Search results
Results from the WOW.Com Content Network
PID controllers often provide acceptable control using default tunings, but performance can generally be improved by careful tuning, and performance may be unacceptable with poor tuning. Usually, initial designs need to be adjusted repeatedly through computer simulations until the closed-loop system performs or compromises as desired.
The Ziegler–Nichols tuning (represented by the 'Classic PID' equations in the table above) creates a "quarter wave decay". This is an acceptable result for some purposes, but not optimal for all applications. This tuning rule is meant to give PID loops best disturbance rejection. [2]
Consider the continuous-time linear dynamic system ˙ = () + () + (), = () + (),where represents the vector of state variables of the system, the vector of control inputs and the vector of measured outputs available for feedback.
For example, the position of a valve cannot be any more open than fully open and also cannot be closed any more than fully closed. In this case, anti-windup can actually involve the integrator being turned off for periods of time until the response falls back into an acceptable range.
The Smith predictor (invented by O. J. M. Smith in 1957) is a type of predictive controller designed to control systems with a significant feedback time delay. The idea can be illustrated as follows.
The following MATLAB code will plot the root locus of the closed-loop transfer function as varies using the described manual method as well as the rlocus built-in function: % Manual method K_array = ( 0 : 0.1 : 220 ). ' ; % .' is a transpose.
Example Let the system be an n dimensional discrete-time-invariant system from the formula: ϕ ( n , 0 , 0 , w ) = ∑ i = 1 n A i − 1 B w ( n − 1 ) {\displaystyle \phi (n,0,0,w)=\sum \limits _{i=1}^{n}A^{i-1}Bw(n-1)} (Where ϕ {\displaystyle \phi } (final time, initial time, state variable, restrictions) is defined as the transition matrix ...
Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. [1] [2] For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions.