Control algorithms, digital

Tj = integral time constant and = derivative time constant. Upon the advent of digital control devices, this basic control algorithm was implemented as a digital approximation ... 

Presently, fieldbus controllers are single-loop controllers with 8- and 16-bit microprocessors and are options to digital field-control devices. These controllers support the basic PID control algorithm... 

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. 

The filter housing is placed inside a Carbolitc PF30 forced air circulation oven. A Carbolite type 201 Temperature Controller is supplied as an integral part of the control section of the oven. It is a digital instrument with PID control algorithm. 

The design of digital control systems will be the subject of Chapter 30, and Chapter 31 will treat the question of experimentally modeling a process. Finally, the on-line coordination of an experimental modeling procedure with a control algorithm will be examined in Chapter 31, in an attempt to develop on-line adaptive control systems. 

The digital control algorithms discussed in Sections 30.2 and 30.3 were designed for set point changes (servo problem). Therefore, the question arises as to how well they perform for load (disturbance) changes. It is a fortuitous coincidence that algorithms such as the deadbeat or Dahlin s perform well for both set point and load changes. 

Digital-analog converter, 560 Digital computer (see Computer, digital) Digital computer control loops, 561-66 Digital control algorithms, 634-38, 640-47, 650-54... 

In the preceding section the analysis was centered around the response of the discrete components in a direct digital control (DDC) loop with characteristic representative the control algorithm. The use of z-transforms allowed easy and straightforward development of simple input-output models through the discrete transfer functions. 

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). 

What is a discrete transfer function, and what is it needed for Develop the discrete transfer function for (a) a proportional control algorithm, (b) the velocity form of a PI control algorithm, and (c) a second-order digital filter. 

How do we tune digital control algorithms In general, the available... 

There are a variety of specifications that we can impose on the closed-loop response y(z) for a given step change in ySp(z). It is clear that depending on the response specifications, we can derive a series of alternative digital control algorithms. Let us now examine the most commonly used among them. 

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