Tuning discrete time controllers

A related approach which has been used successfully in industrial applications occurs in discrete-time control. Both Dahlin (43) and Higham (44) have developed a digital control algorithm which in essence specifies the closed loop response to be first order plus dead time. The effective time constant of the closed loop response is a tuning parameter. If z-transforms are used in place of s-transforms in equation (11), we arrive at a digital feedback controller which includes dead time compensation. This dead time predictor, however, is sensitive to errors in the assumed dead time. Note that in the digital approach the closed loop response is explicitly specified, which removes some of the uncertainties occurring in the traditional root locus technique. 

DO profile during control. The sensitivity of the DO concentration to load changes is largest in subreactor 3, so DO(3) has been chosen for control. With a discrete time controller supplied with a feed-forward signal from the influent flow rate the total air supply to the four subreactors was controlled to keep DO(3) as constant as possible, fig 9. Even if the regulator is not optimally tuned, the improvement of the aerator performance as seen by the DO profile is significant. 

Pattern recognition self-adaptive controllers exist that do not explicitly require the modeling or estimation of discrete time models. These controllers adjust their tuning based on the evaluation of the system s closed-loop response characteristics (i.e., rise time, overshoot, settling time, loop damp-... 

In earlier chapters, Simulink was used to simulate linear continuous-time control systems described by transfer function models. For digital control systems, Simulink can also be used to simulate open- and closed-loop responses of discrete-time systems. As shown in Fig. 17.3, a computer control system includes both continuous and discrete components. In order to carry out detailed analysis of such a hybrid system, it is necessary to convert all transfer functions to discrete time and then carry out analysis using z-transforms (Astrom and Wittenmark, 1997 Franklin et al., 1997). On the other hand, simulation can be carried out with Simulink using the control system components in their native forms, either discrete or continuous. This approach is beneficial for tuning digital controllers. 

Compare the closed-loop performance of a discrete PI controller using the ITAE (disturbance) tuning rules in Table 12.3. Ajpproximate the sampler and ZOH by a time delay equal to Ar/2. Use Simulink to check the effect of samphng period for different controllers, with Af = 0.05, 0.25,0.5, and 1.0 min. 

We have presented a number of different approaches for designing digital feedback controllers. Digital controllers that emulate continuous-time PID controllers can include a number of special features to improve operability. Controllers based on Direct Synthesis or IMC can be tuned in continuous or discrete time, avoid ringing, eliminate offset, and provide a high level of performance for set-point changes. Minimum variance control can be very effective if a disturbance model is available. 

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