Constant Steady State Error
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
Steady State Error Matlab
is defined as the difference between the input (command) and steady state error matlab code the output of a system in the limit as time goes to infinity (i.e. when the steady state error matlab transfer function response has reached steady state). The steady-state error will depend on the type of input (step, ramp, etc.) as well as the system type (0, I,
Find Steady State Error Matlab
or II). Note: Steady-state error 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 not reach a finite steady-state value. Calculating steady-state errors Before
Steady State Error In Control System
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 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 ste
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 type (0, I, or II). Note: Steady-state steady state error for ramp input error analysis is only useful for stable systems. It is your responsibility to check
Steady State Error From Bode Plot
the system for stability before performing a steady-state error analysis. Many of the techniques that we present will give an answer even steady state error wiki if the system is unstable; obviously this answer is meaningless for an unstable system. Calculating steady-state errors Before talking about the relationships between steady-state error and system type, we will show how to calculate error http://ctms.engin.umich.edu/CTMS/index.php?aux=Extras_Ess 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 equivalent to the following system: We can calculate the steady state error for this system from either the open or closed-loop https://www.ee.usyd.edu.au/tutorials_online/matlab/extras/ess/ess.html 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 error constants). These constants are the position constant (Kp), the velocity constant (Kv), and the acceleration constant (Ka). Knowing the value of these constants as well as the system type, we can predict if our system is going to have a finite steady-state
the input function type 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