Give the Advantages of a Digital Control System Over a Continuousdata Control System

Basic principles of control systems in textile manufacturing

S.S. Saha , in Process Control in Textile Manufacturing, 2013

2.4 Digital control systems

The extraordinary development of digital computers (microprocessors, microcontrollers) and their extensive use as controllers in a variety of fields and applications, has brought about important changes in the design of control systems. The superior performance, low cost and design flexibility now available in various types of control systems has significantly increased the popularity of digital controllers over analogue controllers in many applications.

In principle, a digital control system is similar to an analogue control system. Here, the analogue controller block is replaced with a digital computer, which performs the task of generating the required signal for the actuator, as shown in Fig. 2.18. Since digital computers deal only with binary numbers, an analogue-to-digital (A/D) converter is required before the controller stage for converting the analogue error signal into digital form. It does so by sampling the analogue signal at periodic intervals and then holding over the sampling interval. Conversely, a digital-to-analogue (D/A) converter is also required after the controller stage as the actuator operates on the analogue signal.

2.18. Block diagram of closed-loop digital control system.

The digital controllers have several advantages over analogue schemes, some of which are as follows:

•

Flexibility in control action: modification of an analogue controller can only be made through rewiring and replacement of a component, whereas a simple change to the computer program is all that is required for the modification of a digital controller.

•

Reduced cost involvement for addition of further control loops: the addition of extra loops in digital controllers merely requires any extra hardware to be connected up to the same computer, whereas additional hardware loops would otherwise be required for an analogue controller.

•

Improved user interface: digital controller information can be displayed graphically on a monitor when required, as opposed to the analogue alternative of employing a large panel for displaying limited information.

•

Adaptive control: digital controllers can be modified online, that is, even when the system is in operation.

•

Cost effective: due to the rapid development of VLSI technology, the cost of digital controllers is decreasing in comparison to that of analogue controllers, especially for applications requiring high accuracy and optimum performance.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780857090270500023

Control Systems

William Bolton , in Instrumentation and Control Systems (Third Edition), 2021

4.6 Digital Control Systems

With analog control systems all the signals are analogs, i.e. a scaled version, of the quantities they represent. Digital signals, however, are sequences of pulses, i.e. on–off signals, with the value of the quantity being represented by the sequence of on–off signals. Most of the signals being controlled are analog and thus it is necessary with a digital control system to convert analog inputs into digital signals for the controller and then the digital outputs from the controller to analog for the process being controlled. Thus analog-to-digital converters (ADCs) (see Chapter 2.9.5) and digital-to-analog converters (DACs) (see Chapter 2.9.6) are used. Figure 4.29 shows the basic form of a closed-loop digital control system.

Figure 4.29. The basic elements of a digital closed-loop control system.

Digital controllers can be microcontrollers or computers. A microcontroller is an integration of a microprocessor with memory, input/output interfaces and other peripherals such as timers on a single chip (see Chapter 2.9.7). The microcontroller effectively incorporates the comparison element, the controller, the DAC and the ADC. At some particular instant the microcontroller samples its input signals. There is then an input of the required analog value to the microcontroller and the measured analog value of the output. It then carries out its program and gives an analog output to the correction element. The microcontroller then repeats its program for the next sample of signals. The program followed by the microcontroller is thus:

Take a sample of the signals at its inputs, i.e. read the required value input and read the actual measured value of the output, i.e. the feedback signal, at its ADC input port

Calculate the error signal

Calculate the required controller output

Send the controller output to its DAC output port

Wait for the next sampling interval

Repeat the process.

Digital control has advantages over analog control in that digital operations can be easily controlled by a program, i.e. a piece of software, information storage is easier, accuracy can be greater and digital circuits are less affected by noise.

As an illustration of a digital control system, Figure 4.30 shows the system for the control of the speed of rotation of a motor shaft which was represented by an analog system in Section 4.4.1.

Figure 4.30. Control of the speed of rotation of a shaft.

The control systems so far considered are essentially concerned with a single loop for which there is a single set point, a single controlled variable and a single actuator. However, in many control situations there are more than one variable being controlled. Modern automobiles have engine management microcontrollers which are used to exercise control over the large number of systems in such automobiles. The engine control unit aims to ensure that the engine operates at optimal conditions at all times and thus exercises control over such items as fuel injection, spark timing, idle speed and anti-knock. It does this by taking inputs from a number of sensors, interpreting the values and then giving output to adjust the operation of the engine. There are also systems for such items as braking and traction control, suspension control, cruise control, air conditioning, air-bag systems and security systems.

While with control systems having more than one variable, more than one sensor and more than one actuator it would be possible to wire each situation independent of the other with its own controller, there are advantages in using a single controller to control the inputs for more than one sensor. This does allow more than one variable to be taken into account in arriving at the optimum outputs for sensors but also it is possible to simplify the wiring by using a bus connector so that each sensor and actuator is connected locally into a common connection termed a bus (Figure 4.31). Sensors and actuators are then in communication with the bus controller via a common connection, each such sensor and actuator being uniquely identified to the controller so that information can be supplied from supervisory control to specific sensors and specific actuators and receive information back from them.

Figure 4.31. A bus system.

The term fieldbus is used for such a bus system that conforms to the IEC 61158 specification, there being a number of such bus systems. The standard defines the physical means by which the buses can be realised and the means by which devices connected to a bus can communicate with a controller and receive control instructions. Fieldbus are bi-directional, digital serial networks with the data being put on bit by bit along a single connector. In process control, the main buses used are the FOUNDATION Fieldbus and PROFIBUS PA. FOUNDATION Fieldbus is a digital, serial, two-way communication system widely used as the network in process industries. PROFIBUS was designed specifically for use with programmable logic controllers in control networks (see Chapter 7). The bus most used in automobiles is the CAN bus (see Chapter 13 for more discussion of bus systems).

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780128234716000046

Implementing Digital Feedback

Alex Krasner , in Power Converters with Digital Filter Feedback Control, 2016

Abstract

Developing digital controllers requires the designer to assess both the analog circuitry around the controller and the digital logic within the controller. When implementing a digital controller, there are no limitations on how to interface the analog environment with the digital logic. Several main concerns must be addressed for proper integration. First, supplying DC power rails to the controller and providing local digital and analog grounds to limit noise and ground loops. Second, signal conditioning and data acquisition via analog-to-digital converters. This includes adequate filtering, buffering, and scaling of analog signals so that they can be accurately quantized without aliasing and error. Third, representation of data in the digital domain via fixed-point representation. Fourth, implementation of digital feedback loops and filters. Digital filters are sensitive to quantization error, sampling rate, and timing constraints; they can become unstable if any is improperly set. This can lead to unwanted effects within the control loop. And finally, implementation of gate drivers to translate the digital logic to the power supply control. When all of these concerns are addressed, then the digital controller can be implemented and will rival the performance of "analog" IC, which are normally used for power supply control applications.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780128042984000113

Introduction

Edmund Lai PhD, BEng , in Practical Digital Signal Processing, 2003

1.4.4 Control applications

A digital controller is a system used for controlling closed-loop feedback systems as shown in Figure 1.8. The controller implements algebraic algorithms such as filters and compensatory to regulate, correct, or change the behavior of the controlled system.

Figure 1.8. A digital closed-loop control system

Digital control has the advantage that complex control algorithms are implemented in software rather than specialized hardware. Thus the controller design and its parameters can easily be altered. Furthermore, increased noise immunity is guaranteed and parameter drift is eliminated. Consequently, they tend to be more reliable and at the same time, feature reduced size, power, weight and cost.

Digital signal processors are very useful for implementing digital controllers since they are typically optimized for digital filtering operations with single instruction arithmetic operations. Furthermore, if the system being controlled changes with time, adaptive control algorithms, similar to adaptive filtering discussed above, can be implemented.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780750657983500011

Review of the Frequency Domain

George Ellis , in Observers in Control Systems, 2002

3.2.6 Sample-and-Hold

Digital controllers calculate the output once each cycle and hold it constant until the next cycle. This sample-and-hold (S/H) is present in virtually all digital systems. The effect of holding the output constant introduces phase lag because the output is aging from the time it is stored. At the start of the cycle the data is fresh, but by the end of the cycle, the output is a full cycle old. Since the stored data are, on average, one-half cycle old, the S/H acts approximately like a delay of a half cycle

(3.12) $T_{\text{S}/\text{H}}\left(z\right)\simeq e^{-sT/2}=1\angle \left(-\omega T/2\right)\text{rad}$

or, in degrees and Hz,

(3.13) $T_{\text{S}/\text{H}}\left(s\right)\simeq 1\angle {\left(-180\times F\times T\right)}^{°}.$

At higher frequencies, the S/H also begins attenuating the input. The more exact transfer function for S/H is

(3.14) $T_{\text{S}/\text{H}}\left(z\right)=\frac{z-1}{Tz}\left(\frac{1}{s}\right).$

which is digital differentiation in series with analog integration. This form is shown as a zero-order hold in [7, p. 754, although the T is not included. Few textbooks include the T, although it is required to reflect the sample-and-hold's intrinsic unity DC gain. Recognizing that z=e ^sT, some algebra can provide Equation 3.14 in a simpler form for sinusoidal excitation:

$\begin{array}{ll}{T}_{s/H}\left(z\right)& =\frac{z-1}{Tz}\left(\frac{1}{s}\right)\\ & =\frac{e^{sT}-1}{e^{sT}}\left(\frac{1}{Ts}\right)\\ & =\frac{e^{sT/2}-e^{-sT/2}}{e^{sT/2}}\left(\frac{1}{Ts}\right).\end{array}$

To apply steady-state sinusoids, set s=j ω,

(3.15) $\begin{array}{ll}{T}_{s/H}\left(z\right)& =\frac{e^{j\omega T/2}-e^{-j\omega T/2}}{e^{j\omega T/2}}\left(\frac{1}{Tj\omega }\right)\\ & =e^{-j\omega T/2}\times \frac{e^{j\omega T/2}}{2j}\times \frac{1}{\omega T/2}\\ & =e^{-j\omega T/2}\times \frac{\sin \left(\omega T/2\right)}{\omega T/2}\\ & =\left(\frac{\sin \left(\omega T/2\right)}{\omega T/2}\right)\angle \left(-\omega T/2\right)rad.\end{array}$

So, the precise sample-and-hold (Equation 3.15) and the approximation (Equation 3.12) have the identical phase lag, but different gains. The gain term, sin(ωT/2)/(ωT/2), also known as the sync function, is nearly unity for most frequencies of interest. For example, at one fourth the sample frequency (ω= 2π/4T), the sync function evaluates to 0.9dB, which is a value so close to 0dB that it can usually be ignored. And recognizing that usually the system bandwidth will be at much lower frequencies, say one tenth the sample frequency, there is rarely much interest in the precise gain at so high a frequency. This is why the simpler Equation 3.12 is accurate enough to use in most control systems problems.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780122374722500043

The z-Domain

George Ellis , in Control System Design Guide (Fourth Edition), 2012

5.6.3 Sample-and-Hold

Digital controllers calculate outputs once each cycle. That output is stored, often in a D/A (digital-to-analog) converter, and then held constant until the next cycle. This function, sample (output to D/A)-and-hold (keep constant for one cycle), is rare in analog systems but present in virtually all digital systems.

The effect of holding the output constant introduces phase lag because the output is getting old from the time it is stored. By the end of the cycle, the output is a full cycle old. As discussed in Section 4.2.1, since the data is, on average, one-half cycle old, the sample-and-hold (S/H) acts like a delay of a half-cycle. That is, in fact, an excellent approximation:

(5.30) $T_{S/H}(z)\mathrm{\approx }{e}^{-sT/2}=1\angle (-\mathrm{\omega }T/2)\text{rad}$

or, with the result in degrees and F in Hz,

(5.31) $T_{S/H}(s)\mathrm{\approx }1\angle (-180\times F\times T)°$

At higher frequencies, the S/H also begins attenuating the input somewhat. The more exact transfer function for S/H is

(5.32) $T_{S/H}(z)=\frac{z-1}{Tz}\left(\frac{1}{s}\right)$

which turns out to be digital differentiation cascaded with analog integration. This form is shown as a zero-order hold in Ref. 33, although the T is not included. Few textbooks include the T, although it is required to reflect the sample-and-hold's intrinsic unity DC gain.

Recognizing that z  = e^sT , some algebra can provide Equation 5.32 in a simpler form for sinusoidal excitation:

$\begin{array}{c}{T}_{S/H}(z)=\frac{z-1}{Tz}\left(\frac{1}{s}\right)\\ =\frac{e^{sT}-1}{e^{sT}}\left(\frac{1}{Ts}\right)\\ =\frac{e^{sT/2}-e^{sT/2}}{e^{sT/2}}\left(\frac{1}{Ts}\right)\end{array}$

To apply steady-state sinusoids, set s  = jω

(5.33) $\begin{array}{c}{T}_{S/H}(z)=\frac{e^{j\mathrm{\omega }T/2}-e^{-j\mathrm{\omega }T/2}}{e^{j\mathrm{\omega }T/2}}\left(\frac{1}{Tj\mathrm{\omega }}\right)\\ =e^{-j\mathrm{\omega }T/2}\times \frac{e^{j\mathrm{\omega }T/2}-e^{-j\mathrm{\omega }T/2}}{2j(\mathrm{\omega }T/2)}\\ =e^{-j\mathrm{\omega }T/2}\times \frac{\sin (\mathrm{\omega }T/2)}{\mathrm{\omega }T/2}\\ =\left(\frac{\sin (\mathrm{\omega }T/2)}{\mathrm{\omega }T\text{/2}}\right)\angle -\mathrm{\omega }T/2\text{rad}\end{array}$

So the precise sample-and-hold (Equation 5.33) and the approximations presented in Equations 5.30 and 5.31 (and Equation 4.1) have the same phase lag (   −ωT/2 radians) but different gains. The gain, sin (ωT/2)/(ωT/2), also known as the sync function, is nearly unity for most frequencies of interest. For example, at one-fourth the sample frequency (ω   =   2π/4T), the sync function evaluates to 0.9, or about   −1 dB, which is a value so close to 0 dB that the difference can usually be ignored. And recognizing that the system bandwidth will usually be at much lower frequencies, say, 1/10^th the sample frequency, there is rarely interest in the precise gain at so high a frequency. Even at the Nyquist frequency, the sync function evaluates to 0.637, or   −4 dB, a value that can often be ignored, considering that this is the highest frequency the system can process. This is why the simpler forms (Equations 4.1, 5.30, and 5.31) are sufficiently accurate to use in most controls problems.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780123859204000059

Power Outputs

Martin Bates , in Interfacing PIC Microcontrollers (Second Edition), 2014

7.9.4 Analogue Servo

Before digital controllers became available, analogue position and speed control was used in servo systems. In a basic position system, a potentiometer (pot) attached to the motor shaft provides a voltage that represents its current position ( Figure 7.21(b)). The required position is set on a manual pot (or from an external controller) connected to one input of a difference amplifier, with the feedback voltage applied to the other input. A linear power amplifier (see above) then drives the motor until the voltages match and the motor stops.

An equivalent speed control system would use a tachogenerator (tacho) to measure the output shaft speed. This is a small d.c. generator that outputs a voltage or current in proportion to the speed of the shaft (a permanent magnet d.c. motor will produce this effect if the shaft is driven and the voltage measured at the terminals). As in the position servo, a difference amplifier controls the motor power until the target speed is achieved. This system illustrates the operation of a PID (proportional, integral and derivative) controller, which is still relevant to digital controllers because the mechanical load will produce the same responses due to inertia and friction.

The dynamic response is shown in Figure 7.21(c). Depending on the tuning of the amplifier and the physical characteristics of the system, the output can respond to a step change at the input in two main ways. If the slew rate of the system is slow, an under-damped response will be obtained. If too fast, the output can overshoot the target position and exhibit damped oscillation until finally settling to the target position. The ideal response is critically damped, where the response is as fast as possible without overshooting.

PID control requires the transient behaviour of the amplifier to be adjustable. The system response can be represented by a second-order differential equation, and PID control corresponds to adjusting the constants in that model to modify the transient and steady-state response of the system. This form of control can also be implemented in a digital controller using a fast DSP (digital signal processor) chip, where the PID variables are controlled in software. The motor drive amplifier would then be controlled via a high-speed DAC and the shaft speed monitored by a tachometer (speed) or pot (position) and ADC.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780080993638000078

Industrial control systems

Peng Zhang , in Advanced Industrial Control Technology, 2010

(d) Real-time controllers

Real-time digital controllers are special-purpose industrial devices used to implement real-time control systems. There are two types; the first are called real-time controllers, and are specially made industrial computers that are adapted for industrial process and production controls. The second are purpose-built digital controllers such as PLC, CNC, PID, and fuzzy-logic controllers which are embedded with a RTOS in their own microprocessor units. The first type was discuss in the section on hardware. The second kind of digital controllers will be discussed in Part 4 of this textbook.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9781437778076100014

Modern Control Architectures and Implementation

Óscar Lucía , ... José I. Artigas , in Control of Power Electronic Converters and Systems, 2018

29.4.1 Introduction

Assuming that the digital controller is described using a HDL, such as VHDL, the power converter and the digital controller must be simulated together in order to verify the functionality of the HDL description and to select the word length of the signals in the controller architecture.

There are different alternatives to simulate this mixed (analog + digital) system [21,22]. One approach is to use mixed-signal simulation tools. Another approach is to describe the power electronic converter in VHDL and use only an event-driven simulator.

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780128161364000300

Introduction to Digital Signal Processing

Ian Grout , in Digital Systems Design with FPGAs and CPLDs, 2008

Example 4: Proportional (P) Control

Consider a digital controller that is to perform proportional control. The controller will accept two inputs, the command input and feedback signals, and will output a single controller output, the controller effort signal. The two inputs are initially subtracted and multiplied by a gain value (the proportional gain Kp is set here to +7). This gain value is held in a ROM. The arrangement for this controller is shown in Figure 7.29, and here, the internal wordlength increases as the values pass through the arithmetic operations, but finally will be limited to eight bits at the controller output (the inputs are also eight bits). The multiplication in this example is undertaken using a digital multiplier. Figure 7.30 provides the VHDL code for the structure of this design. In this implementation, each block will be coded as a unique entity-architecture pair, although this might not necessarily be the best solution. The design here is purely combinational logic and as such includes no clock or reset inputs.

Figure 7.29. Digital proportional gain

Figure 7.30. Digital proportional gain VHDL structure code

Figure 7.31 shows the schematic for the synthesized VHDL code using the Xilinx^® ISE™ tools. When a digital multiplier is required and the coefficient is fixed, then an alternative to using a digital multiplier is to use a shift-and-add operation. For example, multiplying a value by 2 is a shift-left operation by one bit—simple and easy to do in digital logic and avoids the need for a large digital multiplier.

Figure 7.31. Digital proportional gain schematic for the synthesized VHDL code

Read full chapter

URL:

https://www.sciencedirect.com/science/article/pii/B9780750683975000076

blaggreaddligning.blogspot.com

Source: https://www.sciencedirect.com/topics/engineering/digital-controller

Share this post