Ramp Error Constant
Contents |
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 velocity error constant of a system in the limit as time goes to infinity (i.e.
Steady State Error Matlab
when the response has reached steady state). The steady-state error will depend on the type of input (step, ramp, etc.) steady state error in control system pdf as well as the system type (0, I, or II). Note: Steady-state error analysis is only useful for stable systems. You should always check the system for stability before performing a how to reduce steady state error steady-state error analysis. Many of the techniques that we present will give an answer even if the error does 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
Steady State Error In Control System Problems
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 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
the input function type determine the steady state error for a unit step input are used in Table 7.2 to get the proper static
Steady State Error Wiki
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
Error Click here to return to the Table of Contents Why Worry About Steady State Error? Control systems are used to control some physical variable. That variable may be a https://www.facstaff.bucknell.edu/mastascu/eControlHTML/Design/Perf1SSE.htm temperature somewhere, the attitude of an aircraft or a frequency in a communication system. Whatever the variable, it is important to control the variable accurately. If you are designing a control system, how accurately the system performs is important. If it is desired to have the variable under control take on a particular value, you will want the variable to get as close to the desired value as steady state possible. Certainly, you will want to measure how accurately you can control the variable. Beyond that you will want to be able to predict how accurately you can control the variable. To be able to measure and predict accuracy in a control system, a standard measure of performance is widely used. That measure of performance is steady state error - SSE - and steady state error is a concept steady state error that assumes the following: The system under test is stimulated with some standard input. Typically, the test input is a step function of time, but it can also be a ramp or other polynomial kinds of inputs. The system comes to a steady state, and the difference between the input and the output is measured. The difference between the input - the desired response - and the output - the actual response is referred to as the error. Goals For This Lesson Given our statements above, it should be clear what you are about in this lesson. Here are your goals. Given a linear feedback control system, Be able to compute the SSE for standard inputs, particularly step input signals. Be able to compute the gain that will produce a prescribed level of SSE in the system. Be able to specify the SSE in a system with integral control. In this lesson, we will examine steady state error - SSE - in closed loop control systems. The closed loop system we will examine is shown below. The system to be controlled has a transfer function G(s). There is a sensor with a transfer function Ks. There is a controller with a transf
be down. Please try the request again. Your cache administrator is webmaster. Generated Tue, 25 Oct 2016 20:54:08 GMT by s_wx1062 (squid/3.5.20)