ball and beam, system. need to be modelled in matlab
1 CONTROL STUDIO A Project Description 1. Gantry crane Why gantry crane systems? A gantry crane is a crane mounted on a moving gantry to allow horizontal movement along an axis. Gantry cranes have a wide variety of applications in many industrial and construction settings as shown in figure 1.1. Smaller cranes are often mounted in factories and industrial complexes to allow movement of heavy loads such as bulk raw material and waste or used on assembly lines of large machinery. These cranes tend to be mounted on walls. On a larger scale, gantry cranes are used for maritime work; the overhead nature allows the crane to be mounted over a channel to allow ships to pass beneath it and facilitate easy loading and unloading heavy cargo without needing the large amount of space and clearance for traditional boom cranes. As the load is suspended from the gantry, it acts as a pendulum upon application of external forces such as the motion of the gantry or a disturbance such as wind and impact. This necessitates a method to stabilise the load to minimise the effect of disturbances upon the load. Side-view of Super-PostPanamax portainer crane at the APM Terminal in the Port of Rotterdam A ZPMC gantry crane used for construction of the British aircraft carrier HMS Queen Elizabeth Figure 1.1: Some applications of gantry cranes 1 1 Source: https://en.wikipedia.org/wiki/Gantry_crane 2 Control objectives The goal of this project is to develop a control scheme for a controllable Gantry Crane consisting of a track, trolley and hoist along with control interface as shown in figure 1.2. The controller must minimise the effect of disturbance upon the pendulum by moving the trolley to negate the movement of the suspended mass. Figure 1.2: The gantry crane Control requirements • Overshoot < 15%="" •="" settling="" time="">< 5="" s="" •="" steady="" state="" accuracy="">< 10%="" •="" swing="" angle="">< 150="" •="" test="" three="" types="" of="" controllers="" 2.="" ball="" and="" beam="" why="" ball="" and="" beam="" systems?="" most="" control="" problems="" that="" we="" meet="" in="" practical="" world="" are="" straightforward="" to="" control.="" for="" a="" fixed="" input="" signal,="" the="" output="" stays="" more="" or="" less="" constant.="" an="" important="" set="" of="" systems="" however="" are,="" either="" by="" design="" or="" nature,="" unstable="" and="" feedback="" control="" is="" essential="" to="" make="" them="" operate="" safely.="" many="" modern="" industrial="" processes="" and="" technological="" systems="" are="" intrinsically="" unstable="" could="" be="" used="" without="" stabilizing="" feedback="" control.="" 3="" figure="" 2.1:="" aircraft="" roll="" control="" is="" a="" key="" real-world="" application="" of="" the="" ball="" and="" beam="" experiment="" important="" practical="" examples="" of="" unstable="" systems="" are:="" 1.="" in="" the="" chemical="" process="" industries="" -="" the="" control="" of="" exo-thermic="" chemical="" reactions.="" if="" a="" chemical="" reaction="" generates="" heat="" and="" yet="" the="" reaction="" gets="" faster="" as="" temperature="" increases,="" then="" control="" must="" be="" used="" to="" stabilise="" the="" temperature="" of="" the="" chemical="" reaction="" to="" avoid="" a="" ‘run-away’="" reaction.="" exothermic="" reactions="" are="" used="" to="" produce="" many="" everyday="" chemical="" products="" –="" without="" feedback="" control="" these="" products="" would="" not="" be="" available="" to="" us.="" 2.="" in="" power="" generation="" –="" the="" position="" control="" of="" the="" plasma="" in="" the="" joint="" european="" torus="" (jet).="" the="" object="" here="" is="" to="" control="" the="" vertical="" position="" of="" a="" plasma="" ring="" inside="" a="" hollow="" donut-="" shaped="" metal="" container.="" the="" control="" is="" by="" using="" magnetic="" fields="" applied="" through="" the="" donut="" and="" the="" plasma="" moves="" vertically="" in="" an="" unstable="" manner="" in="" response="" to="" the="" control="" fields.="" to="" understand="" the="" problem,="" imagine="" pressing="" a="" wet="" ball="" of="" soap="" in="" between="" the="" flat="" of="" your="" (slippery)="" hands.="" as="" you="" increase="" the="" pressure="" on="" the="" soap="" so="" it="" will="" slip="" out="" faster="" when="" you="" alter="" the="" relative="" angles="" of="" your="" hands,="" (it’s="" the="" same="" problem="" trying="" to="" hold="" a="" hamster).="" 3.="" in="" aerospace="" –="" the="" control="" of="" a="" rocket="" or="" aircraft="" during="" vertical="" take-off.="" the="" angle="" of="" thruster="" jets="" or="" diverters="" must="" be="" continually="" controlled="" to="" prevent="" the="" rocket="" tumbling="" or="" the="" aircraft="" tipping.="" without="" feedback="" control="" to="" stabilise="" the="" movement,="" there="" would="" be="" no="" space="" rockets="" and="" the="" famous="" hawker="" harrier="" ‘jump-jet’="" would="" have="" remained="" a="" dream="" on="" the="" desks="" of="" sir="" sydney="" camm="" and="" his="" engineers="" at="" the="" hawker="" aircraft="" company.="" the="" control="" of="" unstable="" systems="" is="" critically="" important="" to="" many="" of="" the="" most="" difficult="" control="" problems="" and="" must="" be="" studied="" in="" the="" laboratory.="" the="" problem="" is="" that="" real="" unstable="" systems="" are="" usually="" dangerous="" and="" cannot="" be="" brought="" into="" the="" laboratory.="" the="" ball="" and="" beam="" system="" 4="" was="" developed="" to="" resolve="" this="" paradox.="" it="" is="" a="" simple,="" safe="" mechanism="" and="" yet="" it="" has="" the="" important="" dynamic="" features="" of="" an="" unstable="" system.="" 2="" control="" objectives="" the="" ball="" and="" beam="" module="" consists="" of="" a="" steel="" rod="" in="" parallel="" with="" a="" nickel-chromium,="" wire-wound="" resistor="" forming="" the="" track="" on="" which="" the="" metal="" ball="" is="" free="" to="" roll.="" the="" track="" is="" effectively="" a="" potentiometer,="" outputting="" a="" voltage="" that’s="" proportional="" to="" the="" position="" of="" the="" ball="" (figure="" 2.2).="" the="" control="" job="" is="" to="" automatically="" regulate="" the="" position="" of="" the="" ball="" on="" the="" beam="" by="" changing="" the="" angle="" of="" the="" beam.="" this="" is="" an="" interesting="" control="" task="" because="" the="" ball="" does="" not="" stay="" in="" one="" place="" on="" the="" beam="" but="" moves="" with="" an="" acceleration="" that="" is="" proportional="" to="" the="" tilt="" of="" the="" beam.="" in="" control="" technology,="" the="" system="" is="" open="" loop="" unstable="" because="" the="" system="" output="" (the="" ball="" position)="" increases="" without="" limit="" for="" a="" fixed="" input="" (beam="" angle).="" feedback="" control="" must="" be="" used="" to="" keep="" the="" ball="" in="" a="" desired="" position="" on="" the="" beam.="" figure="" 2.2:="" an="" overall="" look="" of="" the="" ball="" and="" beam="" system="" control="" requirements="" •="" overshoot="">< 15%="" •="" settling="" time="">< 5="" s="" •="" steady="" state="" accuracy="">< 1="" cm="" •="" test="" three="" types="" of="" controllers="" 3.="" magnetic="" levitation="" why="" magnetic="" levitation="" systems?="" magnetic="" levitation="" is="" the="" method="" in="" which="" an="" object="" is="" suspended="" in="" air="" by="" the="" use="" of="" magnetic="" fields="" and="" no="" other="" support.="" there="" is="" already="" a="" myriad="" of="" ways="" in="" which="" the="" principle="" 2="" peter="" wellstead,="" ball="" and="" beam="" 1:="" basics,="" control="" systems="" principles.co.uk="" 5="" of="" magnetic="" levitation="" is="" used="" in="" everyday="" life.="" one="" of="" these="" examples="" are="" the="" number="" of="" maglev="" trains="" which="" operate="" around="" the="" world="" as="" shown="" in="" figure="" 3.1.="" the="" maglev="" trains="" are="" able="" to="" move="" without="" making="" contact="" with="" the="" ground="" using="" permanent="" magnets="" to="" produce="" lift="" and="" propulsion="" forces.="" this="" will="" consequently="" reduce="" friction="" by="" a="" great="" extent="" allowing="" for="" very="" high="" speeds="" usually="" between="" 200-400="" miles.="" transrapid="" 09="" at="" the="" emsland="" test="" facility="" in="" germany="" scmaglev="" test="" track="" in="" yamanashi="" prefecture,="" japan="" figure="" 3.1:="" maglev="" trains.3="" magnetic="" levitation="" is="" also="" used="" for="" contactless="" melting,="" magnetic="" bearings="" and="" for="" product="" display="" purposes="" (see="" figure="" 3.2).="" melt="" metal="" with="" magnets="" magnetic="" bearing="" figure="" 3.2:="" applications="" of="" magnetic="" levitation="" control="" objectives="" the="" main="" objective="" of="" this="" project="" is="" to="" design="" a="" controller="" which="" is="" able="" to="" levitate="" a="" steel="" ball="" between="" a="" pedestal="" position="" sensor="" and="" the="" electromagnet.="" the="" controller="" should="" control="" the="" coil="" current="" which="" then="" in="" turn="" controls="" the="" magnetic="" force="" required="" to="" lift="" the="" ball="" and="" counteract="" the="" forces="" due="" to="" gravitational="" acceleration.="" 3="" https://en.wikipedia.org/wiki/maglev="" 6="" figure="" 3.3:="" the="" magnetic="" levitation="" module="" in="" control="" lab.="" control="" requirements="" •="" be="" able="" to="" levitate="" the="" ball="" •="" settling="" time="">< 5="" s="" •="" test="" three="" types="" of="" controllers="" 4.="" pneumatic="" rotary="" pendulum="" why="" pneumatic="" rotary="" pendulum?="" pneumatic="" rotary="" actuators="" are="" commonly="" used="" to="" convert="" compressed="" air="" pressure—in="" the="" form="" of="" a="" cylinder="" stroke—into="" an="" oscillating="" rotary="" motion.="" in="" essence,="" this="" is="" a="" switched="" actuator,="" i.e.,="" the="" torque="" that="" can="" be="" applied="" to="" the="" rotary="" mechanism="" can="" take="" only="" three="" possible="" values,="" maximum="" in="" clockwise="" direction,="" maximum="" in="" counter-clockwise="" direction,="" and="" null.="" these="" actuators="" are="" commonly="" used="" in="" industrial="" applications="" such="" as="" conveying,="" clamping,="" transferring="" parts,="" positioning,="" and="" controlling="" valves.="" like="" other="" pneumatic="" components,="" they="" are="" durable,="" offer="" simplicity="" and="" high="" force="" for="" their="" size,="" and="" can="" operate="" in="" hazardous="" environments.="" for="" instance,="" they="" can="" be="" found="" in="" food="" mixers="" (since="" no="" lubricants="" are="" required),="" and="" diesel="" and="" petrol="" pumps="" for="" safety="" reasons.="" 7="" air-operated="" rotary="" gear="" pump="" for="" fast="" and="" safe="" dispensing="" of="" diesel="" and="" petrol="" industrial="" food="" mixer="" and="" drier="" complying="" sanitary="" standards="" figure="" 4.1:="" applications="" of="" pneumatic="" rotary="" actuators.="" controlling="" a="" pneumatic="" rotary="" pendulum="" can="" also="" help="" one="" to="" understand="" how="" the="" attitude="" of="" satellites="" and="" spacecrafts="" are="" governed="" in="" the="" space.="" in="" particular,="" attitude="" manoeuvres="" involve="" changing="" the="" orientation="" of="" the="" spacecraft="" in="" any="" of="" three="" possible="" axes="" (called="" roll,="" pitch,="" and="" yaw).="" for="" instance,="" to="" rotate="" a="" spacecraft,="" a="" pair="" of="" thruster="" rockets="" on="" opposite="" sides="" of="" the="" vehicle="" are="" fired="" in="" opposite="" directions.="" to="" stop="" the="" rotation,="" a="" second="" pair="" is="" fired="" to="" produce="" an="" opposing="" force.="" figure="" 4.2:="" attitude="" control="" of="" spacecrafts="" and="" satellites="" control="" objectives="" the="" pneumatic="" rotary="" pendulum="" is="" one="" of="" the="" most="" dynamic="" projects="" in="" the="" field="" of="" automatic="" control.="" the="" system="" is="" a="" bi-directional="" rotating="" pendulum="" whose="" direction="" is="" controlled="" by="" means="" of="" air="" pressure="" supplied="" from="" a="" jet.="" a="" pressure="" of="" about="" 200="" kpa="" is="" used="" to="" drive="" the="" 8="" system.="" the="" main="" objective="" of="" the="" system="" is="" to="" control="" the="" flow="" of="" the="" air="" using="" electrically="" operated="" solenoid="" valves="" which="" open="" and="" close="" and="" thus="" switching="" the="" direction="" of="" the="" air="" flow="" as="" required.="" hence,="" the="" position="" of="" the="" pendulum="" is="" controlled="" effectively="" via="" ‘discrete’="" inputs="" with="" the="" help="" of="" control="" valves.="" figure="" 4.3:="" the="" pneumatic="" rotary="" pendulum="" control="" requirements="" •="" overshoot="">< 15%="" •="" settling="" time="">< 10="" s="" •="" steady="" state="" accuracy="">< 50 • test three types of controllers 5. rotary inverted pendulum why inverted pendulum? an inverted pendulum is a pendulum that has its center of mass above its pivot point. it is unstable and without additional help will fall over. arguably the most prevalent example of a stabilized inverted pendulum is a human being. a person standing upright acts as an inverted pendulum with his feet as the pivot, and without constant small muscular adjustments would fall over. the inverted pendulum 50="" •="" test="" three="" types="" of="" controllers="" 5.="" rotary="" inverted="" pendulum="" why="" inverted="" pendulum?="" an="" inverted="" pendulum="" is="" a="" pendulum="" that="" has="" its="" center="" of="" mass="" above="" its="" pivot="" point.="" it="" is="" unstable="" and="" without="" additional="" help="" will="" fall="" over.="" arguably="" the="" most="" prevalent="" example="" of="" a="" stabilized="" inverted="" pendulum="" is="" a="" human="" being.="" a="" person="" standing="" upright="" acts="" as="" an="" inverted="" pendulum="" with="" his="" feet="" as="" the="" pivot,="" and="" without="" constant="" small="" muscular="" adjustments="" would="" fall="" over.="" the="" inverted="">