresented to illustrate the effectiveness of our hybrid controlscheme. Some different techniques are implemented on alinearized model of quadrotor and a comparison of theobtained results has been presented [7]. In this paper,SMC has been picked as controller due to its robustnessto the model uncertainties, parametric vulnerabilities andexternal aggravations. This sliding mode controller iscapable of making the quadrotor reach and stay withinthe desired altitude with desired rotations.Fault Tolerant Control System (FTCS) is a controlframework with the capacity to endure faultsautomatically and proceed with its intended operation incase of a failure in some of its segments [8]. FTCSs areclassified into two major categories, i.e. Passive FTCSand Active FTCS. The Passive FTCSs can only handlepre-defined faults with the controller tuned to fixed gainswhereas in case of AFTC systems, the fault is detected,diagnosed, and estimated, and the controller isreconfigured online [5], [9], [10], [11]. The popularapproaches toward fault-tolerant control includes SMC[5], [12], [13], [14], Model predictive Control (MPC) [15]which also allow operation under fault free conditions. Alarge measure of existing exploration has tended to theFTCS for quadrotor UAVs but still there existsconsiderable room for improvement. Some of theseefforts addressing the fault tolerance issue include hybridswitching fault-tolerant control [12], Adaptive observersfor the magnitude estimation of complex and timevarying actuator faults [14], Terminal SMC for robustcontrol operations in unstructured environments [6], [16],and the non-linear SMC observer used as Fault Diagnosisand Identification (FDI) unit for the online detection andestimation of fault magnitudes [17]. The type of faultaddressed in this paper is the Loss of Effectiveness (LOE)in the thrust of actuators which is actually the mostcommon type of actuator faults. Passive FTC isimplemented for a pre-defined set of actuator faults.Divided state feedback (DSF) involves sensoryfeedback with time delays, and DSF control, whichentails control with feedback delays, is capable ofdelivering an improved stabilization and transientresponse [18]. It is worth noting that time delaysdependably exist in genuine control frameworks becauseof estimations by means of sensors, and so forth. TheIndex Termsβdivided state feedback control, Sliding ModeControl (SMC), actuator faults, quadrotor UAV, FaultTolerant Control (FTC), time delaysI.INTRODUCTIONUnmanned Aerial Vehicles (UAVs) aka drones havebecome popular in recent years for a variety ofapplications such as security, payload delivery, militaryand traffic surveillance, photography, wild-lifemonitoring, etc. It has also become a fascinating area ofresearch for control engineers due to the challengesinvolved. A quadrotor UAV has six degrees of freedom(6DOF) that represent three angular and threetranslational motions i.e. roll, pitch, and yaw, and x, y, z,respectively. Quadrotor consists of four propellers thatare mounted on the corners of an X-shaped frame. Theposition and orientation of the UAV in space is controlledby controlling the speed of the propellers. Since we havefour inputs controlling 6DOF, the UAV represents anunder actuated electromechanical system.Quadrotor UAV models have been used by numerousresearchers as a promising candidate plant for theexperimentation and testing of control algorithms [1].Diverse control techniques for the most part intended forUAVs are feedback linearization [2], [3], back-steppingcontrol [4], and siding mode control (SMC) [5], [6].Manuscript received November 22, 2018; revised July 22, 2019. 2020 Int. J. Mech. Eng. Rob. Resdoi: 10.18178/ijmerr.9.1.1-61
International Journal of Mechanical Engineering and Robotics Research Vol. 9, No. 1, January 2020control the rotational subsystem, and, combined with π1 ,form the control inputs for the translational subsystem.These inputs are defined as,history of βDelayed Controlβ is quite old and results havebeen obtained to accomplish execution for theframeworks comparable to conceivable [19]. Further,practical implementation of the control technologyinvariably involves time lags due to sensing,communication and processing times. These delays needto be appropriately addressed in the control design. Thehistory of the βDelayed Controlβ case is quite old andcontroller delays were used to advantage [19]. This andother investigations, e.g., [20], concluded that a systemwith or without process delays could be stabilized withsatisfactory performance by a controller with time delayprovided the time delay was kept bounded [18]. In thispaper, DSF control integrated with passive FTC isapplied to a quadrotor subject to its potential value indelivering an improved stabilization and transientresponse as compared to other conventional controltechniques.This paper is organized as follows. In section II, thenonlinear dynamical model, the rotor model, and thelinear state-space model of a quadrotor UAV arepresented. In section III, passive FTC based on SMC isdesigned in the presence of actuator faults. In section IV,DSF control is integrated with passive FTC and SMC andsimulation results are presented to show the viability ofour design. Finally, conclusions are stated in section V.II.π1 π(πΊ12 πΊ22 πΊ32 πΊ42 )π2 π(πΊ42 πΊ22 )π3 π(πΊ32 - πΊ12 )π4 π(πΊ22 πΊ42 πΊ32 πΊ12 )where,b thrust co-efficientd drag co-efficientπ πΊ2 πΊ4 πΊ1 πΊ3π Speed of rotation of each propellerB. Rotor ModelThe rotor model [1] consists of DC motor equations,given as:πππΏ π π π ππ πππ‘π½π πππ‘ ππ ππ(3)The dynamics of the DC-motor are approximated as:π½π πππ‘2ππ (π ) π - ππ (ππ /R) U(4)where π Angular Speed of motor, U Motor Input,ππ Motor Load, ππ Motor Torque, ππ Torque constant,R Motor Resistance, ππ Back emf constant, J MotorInertia.SYSTEM MODELA. Nonlinear Dynamic ModelC. State Space RepresentationThe state-space representation of the quadrotor UAVconsists of 12 states (six positions and six velocities,three each for translation and rotation). The statevariables x1, x3, and x5 represent the x, y, and altitudeposition while x7, x9, and x11 represent the roll, pitch,and yaw angles respectively.The corresponding nonlinear state-space representationis given as:Figure 1. Quad rotor UAVThe nonlinear dynamical model of the quadrotor UAV(see Fig. 1) is derived using Euler-Lagrange terminologyand is comprised of the following equations [1].π₯1Μ π₯2π·Μ πΜ πΉΜ (πΌπ¦ -πΌπ§ ) / πΌπ₯ (π½π /πΌπ₯ ) πΜ π (π2 /πΌπ₯ )π₯3Μ π₯4π₯2Μ (π1 /π)(cos π₯7 sin π₯9 cos π₯11 sin π₯7 sin π₯11 )π₯4Μ (π1 /π)(cos π₯7 sin π₯9 cos π₯11 sin π₯7 cos π₯11 )πΜ π·Μ πΉΜ (πΌπ§ -πΌπ₯ ) / πΌπ¦ (π½π /πΌπ¦ ) πΜ π (π3 /πΌπ¦ )πΜ πΜ π·Μ (πΌπ₯ -πΌπ¦ )/ πΌπ§ ) (1/πΌπ§ )π4π₯5Μ π₯6(1)π₯6Μ (π1 /π)(cos π₯7 cos π₯9 ) ππ1π₯Μ (cos Ξ¦ sin π cos π sin π· sin π) ( )(5)π₯7Μ π₯8ππ1π¦Μ (cos Ξ¦ sin π sin π sin π· cos π) ( )π1π₯8Μ [(π½π¦ π½π§ ) π₯10 π₯12 π½π ππ₯10 ππ2 ] ( )π½π₯π₯9Μ π₯10ππ§Μ g (cos π· cos π) ( 1 )π1π₯10Μ [(π½π§ π½π₯ ) π₯8 π₯12 π½π ππ₯8 ππ3 ] ( )π½π¦where Ξ¦, π, Ξ¨ and x, y, z are the roll, pitch, and yawangles, and the linear positions, respectively, with respectto the inertial frame of reference. The inputs π2 , π3 , π4 2020 Int. J. Mech. Eng. Rob. Res(2)π₯11Μ π₯122
International Journal of Mechanical Engineering and Robotics Research Vol. 9, No. 1, January 20201π₯12Μ [(π½π₯ π½π¦ ) π₯8 π₯10 πΆπ π4 ] ( )π4 π½π§III.ππ₯ FAULT-TOLERANT SLIDING MODE CONTROLππ¦ A. Sliding Mode ControlIn this section, an SMC to control the translational androtational motions of a quadrotor UAV is designed. Weconsider the nonlinear dynamic equation for the altitude,which is given as:π§Μ -g (cosΞ¦cosπ) π1 /mπ½π§πΆπ[-(π½π₯ -π½π¦ )πΜπ·Μ πΉπΜ ππΉ ππΉΜ πΎπΉ sat(S) ππ ππΉ ]ππ1ππ1[π₯πΜ ππ₯ ππ₯Μ πΎπ₯ sat(S) ππ ππ₯ ][π¦πΜ ππ¦ ππ¦Μ πΎπ¦ sat(S) ππ ππ¦ ]Once all the control efforts are designed, the desiredoutput of each actuator is obtained via the followingtransformation [5].(6)where π1 is the control input. We next define a slidingsurface βSβ such that the system tracks the desiredtrajectory, i.e. π§π (t) z (t).ππ§ ππ§Μ ππ§ ππ§ ππ ππ§(13)where βbβ and βdβ are the thrust and drag co-efficientrespectively.(7)where ππ§ π§π β z is the altitude error, and the integralterm is added to minimize the steady-state error and thefault effect.ππ§Μ ππ§Μ ππ§ ππ§Μ ππ ππ§B. Actuator Faults and Passive Fault Tolerant ControlSMC is a nonlinear robust controller which is capableof stabilizing the control of a quadrotor UAV in thepresence of external disturbances as far as the system isoperating under normal conditions. The question whicharises here is that what would happen if a fault occurs?Two of the most common faults that occur on these typesof nonlinear dynamical systems are the sensor faults andactuator faults. The type of fault addressed in this paper isthe Loss of Effectiveness (LOE) in the thrust of actuators,which is a common type of actuator fault. Such faultsmay occur due to actuator wear out, mainly the bearing,or the damage to a rotor in the case of collision.The fault can be modelled in the system as(8)The stability of the controller can be investigated viaLyapunov methods.In particular, choosing theLyapunov function as V 1/2(ππ§π ππ§ ) results in a negativedefinite time derivative (πΜ ππ§ ππ§Μ -π ππ§ ). Accordingly,the control effort π1 is selected as:π1 πcos(π·)cos(π)[g π§πΜ ππ§ ππ§Μ πΎπ§ sign(S) ππ ππ§ ] (9)In order to satisfy the reachability condition, i.e. toforce system trajectories to reach and stay on the slidingmanifold, S 0 in finite time ( ππ§ ππ§Μ -π ππ§ ), adiscontinuous term is added to π1 , where sign(S) isdefined as:1sign (S) { 0 1πππππππ 0π 0π 0πΉππ π π 22πππ π π ππππ π π π πHere i 1-4, while βbβ and βkβ are the thrust and dragcoefficients, respectively. The state-space model assumesthe following form:πΉπ πΉ diag [π1 ,π2 ,π3 ,π4 ] , 0 ππ 1In our work, the inputs are first decomposed intoindividual thrust forces and a fault is injected into them,which is then fed into the system model. The followingblock diagram (see Fig. 2) demonstrates the concept ofFTC strategy.(11)IV.π½ππDIVIDED STATE FEEDBACK CONTROLDSF Control is a novel control technique thatcomprises of control with feedback delays. Technically, itis the establishment of partitioned sampling that yields[-(π½π₯ -π½π₯ )π·Μ πΉΜ π½π π·Μ ππΜ ππ ππΜ πΎπ sat(S) ππ ππ ] 2020 Int. J. Mech. Eng. Rob. Res(16)whereπ2 π₯[-(π½π¦ -π½π§ )πΜπΉΜ π½π πΜ π·πΜ ππ· ππ·Μ πΎπ· sat(S) ππ ππ· ]π½π¦(15)Figure 2. Block DiagramIn the above, π represents a boundary layer around thesliding surface βSβ. The remaining control effortsdesigned on same lines are given asπ3 (14)(10)The main drawback of SMC is the chattering effectproduced by the discontinuous βsign(S)β term in thecontroller. In order to overcome this problem, we mayreplace the sign function with a saturation function.Under this modified control, the system is guaranteed toreach and stay on the manifold ππ§ 0. The same steps arethen followed to derive the other control efforts, i.e. π2 ,π3 , π4 and ππ₯ , ππ¦ , where ππ₯ and ππ¦ are the controlefforts required for x and y positions.π πππ(π)Sat(S) {(π/π )(12)3
International Journal of Mechanical Engineering and Robotics Research Vol. 9, No. 1, January 2020results. Table I above shows the range of time delaysincorporated in our design.The DSF Control problem can be viewed as anoptimality problem as investigation shows an initialimprovement, followed by deterioration of performancewith an increase in time delays. We have found theoptimum values of time delays for improved results. TheDSF control thus improves the stability and transientresponse of the system, by making use of delays in thefeedback path. The bounds on the values of the delayssatisfy the stability criteria [18].the proposed feedback [1]. The block diagram abovedepicts a general overview of DSF control, see Fig. 3. Letus consider a framework [18] with variable time delaysπ₯Μ (π‘) ππ 0 π΄π π₯(π‘ πππ (π‘) π΅π’(17)where π₯ π π , πππ (π‘) [0, π π ] , π 1, 2, . , π are thedelays present in the system. The parameters defined forstability criterion [18] areπ 2π Μ βπβ, π Μ ππ, πΏπΉ ππ 0βπ΄π β πβπ΅πΎβπ ππ 1 ππ 0βπ΄π π΄π β 2πβπ΅πΎβ ππ 1βπ΄π β πβπ΅πΎββπ΄0 β π 2 βπ΅πΎβ2B. Computer SimulationsWe present computer simulation results to illustrate theviability of our hybrid control design. Fig. 4 demonstratesthe trajectory comparisons when the system is required totrack a position of {10m, 10m} along the x and ydirections, respectively. The figure shows a comparisonbetween the results generated by applying a conventionalpassive fault-tolerant SMC and passive fault-tolerantSMC integrated with the DSF Control, see Fig. 4. Thesimulation results clearly demonstrate that the DSFcontrol integrated with passive fault-tolerant SMCdelivered an improved response as compared to the casewithout DSF control. The DSF control has its potentialincentive for speeding up the response of systems [18]and has outperformed the conventional passive faulttolerant sliding mode control. Fig. 5 shows the controlefforts required for the accomplishment of the task.(18)Figure 3. DSF control schemeA. Control LawThe DSFC law for (18) is defined as:π’(π‘) πΎ ππ 1 πΎπ (π‘)π₯(π‘ πππ (π‘))(19)The stability of the closed-loop system is determinedvia the following result [18].Corollary [18]: Given a deterministic delayed system(17), design the DSFC law as (19), if the upper headed Ο1for the time delays, with 0 π ( ) is sufficiently little2πto such an extent that π 0, where π 2πΏπΉ , and thelattice P is sure answer for the Riccati-Ito network [18],with πΉπ 0, π 1,2, . , π then the harmony x 0 (17) isglobally asymptotically stable in mean square.Time delays generally lead to oscillations, however,DSF control defines bounds on the state feedback delayssuch that the system delivers an improved stabilizationand transient state response [18].(a)(b)TABLE I. DSF CONTROL TIME DELAYSStatesx-positiony-positionAltitudeRoll anglePitch angleYaw anglex-position ratey-position rateAltitude rateRoll ratePitch rateYaw rateOptimal Delays rior Delays (sec) 0.25 0.3 0.1 0.045 0.045 0.005 0.01 0.01 0.01 0 0 0(c)(d)A detailed mathematical procedure for computation ofbounds on time delays is presented in [18], [19]. Sinceour system and control are nonlinear, we have determinedthe values of time delays on the basis of simulation 2020 Int. J. Mech. Eng. Rob. ResFigure 4. Comparison of DSF Control with Passive FTC based on SMC:(a) Roll Angle; (b) Pitch Angle; (c) X-Displacement; (d) YDisplacement4
International Journal of Mechanical Engineering and Robotics Research Vol. 9, No. 1, January 2020and paper revision. Kamran Iqbal: Research supervisionand paper revision.ACKNOWLEDGEMENTThe first author is very much thankful for the fundingsupport by UA little rock Graduate School, George W.Donaghey college of Engineering and InformationTechnology in form of research travel grant.(a)REFERENCES[1] S. Bouabdallah, "Design and control of quadrotors withapplication to autonomous flying," PhD Thesis, Swiss FederalInstitute of Technology, Lausanne (EPFL), 2007.[2] A. Benallegue, A. Mokhtari, and L. Fridman, "High order slidingmode observer for a quadrotor UAV," International Journal ofRoust and Nonlinear Control, vol. 18, no. 4-5, pp. 427-440, 10-25March 2008.(b)[3] H. Voos, "Non-linear control of a quadrotor micro-uav usingfeedback-linearization," in Proc. IEEE Internaton Conference onMechatronics, Malaga, Spain, April 2009.[4] S. Bouabdallah and S. Roland, "Back-stepping and sliding modecontrol techniques appliad to an indoor micro quadrotor," in Proc.IEEE International Conference on Robotics and Automation,Barcelona, Spain, 2005.[5] F. Sharifi, M. Mirzaei, B.W. Gordon, and Y. Zhang, "Fault tolerantcontrol of a quadrotor UAV using sliding mode control," in Proc.Conference on Control and Fault Tolerant Systems, 2010.(c)[6] S. T. Venkatarman and S. Gulati, "Control of nonlinear systemsusing terminal sliding mode control," in American ControlConference, 1992.[7] S. Bouabdallah, N. Andre, and S. Roland, "PID Vs LQ controltechniques applied to an indoor Micro Quadrotor," in IEEE/RSJInternational Conference on Intelligent Robots and Sytems,Sendai, Japan, 2004.(d)Figure 5. (a) Control Effort U1; (b) Control Effort U2; (c) ControlEffort U3; (d) Control Effort U4V.[8] Y. M. Zhang and J. Jiang, "Bibliographical review onreconfigurable fault-tolerant control systems," Annual Reviews inControl, vol. 32, no. 2, pp. 229-252, 2008.CONCLUSION[9] H. Khebbache, B. Sait and F. Yacef, "Robust stabilization of aquadrotor aerial vehicle in presence of sensor failures,"International Journal of Control, 2012.This paper considered the fault-tolerant control of anonlinear model of quadrotor UAV in the presence ofcontrol and/or sensory delays. An SMC provided goodtracking performance under actuator fault conditions. Inparticular, we implemented a passive FTC that wasdesigned for a pre-defined set of actuator faults. The FTCperformance was observed to deteriorate in the presenceof communication and sensory delays. Finally, a DSFcontrol integrated with passive Fault-Tolerant SMCdemonstrated improved stabilization, robustness andtransient response in computer simulations.[10] H. Khebbache, B. Sait, F. Yacef and Y. Soukkou, "Robuststabilization of a quadrotor aerial vehicle in presence of actuatorfaults," International Journal of Information Technology, Controland Automation, vol. 2, pp. 1-13, 2012.[11] T. Li, Y. Zhang and B. Gordo, "Fault tolerant control applied to aquadrotor unmanned helicopter," in Proc. ASME/IEEEInternational Conference on Mechatronic and Embedded Systemsand Applications, Washington, DC, USA, August, 2011.[12] A. R. Merheb and H. Noura, "Fault severity based integrated faulttolerant controller for quadrotor UAVs," in InternationalConference on Unmanned aircraft systems (ICUAS).[13] C. Zhaohui and H. Noura, "Composite fault tolerant control basedon fault estimation for quadrotor UAVs," in Proc. 8th IEEEConference on Industrial Electronics and Applications,Melbourne, VIC, Australia, June 2013.CONFLICT OF INTERESTThere is no conflict of interest from any author forpublishing this work. The authors declare that theresearch was conducted in the absence of any commercialor financial relationships that could be construed as apotential conflict of interest.[14] H. Yang, B. Jiang, and K. Zhang, "Direct self-repairing control ofthe quadrotor helicopter based on adaptive sliding mode controltechnique," in Proc. IEEE Chinese Guidance, Navigation andControl Conference, 2014.[15] B. Yu, Y. Zhang, I. Minchala and Y. Qu, "Fault tolerant controlwith linear quadratic and model predictive control techniquesagainst actuator faults in a quadrotor UAV," in Proc. Conferenceon Control and Fault
Diverse control techniques for the most part intended for UAVs are feedback linearization [2], [3], back-stepping control [4], and siding mode control (SMC) [5], [6]. Manuscript received November 22, 2018; revised July 22, 2019. Some different techniques are implemented on a linearized model of quadrotor and a comparison of the
INSTINCT 8 SLIDING DOORS INSTINCT 8 SLIDING DOORS 104 Prices include VAT All dimensions in mm 105 SLIDING DOORS INSTINCT 8 SLIDING DOORS Code Description Adjustment (mm) RRP INS04A0 Instinct 8 1000mm Sliding Door 950-990 676.00 INS04B0 Instinct 8 1100mm Sliding Door 1050-1090 676.00 INS04C0 Instinct 8 1200mm Sliding Door 1150-1190 676.00 INS04DH Instinct 8 1400mm Sliding Door 1350-1390 .
[39], a model predictive control-based nonlinear fault tolerant control was developed for air-breathing hypersonic vehicles. Fault detection and fault-tolerant control were studied for civil aircraft using a siding-mode-based scheme in [40]. With the 3-
Objective 5.2: Plan and implement VMware fault tolerance Identify VMware Fault Tolerance requirements Configure VMware Fault Tolerance networking Enable/Disable VMware Fault Tolerance on a virtual machine Test a Fault Tolerant configuration Determine use case for enabling VMware Fault Tolerance on a virtual machine
An anti-lock braking system control is a rather difficult problem due to its strongly nonlinear and uncertain characteristics. To overcome these difficulties, robust control methods should be employed such as a sliding mode control. The aim of this paper is to give a short overview of sliding mode control techniques implemented in the control .
Mounting the sliding crosscut table to your saw: Before continuing, make sure the sliding table top is locked to the sliding table assembly. If the sliding table top is not locked, pull out the sliding table lock knob on the bottom of the table assembly and rotate it 90 degrees, then release. Slowly slide
Door and Window Sliding Systems 3 Contents www.kawneer.co.uk Door and Window Sliding Systems Product Selector 4 AA 3720 Folding/Sliding Door 6 AA 3572 Lift/Slide Door 14 AA 3110 Horizontal Sliding Window 22 AA 3110HW Healthcare Window 28 AA 3610/AA 3610LS Vertical Sliding Windows 36 Supporting Your Projects 42
Designing Fault Resilient and Fault Tolerant Systems with InfiniBand Dhabaleswar K. (DK) Panda The Ohio State University E-ma
CDS G3 Fault List (Numerical Order) Fault codes may be classified as sticky or not sticky: Type of fault Method to clear Not sticky Clears immediately after the fault is resolved Sticky Requires a key cycle (off and on) after the fault is resolved to clear. CDS G3 Fault Tables 90-8M0086113 SEPTEMBER 2013 Page 2G-3
