Sampling controller direct-digital

For our second sampled-data closedloop system, let us consider the direct digital control (DDC) loop sketched in Fig. 18.12b. The equations describing the system are... 

The direct dependence of microorganisms on pressure changes is negligible provided they do not exceed many bars [18,186,211,474]. However, the partial pressure of dissolved gases and their solubility is indirectly affected and must, therefore, be at least considered if not controlled. A data sampling frequency in the range of a few 100 ms is appropriate for direct digital pressure control (DDC) in laboratory scale bioreactors. 

Equation (29.21) yields the discrete-time (sampled-value) closed-loop response of a direct digital control loop. Its form is very similar to that for continuous analog control loops. 

Consider the block diagram of a direct digital feedback control loop shown in Figure 29.9. Such loops contain both continuous- and discrete-time signals and dynamic elements. Three samplers are present to indicate the discrete-time nature of the set point j/Sp( ), control command c(z), and sampled process output y(z). The continuous signals are denoted by their Laplace transforms [i.e., y(s), Jn(s), and d(s)]. Furthermore, the continuous dynamic elements (e.g., hold, process, disturbance element) are denoted by their continuous transfer functions, H(s), Gp(s), and GAs), respectively. For the control algorithm, which is the only discrete element, we have used its discrete transfer function, D(z). 

A test system, controlled by personal computer (PC), was developed to evaluate the performance of the sensors. A schematic of this system is shown in Figure 3. The signals from the sensors were amplified by a multi-channel electrometer and acquired by a 16 bit analog to digital data acquisition board at a resolution of 0.0145 mV/bit. The test fixture provided the electrical and fluid interface to the sensor substrate. It contained channels which directed the sample, reference and calibrator solutions over the sensors. These channels combined down stream of the sensors to form the liquid junction as shown in Figure 1. Contact probes were used to make electrical connection to the substrate. Fluids were drawn through the test fixture by a peristaltic pump driven by a stepper motor and flow of the different fluids was controlled by the pinch valves. 

Instrument response may be linearly or nonlinearly related to the analyte concentration. Calibration is accomplished by preparing a series of standard solutions of the analyte at known concentrations and me uring the instrument response to each of these (usually after treating them in the same manner as the samples) to prepare an analytical calibration curve of response versus concentration. The concentration of an unknown is then determined from the response, using the calibration curve. With modem computer-controlled instruments, this is often done electronically or digitally, and direct readout of concentration is obtained. 

This is a new feature directly attributable to the discrete-time nature of a digital controller. Therefore, we need to be very careful not to destabilize an otherwise stable loop by an improper selection of the sampling period. Let us use the following parametric values ... 

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