Error State Steady
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MOTORPOSITION SUSPENSION INVERTEDPENDULUM AIRCRAFTPITCH BALL&BEAM Extras: Steady-State Error Contents Calculating steady-state errors System type and steady-state error Example: Meeting steady-state error requirements Steady-state error is defined as the difference between the input (command) and the output of a system in the limit as time goes steady state error matlab to infinity (i.e. when the response has reached steady state). The steady-state error will steady state error wiki depend on the type of input (step, ramp, etc.) as well as the system type (0, I, or II). Note: Steady-state error steady state error example analysis is only useful for stable systems. You should always check the system for stability before performing a steady-state error analysis. Many of the techniques that we present will give an answer even if the error does steady state error equation not reach a finite steady-state value. Calculating steady-state errors Before talking about the relationships between steady-state error and system type, we will show how to calculate error regardless of system type or input. Then, we will start deriving formulas we can apply when the system has a specific structure and the input is one of our standard functions. Steady-state error can be calculated from the open- or closed-loop transfer function for unity feedback
Steady State Error From Transfer Function
systems. For example, let's say that we have the system given below. This is equivalent to the following system, where T(s) is the closed-loop transfer function. We can calculate the steady-state error for this system from either the open- or closed-loop transfer function using the Final Value Theorem. Recall that this theorem can only be applied if the subject of the limit (sE(s) in this case) has poles with negative real part. (1) (2) Now, let's plug in the Laplace transforms for some standard inputs and determine equations to calculate steady-state error from the open-loop transfer function in each case. Step Input (R(s) = 1 / s): (3) Ramp Input (R(s) = 1 / s^2): (4) Parabolic Input (R(s) = 1 / s^3): (5) When we design a controller, we usually also want to compensate for disturbances to a system. Let's say that we have a system with a disturbance that enters in the manner shown below. We can find the steady-state error due to a step disturbance input again employing the Final Value Theorem (treat R(s) = 0). (6) When we have a non-unity feedback system we need to be careful since the signal entering G(s) is no longer the actual error E(s). Error is the difference between the commanded reference and the actual output, E(s)
the input function type steady state error ramp input are used in Table 7.2 to get the proper static steady state theory error constant. There are three of these: Kp (position error constant), Kv (velocity error constant), and Ka (acceleration http://ctms.engin.umich.edu/CTMS/index.php?aux=Extras_Ess error constant). Once you have the proper static error constant, you can find ess. The static error constants are found from the following formulae: Now use Table 7.2 to find ess. Table 7.2 http://www.calpoly.edu/~fowen/me422/SSError4.html Type 0 Type 1 Type 2 Input ess Static Error Constant ess Static Error Constant ess Static Error Constant ess u(t) Kp = Constant Kp = Infinity 0 Kp = Infinity 0 t*u(t) Kv = 0 Infinity Kv = Constant Kv = Infinity 0 0.5*t2*u(t) Ka = 0 Infinity Ka = 0 Infinity Ka = Constant Note that ess has one of three values: 0, a constant, infinity. Notice how these values are distributed in the table. Also note the aberration in the formula for ess using the position error constant. ess is not equal to 1/Kp. Next Page
Du siehst YouTube auf Deutsch. Du kannst diese Einstellung unten ändern. Learn more You're viewing YouTube in German. You can change this preference below. Schließen Ja, ich möchte sie behalten Rückgängig machen Schließen Dieses Video ist https://www.youtube.com/watch?v=PXxveGoNRUw nicht verfügbar. WiedergabelisteWarteschlangeWiedergabelisteWarteschlange Alle entfernenBeenden Wird geladen... Wiedergabeliste Warteschlange __count__/__total__ Final Value Theorem and Steady State Error Brian Douglas AbonnierenAbonniertAbo beenden79.58979 Tsd. Wird geladen... Wird geladen... Wird verarbeitet... Hinzufügen Möchtest du dieses Video später noch einmal ansehen? Wenn du bei YouTube angemeldet bist, kannst du dieses Video zu einer Playlist hinzufügen. Anmelden Teilen Mehr Melden Möchtest du dieses Video melden? Melde dich steady state an, um unangemessene Inhalte zu melden. Anmelden Transkript Statistik 86.290 Aufrufe 708 Dieses Video gefällt dir? Melde dich bei YouTube an, damit dein Feedback gezählt wird. Anmelden 709 11 Dieses Video gefällt dir nicht? Melde dich bei YouTube an, damit dein Feedback gezählt wird. Anmelden 12 Wird geladen... Wird geladen... Transkript Das interaktive Transkript konnte nicht geladen werden. Wird geladen... Wird steady state error geladen... Die Bewertungsfunktion ist nach Ausleihen des Videos verfügbar. Diese Funktion ist zurzeit nicht verfügbar. Bitte versuche es später erneut. Veröffentlicht am 07.04.2013Find my courses for free on konoz! https://konozlearning.com/#!/invitati...The Final Value Theorem is a way we can determine what value the time domain function approaches at infinity but from the S-domain transfer function. This is very helpful when we're trying to find out what the steady state error is for our control system, or to easily identify how to change the controller to erase or minimize the steady state error.Two proofs of the Final Value Theoerm:www.ee.kth.se/~tn/.../Basic.../Initial_and_Final_Value_Theorems_uk.pdfrenyi.ece.iastate.edu/zhengdao/initial-value-theorem.pdfErrata:7:55 I wrote "If all poles are in LHP then type 1 and FV=0" and it should be "If all poles are in the LHP then type 0 and FV=0"11:53 I left the 's' off the final value theorem equation. It should be the limit as s approaches 0 of 's' times the transfer function.Don't forget to subscribe! I'm on Twitter @BrianBDouglas!If you have any questions on it leave them in the comment section below or on Twitter and I'll try my best to answer th