Digital Control Logic

[Cynthia Skane]

Digital control is a branch of control theory that uses digital computers to act as system controllers.Depending on the requirements, a digital control system can take the form of a microcontroller to an ASIC to a standard desktop computer.Since a digital computer is a discrete system, the Laplace transform is replaced with the Z-transform. Since a digital computer has finite precision (See quantization), extra care is needed to ensure the error in coefficients, analog-to-digital conversion, digital-to-analog conversion, etc. are not producing undesired or unplanned effects.

Since the creation of the first digital computer in the early 1940s the price of digital computers has dropped considerably, which has made them key pieces to control systems because they are easy to configure and reconfigure through software, can scale to the limits of the memory or storage space without extra cost, parameters of the program can change with time (See adaptive control) and digital computers are much less prone to environmental conditions than capacitors, inductors, etc.

Although a controller may be stable when implemented as an analog controller, it could be unstable when implemented as a digital controller due to a large sampling interval. During sampling the aliasing modifies the cutoff parameters. Thus the sample rate characterizes the transient response and stability of the compensated system, and must update the values at the controller input often enough so as to not cause instability.

When substituting the frequency into the z operator, regular stability criteria still apply to discrete control systems. Nyquist criteria apply to z-domain transfer functions as well as being general for complex valued functions. Bode stability criteria apply similarly.Jury criterion determines the discrete system stability about its characteristic polynomial.

The digital controller can also be designed in the s-domain (continuous). The Tustin transformation can transform the continuous compensator to the respective digital compensator. The digital compensator will achieve an output that approaches the output of its respective analog controller as the sampling interval is decreased.

Digital control theory is the technique to design strategies in discrete time, (and/or) quantized amplitude (and/or) in (binary) coded form to be implemented in computer systems (microcontrollers, microprocessors) that will control the analog (continuous in time and amplitude) dynamics of analog systems. From this consideration many errors from classical digital control were identified and solved and new methods were proposed:

The digital controller can also be designed in the z-domain (discrete). The Pulse Transfer Function (PTF) G ( z ) \displaystyle G(z) represents the digital viewpoint of the continuous process G ( s ) \displaystyle G(s) when interfaced with appropriate ADC and DAC, and for a specified sample time T \displaystyle T is obtained as:[7]

Where Z ( ) \displaystyle Z() denotes z-Transform for the chosen sample time T \displaystyle T . There are many ways to directly design a digital controller D ( z ) \displaystyle D(z) to achieve a given specification.[7] For a type-0 system under unity negative feedback control, Michael Short and colleagues have shown that a relatively simple but effective method to synthesize a controller for a given (monic) closed-loop denominator polynomial P ( z ) \displaystyle P(z) and preserve the (scaled) zeros of the PTF numerator B ( z ) \displaystyle B(z) is to use the design equation:[8]

Since process time delay manifests as leading co-efficient(s) of zero in the process PTF numerator B ( z ) \displaystyle B(z) , the synthesis method above inherently yields a predictive controller if any such delay is present in the continuous plant.[8]

A programmable logic controller (PLC) or programmable controller is an industrial computer that has been ruggedized and adapted for the control of manufacturing processes, such as assembly lines, machines, robotic devices, or any activity that requires high reliability, ease of programming, and process fault diagnosis.

PLCs can range from small modular devices with tens of inputs and outputs (I/O), in a housing integral with the processor, to large rack-mounted modular devices with thousands of I/O, and which are often networked to other PLC and SCADA systems.[1] They can be designed for many arrangements of digital and analog I/O, extended temperature ranges, immunity to electrical noise, and resistance to vibration and impact.

PLCs were first developed in the automobile manufacturing industry to provide flexible, rugged and easily programmable controllers to replace hard-wired relay logic systems. Dick Morley, who invented the first PLC, the Modicon 084, for General Motors in 1968, is considered the father of PLC.

A PLC is an example of a hard real-time system since output results must be produced in response to input conditions within a limited time, otherwise unintended operation may result. Programs to control machine operation are typically stored in battery-backed-up or non-volatile memory.

The PLC originated in the late 1960s in the automotive industry in the US and was designed to replace relay logic systems.[2] Before, control logic for manufacturing was mainly composed of relays, cam timers, drum sequencers, and dedicated closed-loop controllers.[3]

The hard-wired nature of these components made it difficult for design engineers to alter the automation process. Changes would require rewiring and careful updating of the documentation and troubleshooting was a tedious process.[4] When general-purpose computers became available, they were soon applied to control logic in industrial processes. These early computers were unreliable[5] and required specialist programmers and strict control of working conditions, such as temperature, cleanliness, and power quality.[6]

The PLC provided several advantages over earlier automation systems. It tolerated the industrial environment better than the former systems and was more reliable, compact, and required less maintenance than relay systems. It was easily extensible with additional I/O modules. While relay systems required complicated hardware changes in case of reconfiguration, a PLC can be reconfigured by loading new software. This allowed for easier iteration over manufacturing process design. With a simple programming language focused on logic and switching operations, it was more user-friendly than computers using general-purpose programming languages. Early PLCs were programmed in ladder logic, which strongly resembled a schematic diagram of relay logic. It also permitted its operation to be monitored.[7][8]

In 1968, GM Hydramatic, the automatic transmission division of General Motors, issued a request for proposals for an electronic replacement for hard-wired relay systems based on a white paper written by engineer Edward R. Clark. The winning proposal came from Bedford Associates from Bedford, Massachusetts. The result, built in 1969, was the first PLC and designated the 084, because it was Bedford Associates' eighty-fourth project.[9][10]

One of the first 084 models built is now on display at Schneider Electric's facility in North Andover, Massachusetts. It was presented to Modicon by GM, when the unit was retired after nearly twenty years of uninterrupted service. Modicon used the 84 moniker at the end of its product range until after the 984 made its appearance.[13]

In a parallel development, Odo Josef Struger is sometimes known as the "father of the programmable logic controller" as well.[11] He was involved in the invention of the Allen-Bradley programmable logic controller[14][15][16] and is credited with inventing the PLC initialism.[11][14] Allen-Bradley (now a brand owned by Rockwell Automation) became a major PLC manufacturer in the United States during his tenure.[17] Struger played a leadership role in developing IEC 61131-3 PLC programming language standards.[11]

Many early PLCs were not capable of graphical representation of the logic, and so it was instead represented as a series of logic expressions in some kind of Boolean format, similar to Boolean algebra. As programming terminals evolved, because ladder logic was a familiar format used for electro-mechanical control panels, it became more commonly used. Newer formats, such as state logic[definition needed] and function block diagram exist. Ladder logic remains popular because PLCs solve the logic in a predictable and repeating sequence, and ladder logic allows the person writing the logic to see any issues with the timing of the logic sequence more easily than would be possible in other formats.[18]

Up to the mid-1990s, PLCs were programmed using proprietary programming panels or special-purpose programming terminals, which often had dedicated function keys representing the various logical elements of PLC programs.[9] Some proprietary programming terminals displayed the elements of PLC programs as graphic symbols, but plain ASCII character representations of contacts, coils, and wires were common. Programs were stored on cassette tape cartridges. Facilities for printing and documentation were minimal due to a lack of memory capacity. The oldest PLCs used magnetic-core memory.[19]

Analog signals can use voltage or current that is proportional to the size of the monitored variable and can take any value within their scale. Pressure, temperature, flow, and weight are often represented by analog signals. These are typically interpreted as integer values with various ranges of accuracy depending on the device and the number of bits available to store the data.[24] For example, an analog 0 to 10 V or 4-20 mA current loop input would be converted into an integer value of 0 to 32,767. The PLC will take this value and transpose it into the desired units of the process so the operator or program can read it. Proper integration will also include filter times to reduce noise as well as high and low limits to report faults. Current inputs are less sensitive to electrical noise (e.g. from welders or electric motor starts) than voltage inputs. Distance from the device and the controller is also a concern as the maximum traveling distance of a good quality 0-10 V signal is very short compared to the 4-20 mA signal.[citation needed] The 4-20 mA signal can also report if the wire is disconnected along the path as a

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