Direct digital control

Direct Digital Control ( DDC abbreviated ) is a process control loops with partially contained therein transmission elements of digital processor systems to construct (including AD and DA converter modeling elements) and to calculate their properties.

Central to this is the notion that a digital controller can be described as a linear scanning system: controlled variable and setpoint value are sampled at fixed, regular intervals and converted into digital numeric values ​​, ie quantized. The controller calculates from these quantized parameters in each time step, the manipulated variable outputted at the sampling time and converted into an analog signal. A support member ensures that the control value is applied during the entire time interval until the next sampling. ( The quantization of the sizes also leads to a discrete-value signal. Usually the quantization is chosen, however, so fine that their impact on the dynamics of the control loop can be neglected. )

This particular kind of modeling a certain block can be located at a point of the block diagram of a control circuit thus described Narrow or set which includes the implementation of a control algorithm, which can be largely arbitrarily set and adapted to the control loop needs. Such a block is ( figuratively ) the heart of each DDC controller; its existence suggests that this is realized by a piece of software in a processor system. This has the procedure then commissioned his advent the name: (specifically, process computers ) as the early to mid 1960s by digital microcomputers could be taken " directly " on the structural design of control loops influence for the first time, this was a completely new experience compared to what you knew from the era of dominance of analog technology with respect to the options in dealing with computers, since they had not yet done anything like that in the industrial sector with the new digital technology at the time to the onset of this phase of development. So then you have called this method " Direct Digital Control " / " Direct digital control". With analog technology could indeed change to date and controller parameters, but the structure of the control circuit elements always remained on the installed analog computer components bound, whereas in the direct digital control on the modification of the control algorithm now also the structure of the control circuit elements could be changed, not only the parameters.

Understanding

The conceptual model of the direct digital control regulatory procedure assumes that the actual value signal, which is fed ( to be designed ) controller which is a signal, which is obtained by time discretization of the waveform along the time axis. One thinks in mind that a controller ( see block diagram ) is concretely realized in hardware by a signal processor or a microcontroller, wherein the feedback signal of the control loop - type of control system coming - through you sent analog -to-digital converter, thereby chopped into equidistant steps and is scanned with a point-like tap values ​​, before it is fed to the processor unit. In processing of such a signal by an analog - to-digital converter, the signal is sampled, however, not only on the time axis, but also quantizes the amplitude. So then produced a good approximation of the actual value signal has a value discrete number sequence over the time t, the amplitude values ​​only at the times with k = 0,1,2,3 ... change, where T is the sampling period. Mathematically that is generally one writes for obtained from sampling of numbers, ( for reasons of clarity, here braces the functional transformations, especially the transformation, subject to a series of numbers in parentheses Unlike in mathematics is in control engineering written instead of curly. )

With k = 0,1,2,3 ....

This nature of the actual signal you can now signal processor or microcontroller internally perform a discrete-time Setpoint actual value comparison - this provides with variable size as a guide - and compensate the control variable according to one's desires and specifications. Of course, several control variables can be controlled simultaneously. ( The basic idea of this concept should first be possible simply explains why here first only the control of a single control variable to be explained, however. )

The discrete-time target-actual value difference to the controller block is now supplied, embodying a signal processor or microcontroller, in which a control element algorithm ( for example, a PID element algorithm or the like ) may be implemented in discrete time, with which they are OFF control of the controlled variable. The choice of a proportional - integral-derivative controller as a member is not mandatory here; it has been taken only as examples here because PID limbs are relatively universally applicable in practice.

In order to characterize the PID controller with a discrete-value number sequence, forming the discrete-time analogue of the continuous-time PID controller. This is described by the following equation:

,

Where the transfer coefficient of the controller,

The integral and

The derivative represent.

To form the discrete-time equivalent of replacing the continuous functions and by the number and consequences. For the integral

Take the sum

,

Approximating the surface represented by the integral of the function curve. Finally, replacing the Differenzialquozienten by the Differenzenquozienten

.

So is first obtained for the discrete-time PID algorithm

.

This can also be written as

.

The summation index of the row in this equation one can then still lead to k, by then subtracting the last term of the series extended-range out of order, so cancel out both operations:

.

This is obtained discrete-time PID algorithm.

The numeric value that provides the control element algorithm that must be retrieved exactly once after each sampling period, must each be stored for the duration of the sampling period, and "held" (→ formation of discrete-value numbers in a so-called " step function ") in order of there to be passed through a digital -to-analog converter to the adjacent intervals in numerical values ​​in the form of being able to give it continuous signal to the control device (behind the DA converter) then. This adjustment device acts on the controlled system, on the turn continuously a measurement value is taken, which is in turn fed to the top of said analog-to- digital converter, whereby a closed loop is achieved.

To simplify keep the control loop design calculation, one specifies the additional condition that the closed-loop control blocks of block diagrams as well as pulse sequences may be mathematically linear. ( Certainly it can be shown that a sequence of functionals satisfies the linearity condition. ) [Note 1] In this way, actually obtained with such a model form a linear scanning.

Practical aspects

On the basis of the above, it is clear that in comparison to analogous rules for DDC controller for extended periods, the same hardware can be used, while only the control algorithm as well as external commands for sensors and actuators ( ie, the the controller software products) repeatedly need to be adjusted to the respective control engineering problems. This provides a significant gain in flexibility compared to analog technology dar. Only in multi-year time intervals then the hardware should be replaced, but this always depends on the requirements of specific applications.