control of high-risehigh-speed elevators

7/31/2019 Control of High-risehigh-speed Elevators

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Proceedings o f the American Control ConferencePhiladelphia, Pennsylvania June 1998

Control of high-risehigh-speed levatorsRandy Roberts

Otis Elevator CompanyFive Farm Springs

Farmington, CT 06034-2567Email: robertsr@engl otis.utc.com

ABSTRACTAn analytical framework for the development andevaluation of motion control system concepts for high-rise,high-speed elevators is presented in this paper. Thisproblem definition, which includes a discussion of typicalcontrol system performance requirements, plant modeldynamics and uncertainties, and control system robustnessrequirements, serves as a benchmark for the application andevaluation of advanced control approaches. Uniquefeatures of this problem include time varying dynamics,uncertain structural response, noncolocated control, sensorsuite selection, and separable command and disturbancerejection control system requirements.

1. IntroductionMaintaining or improving elevator performance asbuilding rises and car speeds increase will require new andadvanced control system technologies. Just the 450 meter(1480 ft.) Petronas Towers in Malaysia near completionwhich will make them the worlds tallest buildings, workhas begun on the 460 meter (1510 ft.) Shanghai WorldFinancial Center in China [l].This upward trend is likely tocontinue as a number of proposed plans have beenannounced for mega high-rise buildings to be constructed inthe next millennium with rises in excess of 50 0 meters, someeven topping 2000 meters 121. As might be expected, thereare a number of major engineering challenges associatedwith the design of such mega structures, includingconstruction methods, structural design, infrastructuredesign, and building transportation (elevator) systemdesign [3].

A number of issues arise in the design of effectivetransportation systems for tall buildings using conventionalroped elevator technology [4]. These design problems canbe grouped into three general areas; efficiency, passengercomfort, and safety.

Efficiency can be measured in many ways, butultimately must be related in some way to the following:

how quickly can people can be moved into and out ofwhat level of energy and power is required tohow much volume in the building is consumed by

a building or buildings,achieve these transitions, andthe candidate transportation system.

One way to address this efficiency issue is to increase themaximum speed of high-rise roped elevators from thecurrent top end of 750 meterslminute up to 1000meters/minute or higher in the future [5]. In addition, a

number of concepts have been proposed in which multipleelevator cabs can operate in the same hoistway usingtraditional roped elevator propulsion [6] or ropelesselevator propulsion (e.g., on car linear induction orsynchronous motors) [7].

Another clear goal and priority of these ultra high-riseelevator systems is that they create a comfortableenvironment for their passengers who after all areoccupants or visitors to these monumental landmarkbuildings. Three metrics which are commonly defined toassess passenger comfort in elevators are cab vertical andhorizontal vibration levels, noise, and ear comfort.Acceptable levels of vertical and lateral vibration levels inthese high speed elevators are very small and are typicallyexpressed in milliG target levels (e.g., 8-10milliGs).

The design of a control system to regulate the motion ofa roped elevator is made difficult due in part to the inherentnoncolocated control problem posed by this application.That is, there exists finite transmission delays in thepotentially very long hoistway ropes between the actuationsource (i.e., the drive motor at the top of the building) andthe elevator car which result in significant phase delayswhich must be considered in the control design.

The performance requirements for elevators are verystringent, in a large part due to their live cargo. Presentpositional vertical accuracy requirements for ropedelevators are typically in the range of 0.001% to 0.005% ofthe full range of motion in high-rise elevator applications(e.g., 6 millimeters over potential rises u p to 500 meters).Another complicating factor is the natural shift in the lowfrequency hoistway resonant modes to lower frequencies asthe rise increases, thus it becomes more difficult to achieve astable well damped response at the elevator car in responseto commanded positional changes.

Another consequence of increases in building rises isthe associated decrease in effective rope stiffness whichresults in a requirement for higher position system feedbackbandwidth to minimize cab to building sill gaps duringpassenger loading and unloading transients.

In this paper a framework will be developed for theanalytical assessment and development of advanced motioncontrol concepts for a hypothetical 500 meter rise ropedelevator system. This problem definition is similar to otherrobust control benchmark problems [8], but also includesthe following;

the developed problem is representative of a real worldapplication area with supplied models being validatedusing experimentally collected field measurements,

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time varying linear dynamics are included in the systemplant model to exercise various options for controlsystem design, and

the control problem is broadened to include sensorselection and definition.

2. Elevator Hoistway Dynamics ModelThe basic roped elevator dynamic system, illustrated inFigure 1, consists of four major inertial elements; the drive

sheave, elevator car, counterweight, and compensationsheave,

Car

+Figure 1:Elevator Physical Configuration

There are five major degrees-of-freedom (DOF) in thisconfiguration; rotation of the drive and compensationsheave, and translation of the car, counterweight, andcompensation sheave. Each of the major inertial elementsare connected together with rope segments of whose lengthsvary as the elevator car moves up and down the hoistway.

The control input is the motor torque applied at thedrive sheave and the fundamental controlled variable is thevertical position of the elevator cab.A model of this physical system is presented in Figure2.

Rope 1

k r lF,k r l $

Ropesegment

Rope 3

Q-Ll.

Mcwt

3-Rope 4

Khit* [miiso

x fU I 3U U

U U

Li

H

r

Figure 2 Elevator Dynamical ModelA 3 DOF model of the elevator car is assumed

representing the elevator frame, cab, and rope hitch. Theparameter values for this car model are fixed with theexception of the cab mass (Mcab) which is a variablequantity dependent on the number of elevator passengers.This relationship is given by:where Mcabo is the empty cab mass, Duty is the maximumallowable passenger load, and p is a value from 0-1representing the degree of loading.

Mcab = Mcabo + p*Duty

Another critical feature of this model is therepresentation of the structural dynamics of the hoistwayropes themselves using a lumped mass approximation tocapture the finite force transmission delays in each of thefour different rope segments. Each of these rope segment

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models represents the aggregrate response of what isactually a set of multiple (e.g..5-9) ropes.

The properties of the hoist ropes (i.e,, rope 1 and rope 2which connect the car and counterweight and which ride onthe drive sheave) are:e Mdr = rope density (masdun it length)e Kdr = rope stiffnesdunit length, ande Cdr = rope damping/unit length.

Similarly, properties of the compensation ropes (i.e.,rope 3 and rope 4 which are at the bottom of the car whichride on the compensation sheave) are:eee

Mcr = rope density (mas dun it length)Kcr = rope stiffne dun it length, andCcr = rope damping/unit length.The parameter values for any lumped rope section

model are determined by its rope type (i.e., hoist orcompensation) and length. The values for the lumpedsegment mass and stiffness parameters for these four ropesegments can be approximated as:

mr l =Mdr*L/(n+2)mr2 = Mdr*(H-L)/(n+2)mr3 = Mcr*(H-L)/(n+2)

mr4 = Mcr*L/(n+2)

krl = n*Kdr/Lkr2 = n*Kdr/(H-L)kr3 = n*Kcr/(H-L)kr4 = n*Kcr/L

where n=5 (i.e., a five dynamic lumped massapproximation) is used.

Not shown in Figure 2, but included in the dynamicmodel representation, are viscous friction dampers inparallel with each spring. For the lumped rope modelsthese terms are represented in a similar manner to thestiffness terms as:

cr l = n*Cdr/Lcr3= n*Ccr/(H-L)

cr2 = n*Cdr/(H-L)cr4 = n*Ccr/L

Relative damping values in parallel with cab isolationpads (Kiso) and rope hitch (Khit) are Cis0 and Chitrespectively. In addition, there are absolute viscous frictiondampers (i.e., connected to an inertial ground) for the drivesheave (Cds), compensation sheave rotation (Ccs) andtranslation (Cmm), counterweight (Ccwt), and elevator cab(Ccar) which are not shown in Figure 2.

Thus, the elevator hoistway dynamics can berepresented as a time varying linear state space model of theform:

d d d t = A(L,p)x+ B(L,p)uy = C(L,p)x + D(L,p)u

where p is the payload loading fraction and L is theinstantaneous vertical position of the elevator. In general, pis a fixed constant during elevator transitions and L is atime varying quantity. For design purposes one can definethe local linear hoistway dynamics given a floor position(Flr) by setting

L = Do + Dflr*Flrwhere Do is the nominal spacing at the bottom of thehoistway, Dflr is the floor to floor spacing, and Flr is the

floor landing (i.e., 1-135 in this fictitious 500 meterbuilding).

The input vector to the plant model are;u(1)= drive sheave motor torque (Tm), andu(2) = a disturbance force (Fd) which acts on theelevator cab.There are 27 DOFs in this model, thus the state vector(x) is a 54x1 vector. Theoretically any DOF associated

with the major system inertial elements is measurable andtherefore a candidate for control. However, the maincontrol measurements are the drive sheave velocity (Vds)and the car position (Pcar).

AOLID=MEASUREDI DASHED=MODEL

Too floor I

Vcar(s1Vdsfs)

I I I

0.5 1.0 2.0 4.0 8.0Frequency (Hz)

Figure 3: Model Validation ResultsThis dynamic model has been validated usingexperimentally derived transfer function data collected at a

high rise elevator installation. Figure 3 shows a plot of thetransfer function from Vds to the car velocity (dPcar/dt) asmeasured in three locations (top, midrise, and bottom) of ahigh rise elevator. In this case, p=0.5, and L was fixed atthree values. Small signal excitation commands wereinjected into the system and Vcar and Vds were measured.It can be seen that this analytical model closely replicatesthe measured response, capturing the downward shifting ofresonant modes as the car to drive sheave distanceincreases.

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3. Controller Performance Assessment MetriaThe performance objectives of the elevator vertical

motion control system which are considered here are:1. to move the elevator from one vertical position

(i.e., floor) to another in a controlled manner (i.e..minimize flight times subject to constraints), andto minimize the amount of car to sill dynamicdeflection during passenger loading andunloading transients.

2.

These requirements, in addition to others, will be explicitlydefined in this section.

Criteria 1) One floor transition resgonse requirements:The control system must move the cab position f rom verticalposition A to position B in such a manner as to ensureminimum cab vibration levels while landing in the shortesttime within certain guidelines for landing accuracy andovershoot. For purposes of this analytical assessment, atime-based command trajectory will be assumed to movethe car over a distance of 3.66 meters (12 ft.).

In this case, a two step process is used to create thecommand trajectory. First, a minimum time trajectory iscalculated subject to limits of dictated acceleration (1 m/s2)and jerk (1.5 m/s3). Next, this trajectory is passed througha 1* order low pass filter with a time constant of 0.5 seconds.Figure 4presents plots of the resultant acceleration, velocity,and distance to go as a function of time. It can be seen forthis constrained case the ideal flight time (i.e., the time towithin 6 mm of the destination) is 6.2 seconds.

(m/sec2) 0Acceleration

-11Distance

- 2 20 1 2 3 4 5 6 7 8Time (sec)

Figure 4 Dictated TrajectoriesThe measure of the one floor flight time response will

be the flight time, landing accuracy, and overshoot (i.e., the

maximum incremental displacement beyond the finalsettling position).

Criteria 2) Releveling transient resgonse requirements:A second function of the elevator motion control system isto maintain the cab to sill gap during periods of passengerloading and unloading. This is a disturbance rejectionproperty of the control system which can be modeled byinjecting a time depencfent disturbance force (Fd) into thesimulation.

For analytical assessments the assumed time history ofFd is as shown in Figure 5 below. This assumes that the rateof passenger loading is constant and corresponds to a 15second period to reach the maximum duty level (1800 kg inthis case). This profile is smoothed using a 1.0 second 1*order lag filter.

ForceFd (kN)

Time (sec)Figure 5: Assumed Disturbance Profile

It is desired to minimize the cab displacement duringthis transient. A guideline is that the maximum value ofthis displacement should be less than 6 mm.

Criteria 31 Control system robustness: A keyconsideration in designing the elevator vertical motioncontrol system is that it should be robust to variations inmodeled dynamics and unmodeled dynamics. It is wellknown that the stiffness of typical elevator hoistway ropescan vary considerably during its lifetime due to itsconstruction geometry and materials. Thus, expectedranges of parameter values (e.g., stiffness, damping, andmass) are defined over which any developed control systemmust achieve robust performance.

In particular, it is desired that the control performancegoals as listed above are achieved in the presence ofvariations in the following system model parameters:

+/- 20% variation iin the hoist and compensation ropestiffnesses (i.e., Kdr and Kcr values),+ /- 50% variation in all damping values (i.e., Cdr, Ccr,Ccwt, Ccar, Cds, Chit, Ciso, Ccs.Cmm). and+/ - 10% variation in the torque generator gain value(i.e., Tm = Kfac'Tc, where Tc is the output of the motioncontrol system and Kfac ranges from 0.9-1.1).

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4. ConclusionsThis paper has presented an analytical framework for

the design of advanced motion control concepts for high-rise, high-speed elevators. This formulation serves as abenchmark problem definition for the design andevaluation of advanced control design methodologies,including LMI-based control, model-based fuzzy control,nonlinear control, and robust control formulations.

The assessment of these control concepts involvesconsideration of the following issues:

What is the command tracking performance (i.e., flighttime, position accuracy, position overshoot, ridequality, etc.) and how i s it affected by anticipatedmodel variations?What is the releveling performance (Le,, maximumposition excursion and ride quality) and how is itaffected by anticipated model variations?What are the computational requirements for theproposed control concept?What sensors are used in the control concept and onwhat basis were they selected?Areas for future consideration, but not explicitly part ofHow can the control concept be tuned in the field? Thatis, what types of experimentally derived models arerequired to support the controller gain calculations?What is the optimal trajectory planning algorithm andhow should its design be coordinated with the motioncontrol system design?

this assessment, include:

The author is grateful to Young Man Cho of the UnitedTechnologies Research Center, and Mike Griffin, HelioTinone, and Julian Shull of Otis Elevator Company for theirsuppor t, including data collection and system identification,which lead to the validation results presented in Figure 3.

APPENDIXModel Parameter ValuesRepresentative values for the model parameters for the

elevator dynamic model are as follows:

Inertias:Mcabo = 3400 kgMdr = 17.4 kg/mMCS =2470 kgJcs =334kgm2Duty =I80 0 kg

Stiffnesses:Kdr = 1.74e8NKiso =6e6N/m

Damping:Cdr =7.2e5NsCis0 = 1.2e5 NsCcs = 44 kgm2/sCcwt =40Ns/mCmm =2e4Ns/m

Dimensions:Rs =0.6mH =500m

MfrmMcrMhitJdsP

KcrKhit

CUCdsCcarChit

Do sDflr

= 3410 kg=10.8 kg/m= 90 kg= 1622 kgm2= 0.5

= 9.63e7 N=1.3e6 N/m

= 2.8e5 Ns= 100 kgm2/s= 40 Ns/m= 1.3e3 Ns/ m

= 3.0 m= 3.66 m

References:[l] The 100 Tallest Buildings in the World, Council onTall Buildings and Urban Habitat, Schedule 14.2 Report,Oct. 16, 1996.[2] Fortune, J.W., Mega High-Rise Elevators, ElevatorWorld, July, 95.[3] Ishii, T., Elevatorsfor skyscrapers, EEE Spectrum, Sept.1994.[4] Shigeta, M., Inaba, H., and R. Okada, Super High-speedElevators, Elevator World, April 1995.[5]Barker, F. , Is2,000 Feet Per Minute Enough, March 97,Elevator World.161 Odyssey-TM, The Introduction, Elevator World Nov.96, p. 43.[7] Lacob, M., Elevators on the Move, Scientific America,[8] Wie, B. and Bernstein, D.S., A Benchmark Problem forRobust Control Design ,Proc. American Control Conference,San Diego, CA, May, 1990.

Oct. 1997, pp. 136-137.

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