How To Get Zero Steady State Error
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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 aircraft steady state error matlab or a frequency in a communication system. Whatever the variable, it is important to control steady state error pdf the variable accurately. If you are designing a control system, how accurately the system performs is important. If it is desired to
Steady State Error In Control System Problems
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 the variable. Beyond
How To Reduce Steady State Error
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 is a step function steady state error wiki 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 a closed loop control system. Next, we'll look at
as time goes to infinity (i.e. when the response has reached the steady state). The steady-state error will depend on the type of input (step, ramp, etc) as well as the system
Steady State Error Control System Example
type (0, I, or II). Note: Steady-state error analysis is only useful for steady state error solved problems stable systems. It is your responsibility to check the system for stability before performing a steady-state error analysis. Many velocity error constant of the techniques that we present will give an answer even if the system is unstable; obviously this answer is meaningless for an unstable system. Calculating steady-state errors Before talking about the https://www.facstaff.bucknell.edu/mastascu/eControlHTML/Design/Perf1SSE.htm 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 will apply when we perform a steady state-error analysis. 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 following system: which is https://www.ee.usyd.edu.au/tutorials_online/matlab/extras/ess/ess.html equivalent to the following system: We can calculate the steady state error for this system from either the open or closed-loop transfer function using the final value theorem (remember that this theorem can only be applied if the denominator has no poles in the right-half plane): Now, let's plug in the Laplace transforms for different inputs and find equations to calculate steady-state errors from open-loop transfer functions given different inputs: Step Input (R(s) = 1/s): Ramp Input (R(s) = 1/s^2): Parabolic Input (R(s) = 1/s^3): When we design a controller, we usually want to compensate for disturbances to a system. Let's say that we have the following system with a disturbance: we can find the steady-state error for a step disturbance input with the following equation: Lastly, we can calculate steady-state error for non-unity feedback systems: By manipulating the blocks, we can model the system as follows: Now, simply apply the equations we talked about above. System type and steady-state error If you refer back to the equations for calculating steady-state errors for unity feedback systems, you will find that we have defined certain constants ( known as the static e
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 http://ece.gmu.edu/~gbeale/ece_421/ess_01.html of this error signal as time t goes to infinity (the steady-state error) is the topic of this example. The Final Value Theorem of Laplace Transforms will be 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 that the closed-loop system must be BIBO stable, that is, all poles of the closed-loop steady state 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 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 steady state error 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 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-lo