ACTIVE SWAY CONTROL OF A GANTRY CRANE SYSTEM (SIMULATION USING LQR CONTROLLER) KHAIRUL AZMI BIN MOHD YUSOFF

Transcription

1 ACTIVE SWAY CONTROL OF A GANTRY CRANE SYSTEM (SIMULATION USING LQR CONTROLLER) KHAIRUL AZMI BIN MOHD YUSOFF Ths thess s submtted as partal fulfllment of the requrements for the award of the Bachelor of Electrcal Engneerng (Electroncs) Faculty of Electrcal & Electroncs Engneerng Unverst Malaysa Pahang NOVEMBER, 2010

2 All the trademark and copyrghts use heren are property of ther respectve owner. References of nformaton from other sources are quoted accordngly; otherwse the nformaton presented n ths report s solely work of the author. Sgnature : Author : KHAIRUL AZMI BIN MOHD YUSOFF Date : 21 OCTOBER 2010

3 v I hereby acknowledge that the scope and qualty of ths thess s qualfed for the award of the Bachelor Degree of Electrcal Engneerng (Electroncs) Sgnature : Name : MOHD ANWAR BIN ZAWAWI Date : 21 OCTOBER 2010

4 v ACKNOWLEDGEMENT Wth the name of Allah, The Most Lovng and The Most Compassonate In completng the thess, I had receves helps from many people. They have contrbuted towards my understandng and thoughts. In partcular, I wsh to express my sncere apprecaton to my supervsor, Mr. Mohd Anwar bn Zawaw, for encouragement, gudance and crtcs. Further thanks and extended to my famly, my beloved parents, Mohd Yusoff bn Senk and Wan Maram Wan Adam for ther advce and support at varous occasons. I would lke to gve my sncere apprecaton to all my frends and others especally Nk Mohd Arff bn Nk Abd Kadr and Wan Mohd Safuddn bn W. Zaman who have provded assstance at varous occasons. Wthout them I would not be here.

5 v ABSTRACT Ths project s about the development of Actve Sway Control of a Two- Dmensonal Gantry Crane (2D Gantry Crane) System usng Lnear Quadratc Regulator (LQR) controller. Ths project analyzes on how to reduce the sway angle of the rode when t s released from certan poston. Ths system s a 2D system because the rode s movement s only along the x and y axes. The 2D Gantry Crane system conssts of several elements such as the cart, rode, actuator, payload and controller. The movement of the cart wll cause the swayng moton of the rode because the speed of the cart s drectly proportonal wth the sway angle of the rode. If the speed of the cart s ncreased, the sway angle also ncreases. The swayng moton wll decrease the effcency of the crane system. In order to ncrease the effcency of the crane system, the crane wll need an effcent controller to reduce the sway angle. The rode of the gantry crane wll be controlled by usng LQR controller. LQR s derved by a set of lnear dfferental equaton and the cost s descrbed by a quadratc functonal. The man objectve of LQR controller s to obtan the best performance of dynamc system at the mnmum cost. Performance of the system focuses on the sway angle caused by the rode s movement and the Power Spectral Densty (PSD) of the sway angle response.

6 v ABSTRAK Projek n bertujuan menghaslkan kawalan ayunan dar kren gantr duadmens (2D kren gantr) menggunakan pengawal Lnear Quadratc Regulator (LQR). Projek n menganalss tentang bagamana mengurangkan sudut ayunan batang pemegang dan beban ketka dlepaskan dar kedudukan yang tertentu. Sstem n adalah sstem 2D kerana pergerakan batang beban adalah sepanjang paks x dan y sahaja. Sstem kren gantr 2D n terdr darpada beberapa elemen sepert batang, pemegang, trol dan beban. Gerakan trol akan menyebabkan gerakan ayunan batang pemegang kerana kelajuan trol adalah berkadar terus dengan sudut ayunan batang pemegang. Jka kelajuan trol bertambah, sudut ayunan juga menngkat. Gerakan ayunan akan mengurangkan kecekapan sstem kren. Bag menngkatkan kecekapan sstem kren, kren memerlukan pengawal yang cekap supaya dapat mengurangkan sudut ayunan. Batang pemegang kren akan dkawal menggunakan pengawal LQR. LQR dterbtkan oleh satu persamaan lnear dan kos dwakl oleh fungs kuadratk. Objektf utama pengawal LQR alah bag mengenal past prestas sstem dnamk pada kos yang mnma. Prestas sstem dtentukan berdasarkan sudut ayunan yang terhasl dsebabkan pergerakan batang pemegang kren dan Power Spectral Densty (PSD) respon sudut ayunan.

7 v TABLE OF CONTENTS CHAPTER TITLE PAGE TITLE PAGE DECLARATION DEDICATION ACKNOWLEGEMENT ABSTRACT ABSTRAK TABLE OF CONTENTS LIST OF FIGURES LIST OF ABBREVIATIONS LIST OF TABLES v v v v x x xv 1 INTRODUCTION 1.1 Type of Crane Gantry Crane Tower Crane Boom Crane Gantry Crane Gantry Crane Accdent Report Need For Study Advantages of Gantry Crane Dsadvantages of Gantry Crane Problems Statement 11

8 x 1.11 Objectves Scope of Project Thess Outlne 14 2 LITERATURE REVIEW 2.1 Gantry Crane Lnear Quadratc Regulator Basc Block Dagram of LQR System 19 3 METHODOLOGY 3.1 Gantry Crane Model Descrpton Lnearzaton of the System State Space Representaton of the System Lnear Quadratc Regulator (LQR) Control Scheme Block Dagram of LQR LQR Smulaton (MATLAB) Settng Parameters, Gans, Equatons and Gettng Results 33 4 RESULT AND DISCUSSION 4.1 Result of System Responses wth Varous Parameters and Gans Comparson of Responses Power Spectral Densty 69 5 CONCLUSION 5.1 Concluson System Lmtaton Future Work Recommendaton 84 REFERENCES 8

9 x LIST OF FIGURES FIGURE NO TITLE PAGE 1.1 Gantry Crane Rotary or Tower Crane Boom Crane Industral Gantry Crane Overhead crane Gantry Crane Gantry crane s accdent LQR block dagram Basc LQR system Project Flow Chart Gantry crane n 3-Dmensonal Model of Gantry Crane Basc system of LQR system LQR system D crane subsystems Parameters and equaton for x Parameters and equaton for theta LQR gan Result Wthout controller Response wth default parameter Gan= [ ] of response wth default parameters Response wth L=0.5m 41

10 x 4.5 Gan= [ ] of response wth L=0.5m Response wth L=1.5m Gan= [ ] of response wth L=1.5m Response wth m=2kg Gan= [ ] of response wth m=2kg Response wth m=3kg Gan= [ ] of response wth m=3kg Response wth =0.5 rad Gan= [ ] of response wth =0.5 rad Response wth =1.0 rad Gan= [ ] of response wth =1.0 rad Cart poston for L=0.5, 1.0 and 1.5 m Response of specfcaton of cart poston for L=0.5, 1.0 and 1.5 m Cart speed for L=0.5, 1.0 and 1.5 m Response of specfcaton of cart speed for L=0.5, 1.0 and 1.5 m Cart poston for m=1, 2, 3 kg Response of specfcaton of cart poston for m=1, 2, 3 kg Cart speed for m=1, 2, 3 kg Response of specfcaton of cart speed for m=1, 2, 3 kg Cart poston for =0.5, 1.0, 1.5 rad Response of specfcaton of cart poston for =0.5, 1.0, 1.5 rad Cart speed for =0.5, 1.0, 1.5 rad Response of specfcaton of cart speed for =0.5, 1.0, 1.5 rad Rse tme comparson for all poston data Settlng tme comparson for all poston data Rse tme comparson for all speed data Settlng tme comparson for all speed data 68

11 x 4.32 PSD response wth default parameters Attenuaton level of sway dfferent for default parameters PSD response wth L=0.5 m Attenuaton level of sway dfferent for L=0.5 m PSD response wth L=1.5 m Attenuaton level of sway dfferent for L=1.5 m PSD response wth m=2 kg Attenuaton level of sway dfferent for m=2 kg PSD response wth m=3 kg Attenuaton level of sway dfferent for m=3 kg PSD response wth =0.5 rad Attenuaton level of sway dfferent for =0.5 rad PSD response wth =1.0 rad Attenuaton level of sway dfferent for =1.0 rad 82

12 x LIST OF ABBREVIATIONS LQR PSD M m x x Lnear Quadratc Regulator Power Spectral Densty Mass of trolley (kg) Mass of payload (kg) Poston of trolley (m) Speed of trolley (m/s) x Acceleraton of trolley (m/s 2 ) l Length of rope Load swng angle (rad) Angular acceleraton of the load swng (rad/s 2 ) Intal angle of rope (rad) g Gravty acceleraton (m/s 2 )

13 xv LIST OF TABLES TABLE NO TITLE PAGE 3.1 Parameters for the system Default parameters Default parameters Parameters wth L=0.5 m Parameters wth L=1.5m Parameters wth m=2 kg Parameters wth m=3 kg Parameters wth =0.5 rad Parameters wth =1.0 rad Tr and Ts of cart poston for L=0.5, 1.0 and 1.5 m Tr and Ts of cart speed for L=0.5, 1.0 and 1.5 m Tr and Ts of cart poston for m=1, 2, 3 kg Tr and Ts of cart speed for m=1, 2, 3 kg Tr and Ts of cart poston for =0.5, 1.0, 1.5 rad Tr and Ts of cart speed for =0.5, 1.0, 1.5 rad Rse tme comparson for all poston data Settlng tme comparson for all poston data Rse tme comparson for all speed data Settlng tme comparson for all speed data Default parameters Parameters wth L=0.5 m Parameters wth L=1.5 m 73

14 xv 4.22 Parameters wth m=2 kg Parameters wth m=3 kg Parameters wth =0.5 rad Parameters wth =1.0 rad 81

15 1 CHAPTER 1 INTRODUCTION In our envronment, there s a necessty to transfer objects such as machne, cargo, mechancal components and equpments from one place to another, whether there are far or not. In the workplace, for example, at constructon or ndustral stes, ports, ralway yards and other smlar locatons, specal equpment s needed to transport the materals. These materals are usually heavy, large and hazardous, thus cannot be handlng by workers. In order to make the work easer, cranes have been used to lft, move, poston or place machnery, equpment and other large objects. [6] Cranes are wdely used for transportaton of heavy materal n factores, warehouse, shppng yards, buldng constructon and nuclear facltes. In order to lft heavy payloads n factores, n buldng constructon, on shps and elsewhere, cranes usually have very strong structures. Crane system tends to be hghly flexble n nature, generally respondng to commanded moton wth oscllatons of the payload and hook. The response of ths system to external dsturbances such as wnd s also oscllatory n nature. The swayng

16 2 phenomenon leads to not only lack n effcency of the crane, but also cause safety problem n a complcated workng envronment. Prevously, all cranes were manually operated. But manual operaton became dffcult when cranes became larger, faster and hgher. Due to ths, effcent controllers are appled nto the cranes system to guarantee fast turn over tme and to meet safety requrement [3]. 1.1 TYPE OF CRANE A crane conssts of a hostng mechansm such as hook and a support mechansm such as trolley grder. The hostng mechansm has two man functons. It deposts the payload at the target destnaton and avods the obstacle n the path by lftng and lowerng the payload. The functon of the support mechansm s to move the suspenson pont around the crane workspace [3]. There are many types of crane that been used for these purposes, such as tower crane, overhead crane, boom crane, gantry crane and others[6]. Crane can be classfed based on the degree of freedom whch the support mechansm offers the suspenson pont. There are 3 major types of crane system: (a) Gantry (overhead) crane (b) Rotary (tower) crane (c) Boom crane

17 3 1.2 GANTRY CRANE A gantry crane s composed of a trolley movng n a grder along a sngle axs. In some gantry crane, the grder s mounted on the second set of orthogonal ralngs, addng another degree of freedom of the horzontal plane. Gantry crane s commonly used n factores, Fgure 1.1[3]. Fgure 1.1: Gantry Crane 1.3 TOWER CRANE Tower crane s commonly used n constructon as shown n fgure 1.2. The grder rotates n the horzontal plane about a fxed vertcal axs. The trolley that holds the load can move n radal poston over the grder. The load s attached to the trolley by usng a set of cables.

18 4 Fgure 1.2: Rotary or Tower Crane 1.4 BOOM CRANE For the boom crane, a boom s attached to a rotatng base. The rotatonal movement of the base along wth the elevaton movement of the boom places the boom tp over any pont n the horzontal plane. The load hangs from the tp of the boom by a set of cables and pulleys. The radal and vertcal postons of the load can be changed by manpulatng the elevaton angle of the boom. Boom cranes are very common on shps and n the harbors. Fgure 1.3 shows the example of a boom crane.

19 5 Fgure 1.3: Boom Crane 1.5 GANTRY CRANE There are three man components n a gantry crane whch are trolley, brdge and gantry. Fgure 1.4 shows a typcal gantry crane normally avalable at ports. Trolley wth a movable or fxed hostng mechansm s the load lftng component. It moves on and parallel to a brdge whch s rgdly affxed to a supportng structure called gantry. The gantry extends downward from the brdge to the ground where t can be moblzed on wheels or set of tracks. The moton of the gantry on the ground, the trolley on the brdge and the hostng of the payload provde the 3 degrees of freedom of the payload.

20 6 Fgure 1.4: Industral Gantry Crane Ths type of system tends to be hghly flexble n nature, generally respondng to commanded moton wth oscllatons of the payload and hook. The response of these systems to external dsturbances, such as wnd, s also oscllatory n nature. The swayng phenomenon ntroduces not only less n effcency of the crane, but also cause safety problem n the complcated workng envronment. Gantry crane s smlar to an overhead crane, except that the brdge for carryng the trolley or trolleys s rgdly supported on two or more legs runnng on fxed rals or other runway. To mplement the operaton, the crane operator wll seat nsde the cart, and move the cart wth the load hanged wth t, so that the load can acheve the desred locaton. A real crane may allow a cart movement of 80 to 90 meters [8], regardng on the desred load locaton. Fgure 1.5 and Fgure 1.6 show the llustraton of overhead crane and gantry crane respectvely.

21 7 Fgure 1.5: Overhead crane Fgure 1.6: Gantry Crane 1.6 GANTRY CRANE ACCIDENT REPORT For a crane operator, an experence causng by a crane s accdents can be frghtenng them. There are many cases and ncdent regardng on the crane s accdents. For example, n Aprl 1993, the crane becomes unbalanced durng two separate ncdents at DOE stes n Unted States of Amerca, whch s n Hanford Ste and Bryan Mound Ste. The frst ncdent occurred n 28th aprl 1993, where a crane becomes unbalanced whle the boom was beng lowered. The second ncdent occurred 2 days later, on 30th

22 8 Aprl 1993, whch whle loadng the load, the weght of the load caused the crane to tp forward [1]. From these ncdents, gudelnes have been suggested n usng the cranes. Some of the gudelnes are: () the weght of load must be checked. () crane operatons should be supervsed by qualfed personnel. () crane operators must be famlar wth ther equpment. (v) crane operators must be traned and qualfed to operate ther equpment. Although the gudelnes have been sketched n order to prevent the accdent, the other factors also must be consdered so that the probablty of accdents occurs s small or reduced at an acceptable value. There are many factors that have to be consdered such as the brakng systems, hydraulc and pneumatc components, electrcal equpment, operatonal ads, operatng mechansms, lftng devces, determnng load weght, recognzng mmedate and potental hazards, control systems and others. In term of control systems, the mportant ssue s how to control the load swng. Ths s mportant n order to have a faster operaton whle mantanng the safety. In 14th January 2004 at approxmately 1300 hours, a slng of dunnage, a cargo spreader and pulley frame that were attached to the No. 2 after gantry crane on Tasman Independence fell from ther suspended poston onto the quay. There was damage to the crane, cargo gear equpment and the quay. Fgure 1.7 shows pctures about the accdent.

23 9 Fgure 1.7: Gantry crane s accdent 1.7 NEED FOR THE STUDY From the prevous works, t seems that most researchers have gven a lot of efforts n developng a control algorthms and desgnng controllers that can be used and realzed n nature. Ths ncludes the study related on how to reduce the vbraton, especally n crane, where the controllers that been desgned are mostly to control the load swng. Snce ths s relatvely smple and well defned problem n dynamcs and control, t s surprsng that, t has not been solved exactly, where an exact soluton s here understood to be a control strategy that guarantees complete success n a fnte tme. Most of the crane controllers that have been developed untl now have been far from satsfactory. Once tested n actual operaton, there found to be neffectve and thus were left unused. Ths may due to the standard control feedback strateges that are not well suted to ths problem. Therefore, the problem of controller synthess for a crane s stll under consderaton.

24 10 Regardng on ths matter, n ths study, t seems nterestng f multple pont of vew can be taken n modelng the crane. For ths purpose, gantry crane has been chosen n order to acheve the am. Ths wll nvolves n determnng the relaton between the cart mass, load s mass and the load swng, n order to lookng after the effect of the cart and load s mass to the load oscllaton. Because the operaton of the gantry crane s related wth the movement of the cart and load, the effect that cause a vbraton wll be, whether from the acceleraton that been appled at the cart, or the load and cart s nerta that been exsts because the movement of these objects. 1.8 ADVANTAGES OF GANTRY CRANE There are several advantages of a gantry crane such as: () () () It has mechancal advantage to move loads beyond the normal capablty of a human It can be used both to lft and lower materals and to move them regardng to the type of crane It provdes effectve way to transfer load (faster and easer)