New version page

MSU ME 451 - ME451_L13_SteadyStateError

Documents in this Course
ME451_L5

ME451_L5

10 pages

HW2

HW2

2 pages

Load more

This preview shows page 1 out of 4 pages.

View Full Document
View Full Document

End of preview. Want to read all 4 pages?

Upload your study docs or become a GradeBuddy member to access this document.

View Full Document
Unformatted text preview:

1ME451: Control SystemsME451: Control SystemsDr. Jongeun ChoiDr. Jongeun ChoiDepartment of Mechanical EngineeringDepartment of Mechanical EngineeringMichigan State UniversityMichigan State UniversityLecture 13Lecture 13SteadySteady--state errorstate error2Course roadmapCourse roadmapLaplace transformLaplace transformTransfer functionTransfer functionModels for systemsModels for systems••electricalelectrical••mechanicalmechanical••electromechanicalelectromechanicalBlock diagramsBlock diagramsLinearizationLinearizationModelingModelingAnalysisAnalysisDesignDesignTime responseTime response••TransientTransient••Steady stateSteady stateFrequency responseFrequency response••Bode plotBode plotStabilityStability••RouthRouth--HurwitzHurwitz••NyquistNyquistDesign specsDesign specsRoot locusRoot locusFrequency domainFrequency domainPID & LeadPID & Lead--laglagDesign examplesDesign examples(Matlab simulations &) laboratories(Matlab simulations &) laboratories3Performance measures (review)Performance measures (review)Transient responseTransient responsePeak valuePeak valuePeak timePeak timePercent overshootPercent overshootDelay timeDelay timeRise timeRise timeSettling timeSettling timeSteady state responseSteady state responseSteady state errorSteady state errorNext, we will connect Next, we will connect these measures these measures with swith s--domain.domain.(Today(Today’’s lecture)s lecture)(From next lecture)(From next lecture)4SteadySteady--state error: state error: unity feedbackunity feedbackSuppose that we want output y(t) to track r(t).Suppose that we want output y(t) to track r(t).Error Error SteadySteady--state errorstate errorFinal value theorem Final value theorem (Suppose CL system is stable!!!)(Suppose CL system is stable!!!)Unity feedback!Unity feedback!We assume that the We assume that the CL system is stable!CL system is stable!5Error constantsError constantsStepStep--error (positionerror (position--error) constanterror) constantRampRamp--error (velocityerror (velocity--error) constanterror) constantParabolicParabolic--error (accelerationerror (acceleration--error) constanterror) constantKp, Kv, Ka :Kp, Kv, Ka :ability to reduce steadyability to reduce steady--state errorstate error6SteadySteady--state error for step r(t)state error for step r(t)KpKp7SteadySteady--state error for ramp r(t)state error for ramp r(t)KvKv8SteadySteady--state error for parabolic r(t)state error for parabolic r(t)KaKa9System typeSystem typeSystem type of GSystem type of Gis defined as the order is defined as the order (number) of poles of G(s) at s=0.(number) of poles of G(s) at s=0.ExamplesExamplestype 1type 1type 2type 2type 3type 310Zero steadyZero steady--state error state error If error constant is infinite, we can achieve zero If error constant is infinite, we can achieve zero steadysteady--state error. (Accurate tracking)state error. (Accurate tracking)For step r(t)For step r(t)For ramp r(t)For ramp r(t)For parabolic r(t)For parabolic r(t)11Example 1Example 1G(s) of type 2G(s) of type 2Characteristic equationCharacteristic equationCL system is NOT stable for any K.CL system is NOT stable for any K.e(t) goes to infinity. (Done(t) goes to infinity. (Don’’t use todayt use today’’s results if s results if CL system is not stable!!!)CL system is not stable!!!)G(s)G(s)12Example 2Example 2G(s) of type 1G(s) of type 1By RouthBy Routh--Hurwitz criterion, CL is stable iffHurwitz criterion, CL is stable iffStep r(t)Step r(t)Ramp r(t)Ramp r(t)Parabolic r(t)Parabolic r(t)G(s)G(s)13Example 3Example 3G(s) of type 2G(s) of type 2By RouthBy Routh--Hurwitz criterion, we can show that CL Hurwitz criterion, we can show that CL system is stable.system is stable.Step r(t)Step r(t)Ramp r(t)Ramp r(t)Parabolic r(t)Parabolic r(t)G(s)G(s)14A control exampleA control exampleClosedClosed--loop stable?loop stable?Compute error constantsCompute error constantsCompute steady state errorsCompute steady state errors15Summary and ExercisesSummary and ExercisesSteadySteady--state errorstate errorFor For unity feedbackunity feedback(STABLE!) systems, the system (STABLE!) systems, the system type of the forwardtype of the forward--path system determines if the path system determines if the steadysteady--state error is zero.state error is zero.The key tool is the The key tool is the final value theoremfinal value theorem!!Next, time response of 1stNext, time response of 1st--order systemsorder systemsExercisesExercisesGo over the examples in this lecture.Go over the examples in this


View Full Document
Loading Unlocking...
Login

Join to view ME451_L13_SteadyStateError and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view ME451_L13_SteadyStateError and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?