Feedback relay

It should be noted that Eqs. (14.38) and (14.39) give approximate values for 0) and X. because the relay feedback introduces a nonlinearity into the system. However, for most systems, the approximation is close enough for engineering purposes. 

This method can be extended to evaluate models with more parameters and with diHerent kinds of transfer functions (e.g., underdamped second-order lag) by using hysteresis in the relay feedback or by inserting an additional dead time in the loop to produce a limit cycle with a different frequency. The two autotune tests give four equations so four parameters can be evaluated. 

Simulate several first-order lag and second-order lag plus deadlime processes on a digital computer with a relay feedback. Compare the ultimate gains and frequencies obtained by the auto-tune method with the real values of cu and obtained from the transfer function. 

Y. Cheng-Ching. Autotuning of PID Controllers Relay Feedback Approach (Advances in Industrial Control). Springer-Verlag, London, 1999. 

In any 8mS period. If I am right about the inter-relay feedback, the plug will receive an additional one or two HV pulses. It s not much, but It Is slightly better than before. If it is having an effect, then an 8-cylinder engine is much more likely to run than a 4-cylinder engine which generates only half as many HV pulses per rev. 

A relay-feedback test on the reactor temperature controller is used to obtain the ultimate gain and frequency (K, = 64 and Pv = 10 min), using a 50 K temperature transmitter span and assuming the maximum cooling water flow is twice the steady-state value. The Tyreus-Luyben settings give oscillatory response, so the controller gain is reduced by factor of 2 (Kc = 10, t = 1320 s). 

Relay feedback test %optr 0.25 l.i if errortt>0ioptr 0.25 0.9 tend fj fjss 4 optr ... 

There are two controllers. The proportional reactor level control has a gain of 5. The reactor temperature controller is tuned by running a relay-feedback test. The manipulated variable is the cooling water flowrate in the condenser. With a 50-K temperature transmitter span and the cooling water control valve half open at design conditions, the resulting tuning constants are Kc = 4.23 and = 25 min. 

Figure 3.49 Relay-feedback test with feed manipulation TR — F0.

The tuning of the temperature controller is achieved by mnning a relay-feedback test, which the recent versions of Aspen Dynamics has made quite easy to do. The button on the... 

Figure 3.77 Running relay-feedback test on temperature controller.

It is important to remember that a deadtime or several lags must be inserted in most control loops in order to mn a relay-feedback test. To have an ultimate gain, the process must have a phase angle that drops below —180°. Many of the models in Aspen Dynamics have only a first-order transfer function between the controller variable and the manipulated variable. In the CSTR temperature controller example, the controlled variable is reactor temperature and the manipulated variable is medium temperature. The phase angle of a first-order process goes to only —90°, so there is no ultimate gain. The relay-feedback test will fail without the deadtime element inserted in the loop. 

Figure 3.79 Relay-feedback test dynamic results.

The relay-feedback test results for the reactor temperature controller are shown in Figure 3.97. The Tyreus-Luyben controller settings are Kc = 2.25 and r, = 11.9 min. 

Figure 3.97 Relay-feedback test with LMTD.

Ziegler-Nichols (ZN) and Tyreus-Luyben (TL) PI tunings are evaluated. Ultimate gain and frequency are obtained by performing relay-feedback tests. Temperature control loops have three 20-s lags. The pressure control loop has two 30-s lags. There is a... 

Figure 6.63 shows this new control structure. The setpoint of the temperature controller TC2 is 392 K, and it is direct-acting. With a deadtime of 1 min and a temperature transmitter range of 350-450 K, the relay-feedback test gives Tyreus-Luyben settings of Kc = 14.6 and tj = 10.6 min. Figure 6.64 shows the response of the closedloop system... 

All controllers are PI except for the drum level controller, which is P only. Two 0.5-min lags are assumed in the pressure loop. Three 0.1-min lags are assumed in the temperature loops. Relay-feedback tests are conducted to get the ultimate gain and period, and the Tyreus-Luyben settings are used. 

Control with Only Bypass The important control loop in this process is the temperature controller that manipulates the bypass flow to control the temperature of the mixed hot and cold streams. The controller is direct acting (an increase in temperature opens the bypass valve). A 1-min deadtime is inserted in the loop, and a relay-feedback test is run that gives Tyreus-Luyben settings Kc = 0.48 and T/ = 4.0 min. The temperature transmitter span is 350-450 K. 

The next part involves controller tuning. We must determine the tuning constants for the controllers in the plant. While this task is often performed by using heuristics and experience, it can sometimes be a nontrivial exercise for certain loops. We recommend using a relay-feedback test that determines the ultimate gain and period for the control loop, from which controller settings can be calculated (Luyben and Luyben, 1997). 

On the surface it might appear that partial control does not require a first-principles model for its implementation. After all, M is a regression model and controller tuning is based on relay-feedback information. For simple systems this may be correct. However, for most industrially relevant systems it is not intuitively obvious what constitutes the dominant variables in the system and how to identify appropriate manipulators to control the dominant variables. This requires nonlinear, first-principles models. The models are run off-line and need only contain enough information to predict the correct trends and relations in the system. The purpose is not to predict outputs from inputs precisely and accurately, but to identify dominant variables and their relations to possible manipulators. 

Figures 6.14 and 6.15 give dynamic responses of the tray temperatures, reboiler heat input, and bottoms product impurity. The temperature loops were tuned using the TL (Tyreus-Luyben) tuning rules after the ultimate gain and ultimate frequency had been determined using a relay-feedback test. Two 0.5-minute first-order lags are used in the temperature loop. Temperature transmitter spans are 100T. The ultimate gain and period for the tray 6 temperature loop are 4.2 and 2.7 minutes, and for the tray 14 loop are 12.7 and 2.5 minutes. These results reflect the fact that the process gain is higher when tray 6 is...

The critical product-quality and safety-constraint loops were tuned by using a relay -feedback test to determine ultimate gains and periods. The Tyreus-Luyben PI controller tuning constants were then implemented. Table 11.12 summarizes transmitter and valve spans and gives controller tuning constants for the important loops. Proportional control was used for all liquid levels and pressure loops. 

Perform a relay-feedback test on each temperature, pressure, and... 

To initiate an ATV test, the process should be at steady-state or near steady-state conditions, Cq and Jo- Next, the controller output is set io Cq + h (or Cg - h) until y deviates significantly from Jq. At that point, the controller output is set to Cq - / (or Cq + h), which will turn the process back toward jo- Then, each time y crosses yo. the controller output is switched from Cq + h to Cq - h or from Cq - h to Cg + h. The process is also referred to as a relay feedback experiment. A standing wave is established after 3 to 4 cycles therefore, the values of a and the ultimate period, P , can be measured directly, and the ATV test is concluded. The ultimate gain, K, is calculated by... 

The examples presented in this chapter illustrate these various steps. Once the control structure has been selected, dynamic simulations of the entire process can be used to evaluate controller performance. Commercial software is being developed that will facilitate plantwide dynamic simulation studies. To tune controllers, each individual unit operation can be isolated and controllers tuned using the relay-feedback test (discussed in Chapter 16). 

If the input U does not provide enough excitation of the process over the important frequency range, the model fidelity is poor, particularly in processes with appreciable noise. This is why direct sine wave testing at a frequency near the ultimate frequency and relay feedback testing are such usefril methods. 

Accurate information is obtained around the important frequency, i.e., near phase angles of — 180 . In contrast, pulse testing tries to extract information for a range of frequencies. It is inherently less accurate than a method that concentrates on a specific frequency. Remember, however, that we do not have to specify the frequency. The relay feedback automatically finds it. 

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