Plant transfer function

If the plant dynamics are first-order, then Figure 4.22 can be described as shown in Figure 4.23. The plant transfer function is... 

Inserting the PI control law given in equation (4.68) into the first-order plant transfer function shown in equation (4.60) gives... 

A unity-feedback control system has a nominal plant transfer function... 

For the multivariable case, an uncertainty matrix A must be defined which contains the uncertainty in the various elements of the plant transfer function (and also could include uncertainties in setting control valves or in measurements). 

A 2 x 2 multivariable process has the following openloop plant transfer function matrix ... 

Derive the openloop plant transfer function matrix relating controlled variables Xi and manipulated variables rtlj. 

The use of singular value decomposition (SVD), introduced into chemical engineering by Moore and Downs Proc. JACC, paper WP-7C, 1981) can give some guidance in the question of what variables to control. They used SVD to select the best tray temperatures. SVD involves expressing the matrix of plant transfer function steady state gains as the product of three matrices a V matrix, a diagonal Z matrix, and a matrix. 

The problem of the effect of scaling on singular values is handled by expressing the gains of all the plant transfer functions in dimensionless form. The gains with engineering units are divided by transmitter spans and multiplied by... 

The basic idea in multivariable IMC is the same as in single-loop IMC. The ideal controller would be the inverse of the plant transfer function matrix. This would give perfect control. However, the inverse of the plant transfer function matrix is not physically realizable because of deadtimes, higher-order denominators than numerators, and RHP zeros (which would give an openloop unstable controller). 

Note If we are using a spreadsheet, we will find that changing Rfl does in fact affect the overall loop (even when using conventional op-amp-based error amplifiers). But we should be clear that that is only because by changing Rfl, we have changed the duty cycle of the converter (its output voltage), which thus affects the plant transfer function. Therefore, in that sense, the effect of Rfl is only indirect. We will see that Rfl does not actually enter into any of the equations that tell us the locations of the poles and zeros of the system. 

The plant transfer functions presented earlier were only for voltage mode control. In current mode control, the ramp to the pulse width (duty cycle) modulator is derived from the... 

Figure 7-25 Simplified Plant Transfer Function for Current Mode Control...

Panda investigated the performance of IMC in fluid-bed drying of sand particles, mustard seeds, and wheat grains [19]. The structure of the IMC system for the fluid-bed dryer is depicted in the block diagram shown in Figure 57.6. In this study, IMC uses a process-model transfer function (GJ parallel to the actual plant transfer function (Gp). 

Panda investigated the performance of IMC in fluid-bed drying of sand particles, mustard seeds, and wheat grains [19], The structure of the IMC system for the fluid-bed dryer is depicted in the block diagram shown in Figure 49.6. In this study, IMC uses a process-model transfer function (Gm) parallel to the actual plant transfer function (Gp). A filter is used in the control system to ensure robustness in performance. The exit-air temperature is used for set-point tracking by the IMC. If the system is performed without any oscillations, the overshoots will be tolerable, there will be no offset, and the control scheme will be effective and respond rapidly as described by Panda [19]. 

Consider the feedback system illustrated in Figure 6.1, where u and y are the control signal and measured process output, respectively, r is the setpoint, d is the load disturbance, and C and G denote the controller and plant transfer functions, respectively. We will assume that C has the structure of a PID controller given by... 

Example 6.3. Consider the problem of PID controller design for the following plant transfer function model... 

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