Non Zero Steady State Error
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R(s) can be interpreted as the desired value of the output, and the output of the summing junction, E(s), is the error between the desired and actual output values. The behavior of this error signal as time t goes to infinity (the steady-state error) steady state error example is the topic of this example. The Final Value Theorem of Laplace Transforms will be steady state error matlab used to determine the steady-state error. The one very important requirement for using the Final Value Theorem correctly in this type of application is steady state error in control system problems that the closed-loop system must be BIBO stable, that is, all poles of the closed-loop transfer function C(s)/R(s) must be strictly in the left-half of the s-plane. Steady-state error in terms of System Type and Input Type Input
How To Reduce Steady State Error
Signals -- The steady-state error will be determined for a particular class of reference input signals, namely those signals that can be expressed in the time domain as simple powers of t, such as step, ramp, parabola, etc. The Laplace Transforms for signals in this class all have the form System Type -- With this type of input signal, the steady-state error ess will depend on the open-loop transfer function Gp(s) in a very simple way. We will define steady state error constants the System Type to be the number of poles of Gp(s) at the origin of the s-plane (s=0), and denote the System Type by N. The relation between the System Type N and the Type of the reference input signal q determines the form of the steady-state error. We will see that the steady-state error can only have 3 possible forms: zero a non-zero, finite number infinity As seen in the equations below, the form of the steady-state error only depends on the value of N+1-q. If that value is positive, the numerator of ess evaluates to 0 when the limit is taken, and thus the steady-state error is zero. If N+1-q is negative, the numerator of ess evaluates to 1/0 in the limit, and the steady-state error is infinity. If N+1-q is 0, the numerator of ess is a non-zero, finite constant, and so is the steady-state error. In this case, the steady-state error is inversely related to the open-loop transfer function Gp(s) evaluated at s=0. Under the assumption of closed-loop stability, the steady-state error for a particular system with a particular reference input can be quickly computed by determining N+1-q and evaluating Gp(s) at s=0 if necessary. Transfer function in Bode form A simplification for the expression for the steady-state error occurs when Gp(s) is in "Bode" or "time-constant" form. The conversion from the normal "pole-zero" format for the transfer
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 temperature somewhere, the attitude of an steady state error in control system pdf aircraft or a frequency in a communication system. Whatever the variable, it is important to
Steady State Error Solved Problems
control the variable accurately. If you are designing a control system, how accurately the system performs is important. If it is
Steady State Error Control System Example
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 possible. Certainly, you will want to measure how accurately you can control http://ece.gmu.edu/~gbeale/ece_421/ess_01.html 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 that assumes the following: The system under test is stimulated with some standard input. Typically, the test input https://www.facstaff.bucknell.edu/mastascu/eControlHTML/Design/Perf1SSE.htm 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 transfer function Kp(s) - which may be a constant gain. What Is SSE? We need a precise definition of SSE if we are going to be able to predict a value for SSE in
the input function type http://www.slideshare.net/leonidesdeocampo/lecture12me1766steadystateerror are used in Table 7.2 to get the proper static error constant. There are three of these: Kp (position error constant), Kv (velocity error constant), and Ka (acceleration steady state 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 steady state error 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
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