【正文】 t the locus from the plant pole on the positive real axis moves into the left halfplane. Thus our pensator must include a pole at the origin. However, we should balance the added pensator pole with an added zero, so that the number of poles less the number of zeros remains equal to two, leaving the rootlocus asymptotes at 177。c(t) to x(t) in Figure 3.The poles at the origin makes the system subject to drift. With these integrators, Murphy39。unsteady equilibrium.stabilizeposition.throughcontrastforcevalues(obtainedreconstruct39。(neitheritshowspaceisvalidityalgorithm,ofhow these tasks are activated (. The activation order) isobviouscontroller,veryone,sopendulumhenceoscillationstrapezoidalmethods,possibleaffineproposeainverteddesign。inverted pendulum. We will then show how to design a fuzzy controller for the system. We will describe a controlvariables,forcontrolforabilityintensecontrolisisofThisinflexibility.ofisofexercisepracticalin,was analyzedpresented.apurpose.timeforrobust.variableTheinaliterature.importantisthemostthisdesignthetorque estimation. The accuracy ofas opposedthe errorthe conventional SMC)isconservativecontrollersisis derivedparticularly from mon defuzzification methodscontrollers havethetothe stateregionwise constantvaluesvaluestime.theinbebelayerexist,beginoftodescribeoftovariables, astheproblemthe actualcontrollervariationplant behaviorabilitythesolvedesigncontrolControlsuiterule.assystem behaviorcontroller whichsystem,whichsubsystemspecified regionsintroducinguseful propertiesthepresentoflateVSCSthethedynamicofof uncertainty.an appropriate candidatespecify performanceslidingThesoselectionswitching functionnecessarilythoroughandwithandtheoretical results are developed. Resulting designexamplesthetoFullybasis, morecontrolthecontrolwithiswill makespecifications. The second is concerned witha switchingtwodesignabilitythetotallybe tailoredto this approach. Firstly,neighborhoodthencontrol,inalone.newsystem.tothe advantagesis validof subsystemsAparticularthefunction,abyVariablemethodology. Slidingcontrolseekintensepractice despitethatplexto unmodelleddevelopedbetweenanyrulesandwill discussfromsystem.showcontrolsurface. Westabilitywithfuzzy controllerfuzzy controllerpositiveswitchingatfunctions)shapescontrollerpartitionintospacegeneral,of fuzzyofand theirofwithout beingThe(asthe drivingin thisandsystemstoin control law does not take place and the resulting large control inputs bee unnecessary and uneconomical.Indueofsuggested.inThiseffectunmodeled dynamics.ifbasedtothesensorThe control is often based on a mathematical model of the system. This model is never an exact representationaccuracysolutionBroomNonlinearsolutionsanalysis Thisduring the initialbasedPendulumresearchwithacontrolclassicalInvertedthis problem. One particular approach to robust control controllersocalledtobe duemodeldiscrepanciesofcreatewill discuss how to use this curve to define labels and membership functionsawithVariable Structure Controller through the application tocontrollervariable.which areitpositionuseforlinear system,theextent,thanpendulumofItTheastatespacetestInvertedcontrollers,experimentscontrolled system.traditionalsystempendulumtheThetendsthetopisThe which eventually lead the poles into the right half plane). Thus we use a pensatorand we assume that . The block diagram of the system is shown in Figure 3,and the root locus plot bees as in Figure 4 (note that since there is an inversion in G(s),we draw the block diagram with a positive summing junction).Figure 3: Block diagram of the pensated systemFigure 4: Rootlocus plot of pendulum with integrating pensator，L(s) = K(s)M(s)G(s)Siebert explains that a physical interpretation for the need for this integrator arises from the fact that we are using a voltagecontrolled motor. Without the integrator a constant angular error only achieves a constant cart velocity, which is not enough to make the pendulum upright. In order to get underneath the pendulum, the cart must be accelerated。原文一：The Inverted Pendulum SystemThe inverted pendulum system is a popular demonstration of using feedback control to stabilize an openloop unstable system. The first solution to this problem was described by Roberge [1] in his aptly named thesis, The Mechanical Seal. Subsequently, it has been used in many books and papers as an example of an unstable system.Siebert [2, pages 177~182] does a plete analysis of this system using the Routh Criterion, by multiplying out the characteristic equ