By K. J. Astrom, T. Hagglund
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Since a first-order system is also called a lag the system is also called a multiple lag system. Notice that this formula holds only if the outflow of each tank only depends on its level. This means that there is no interaction between the tanks. 24) which has its maximum max g (t) : K o @ - 7)n-z T(n-2)l n-n+1 for t : (n - I)f . 25) 29 Chapter 2. 12 Cascaded tanks and corresponding block diagram representations. The upper tanks are noninteracting, and the lower are interacting' The step response is characterized by three parametets, Kp, n, and ?.
Nonlinear. General models for nonlinear dynamics are complicated, and there are no good methods for designing PID controllers for such systems. Fortunately, there are special classes of models that are well suited for PID control. A system may be represented as a combination of a static nonlinearity and a linear dynamical system. Such models are quite simple, and they are nicely adapted to PID control, but there are nonlinear systems that cannot be modeled well using this approach. 27a. This model is called a Hammerstein model.
The change in the manipulated variable should be large in order to get a good signal-to-noise ratio but it should not be so large that the process behavior is not linear. The allowable magnitude is also limited by process operation. It is also useful to record the fluctuations in the measurement signal when the control signal is constant. This gives data about the process noise. different amplitudes of the input rignui and at different operating conditions. This gives an indication of the signal ranges when the model is linear.