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The success of proportional-integral-derivative (PID) control in the process industry is based on the ability to stabilize and control around 90% of existing processes. This importance is overshadowed, however, by a lack of performance in some applications. It has been reported that a significant percentage of installed PIDs are operated in manual mode and that 65% of the loops operating in automatic mode generate greater variance in closed-loop operation than in open-loop operation. These challenges motivated the development of the software package robust advanced PID control (RaPlD) for tuning PID controllers. RaPID is an intuitive tool with multiple levels of complexity that can be accessed according to the knowledge of the person commissioning the loop. This article describes the methods and algorithms used by RaPID for tuning PID loops.

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Robust Advanced PID Control (RaPID)

PID Tuning Based on Engineering Specifications

JAIRO J. ESPINOSA OVIEDO, TOM BOELEN, and PETER VAN OVERSCHEE

APPLICATIONS OF CONTROL

he success of proportional-integral-derivative (PID) con-

trol in the process industry is based on the ability to stabi-

lize and control around 90% of existing processes [1]. This

importance is overshadowed, however, by a lack of perfor-

mance in some applications. It has been reported that a signifi-

cant percentage of installed PIDs are operated in manual mode

and that 65% of the loops operating in automatic mode gener-

ate greater variance in closed-loop operation than in open-loop

operation [1], [2]. This lack of performance is, in many cases, the

result of a poorly tuned set of parameters due to

» lack of knowledge among operators and commissioning

personnel

» generic tuning methods based on ad hoc criteria that do

not match specific process needs

» the large variety of PID structures, which leads to errors

during application of tuning rules.

These challenges motivated our development of the software

package Robust Advanced PID Control (RaPID) for tuning PID

controllers. RaPID is an intuitive tool with multiple levels of com-

plexity that can be accessed according to the knowledge of the

person commissioning the loop. This article describes the meth-

ods and algorithms used by RaPID for tuning PID loops.

PROJECT DESCRIPTION

In the project description, the user provides information about the

control loop, such as sampling time, ranges, units, names, and

descriptions of the setpoints, the controlled variable, and the

manipulated variable. These definitions are needed to interpret

sampled data and define the limits of variables. The limits provide

saturation constraints as well as appropriate scaling of variables.

In this phase of the project, the user defines the objective

that must be achieved once the PID is tuned (either distur-

bance rejection or setpoint tracking) as well as the template of

the controller. The template of the controller contains the para-

meter format, which can be selected for several different com-

mercial PID controllers as stand-alone units or integrated in

distributed control system (DCS) units. The templates are

based on the description provided by the manufacturers,

which include Siemens, Emerson, Omron, Honeywell, and

others. The templates provide two benefits: 1) exact knowl-

edge of the controller structure to maximize the performance

of the controller hardware and 2) elimination of the need for

manual conversion of the controller parameters from the tra-

ditional Kp, Ti , and Td to the manufacturer's format. This con-

version reduces errors due to scaling and entering parameters.

The interface also allows the user to employ engineering units

rather than scaled values.

COLLECTION OF PROCESS DATA

Once the elements of a project have been decided, RaPID

uses an input-output experiment to identify the dynamics of

the plant. Experiments are costly because they interrupt nor-

mal plant operations. To minimize the impact of experi-

ments, RaPID determines a set of inputs that can be chosen

according to the present conditions and the features of the

process by adjusting parameters such as amplitude and dc

content. The available predefined input signals include step-

like (step, block, polynomial step, and saturated ramp),

impulse, sine wave (including single sine, swept sine, and

multisine), and noisy inputs, namely, random Gaussian and

pseudorandom binary noise sequence (PRBNS). Users can

also create custom input signals.

Signals generated during the experiment can be loaded

into the program by means of files or by using an object link-

ing and embedding for process control (OPC) connection to

the process computer. The OPC connection provides a reading

and writing connection by which the manipulated variable

(input) signal for the experiment can be designed in RaPID

and sent to the DCS through OPC. The controlled variable

signal is then read back and used for the identification.

IDENTIFICATION

RaPID includes a system-identification algorithm that com-

bines subspace identification and prediction error methods

[3], [4], complemented by an intuitive user interface (see Fig-

ure 1). Once the signals from the experiment are acquired,

RaPID sweeps over a set of structures to test models with

different delays and numbers of poles and zeros. The model

with the best fit is automatically selected. The algorithm

detects integral effects and applies automatic preprocessing

to remove signal offset. Advanced options include signal fil-

tering using lowpass, highpass, bandpass, and bandstop fil-

ters. These filters can be configured by selecting the cutoff

frequencies and the dynamic order. All changes can be pre-

viewed prior to being applied.

The user can also set the maximum delay and the maxi-

mum number of poles and zeros. In many cases, the opera-

tor has a good idea of the dc gain of the process. This prior

knowledge can be used by limiting the dc gain of the

model. During identification, the user can restrict the

FEBRUARY 2006

« IEEE CONTROL SYSTEMS MAGAZINE 15

presence of resonant poles as well as imaginary and right-

half plane zeros. The user can test different models with a

single click, and the model can be evaluated graphically by

comparing the simulated response with the real response or

numerically by calculating an error index, which measures

the portions of the output signal that are not correctly

explained by the model.

Although all models are identified as discrete-time sys-

tems, the results are shown in a continuous representation,

which is more intuitive to the user.

CONTROL DESIGN

PID controllers have traditionally been tuned by prescrib-

ing the shape of the closed-loop step response (Ziegler-

Nichols, Chien-Hrones-Reswick, and Cohen-Coon [1], [2]).

After the parameters are found according to the method, a

trial-and-error approach is used to achieve the desired

response, often sacrificing the robustness provided by the

original parameters.

For controller design, RaPID uses constrained optimiza-

tion to obtain the desired time response while guaranteeing

robustness. Three elements must be defined: control objec-

tive and control structure, cost function, and constraints.

Selection of the optimization criterion (cost function), control

objectives, and constraints can be done through the user

interface as shown in Figures 2 and 3. The user interface

allows interactive design of the controller, including refor-

mulation of the objectives and constraints. These elements

are described in the following sections.

Control Objective and Control Structure

The control objective is chosen by the user according to the

application. Objectives that can be pursued with RaPID include

» tracking, that is, following a prestored or real-time refer-

ence signal (servomechanism problem)

» variance control, that is, keeping the output of the sys-

tem at a setpoint while recovering as quickly as possible

from disturbances (regulator problem).

To achieve these objectives, RaPID optimizes the PID para-

meters

, K

and

as well as the parameters

α, β,

and

of the feedforward action, where the controller is repre-

sented by

16 IEEE CONTROL SYSTEMS MAGAZINE » FEBRUARY 2006

FIGURE 1 Identification panel of RaPID. The dark green signal is the

measured signal (output), the light green signal is the identified

model output, and the red line is the manipulated variable (input).

The tool calculates a set of models with different structures in terms

of poles, zeros, and delays and automatically selects the model

structure with the best performance. The user can select options by

combining this result with prior knowledge about the process.

FIGURE 2 User interface for controller optimization. "Properties"

allows the user to define constraints on noise sensitivity (HF gain)

and robustness. The calculated controller is presented according to

the definitions of the PID controller template. The resulting robust-

ness and noise sensitivity are shown. The user can define the con-

ditions of the test, such as setpoint, disturbance, and load changes.

FIGURE 3 User interface for controller optimization. This window

defines the control objectives, cost function, and overshoot con-

straints. The origin of the variance change is defined by setting the

source either as a load or as an output disturbance. The nominal

operating point is described in the entries Nominal CV (controlled

variable) and Nominal MV (manipulated variable). The cost function

can be selected as either IAE, ITAE, or energy.

U( s) = K

(α R( s ) − Y ( s )) +

(R( s ) − Y ( s ))

+ K

s + P

(β R(s)Y(s)) + K

( s + P

)

(γ R ( s ) − Y ( s ))

+ manual reset .( 1)

A block diagram of the controller (1) is shown in Figure 4.

Table 1 outlines the function of each controller element for the

different control objectives. For instance, when the control

objective is tracking, the feedback and feedforward parameters

are both optimized. On the other hand, when the objective is to

simultaneously achieve tracking and variance control, the feed-

back parameters are employed for variance control while the

feedforward parameters are targeted to the tracking objective.

Optimization Criteria

Once the control objective and the

structure (template) of the controller

have been selected, the next step in

tuning is to select criteria to evaluate

the controllers during optimization.

For optimization, RaPID uses time-

defined criteria and overall error cri-

teria. For a time-defined criterion, the

optimization minimizes the time

needed to reach a given point of the

step response. RaPID includes both set-

tling time and rise time as time-defined criteria.

Alternatively, an overall error criterion eval-

uates the error signal over a period of time (N

samples) in response to a step reference (see

Figure 5). The idea is to capture in a single

number the total deviation between the refer-

ence and the output of the system. The overall

error criteria used by RaPID are

1) integral of absolute error (IAE)

IAE =



k=1

2) energy

E =



k=1

3) integral of time multiplied by the absolute

value of error (ITAE)

ITAE =



k=1

k|e

Optimization Constraints

Optimizing the parameters of the controller based

only on the optimization criteria often results in a

controller with less than satisfactory behavior.

RaPID thus includes various constraints.

FEBRUARY 2006 « IEEE CONTROL SYSTEMS MAGAZINE 17

FIGURE 4 PID control with feedforward PD action and manual reset.

The feedforward action is used only for tracking applications. The

manual reset is a constant value added to the control action to guar-

antee bumpless transfer of the controller from manual to automatic.

PID

E (s)

R (s)

( s )

−

System

Man ual

Reset

TABLE 1

Controller functions for achieving the control objectives.

When the control objective is tracking, the feedback and feedforward

parameters are both optimized. On the other hand, when the objective is to

achieve both tracking and variance control, the feedback parameters focus

on the variance while the feedforward parameters aim at the tracking objective.

Controller Objective

Controller Section

Tracking Variance Variance

Tracking

Feedback Tracking mode Variance mode Variance mode

Feedforward Tracking mode Tracking mode

FIGURE 5 Error-based optimization criteria. The top plot shows a reference signal

and the controlled variable of the system. The error plot shows the tracking error

from the reference, calculated as the difference between the reference and the out-

put. The last three plots show instantaneous values of the signals used to calculate

the performance of the controller. Observe that the IAE criterion penalizes propor-

tionally to the absolute value of the error, the energy criterion penalizes according

to the square of the error (large errors are strongly penalized compared with small

errors), and the ITAE criterion penalizes "late" errors.

0 2 4 6 8 10 12 14 16 18 20

−1

E rror

0 2 4 6 8 10 12 14 16 18 20

0.5

IAE

0 2 4 6 8 10 12 14 16 18 20

0.5

Energy

0 2 4 6 8 10 12 14 16 18 20

ITAE

Ref vs Out

Overshoot

This constraint allows the user to specify the maximum per-

missible overshoot. This constraint can be invoked only for the

tracking control objective.

Saturation

The saturation constraint restricts the actions of the controller

to the actuator's physical limits, thus avoiding integrator

windup, which can result in poor performance or instability.

High-Frequency Gain

This constraint on the controller gain limits the effects of the

high-frequency measurement noise on the actuator. Selecting the

maximum high-frequency gain (HF-Gain) provides a trade-off

between the speed of the controller and its sensitivity to noise.

When HF-Gain is selected to be too small, the controller reacts

slowly in tracking and variance control.

Robustness

RaPID can guarantee robust stability and performance of

the optimized PID values through a robustness constraint.

Specifically, RaPID uses a parabolic constraint to prevent

the Nyquist curve from encircling the -1 point. Figure 6

illustrates the parabolic constraint, while Figure 7 com-

pares the performance of an initial PID controller with a

PID controller optimized by RaPID.

CONCLUSIONS

RaPID has been applied to hundreds of PID loops ranging from

mechanical systems to process control loops and embedded

applications. Power plants, refineries, chemical plants, and

food and beverage plants are just a few of the applications that

have benefited from this methodology.

RaPID enhances stability and safety in plant operation

while improving productivity. We believe that the robustness

of the controllers is the most likely explanation for the success

of RaPID. Reduction in down times due to actuator failures

has also been observed This reduction can be explained by the

limitation of the influence of sensor noise on the control

actions, thanks to the constraint on the HF-Gain of the con-

troller made possible by optimization. Energy savings and

increased production have also been reported; these improve-

ments are likely due to better tuning for variance control.

AUTHOR INFORMATION

Jairo J. Espinosa Oviedo (Jairo.Espinosa@ipcos.be) obtained

his electronics engineering degree from the Universidad

Distrital de Bogotá, Colombia, and master's (cum laude)

and Ph.D. (magna cum laude) degrees in electrical engi-

neering from the Katholieke Universiteit Leuven, Belgium.

He is currently a research and development engineer for

IPCOS N.V. in Leuven, Belgium. He combines his work at

IPCOS with teaching assignments at the Universidad de

Ibagué in Colombia. He is the author of Fuzzy Logic, Identi-

fication and Predictive Control.

18 IEEE CONTROL SYSTEMS MAGAZINE » FEBRUARY 2006

FIGURE 7 User interface for controller comparison. The user inter-

face shows the closed-loop simulation response of the controller

with the original PID settings (black) and the PID settings obtained

with RaPID (green). The upper figure shows the controlled variable

and the reference while the lower plot shows the manipulated vari-

able and the load disturbance. The figure shows a test in which the

setpoint (blue) is changed at time 600 s; once the plant has reached

this setpoint a load disturbance is applied (yellow). The table pro-

vides a numerical comparison of various performance measures for

the controllers.

FIGURE 6 Nyquist plot and the parabolic robustness constraint. Dur-

ing controller optimization, the robustness constraint (black) is

approximated by a parabola (magenta), which passes through the

intersection points of the robustness circle with the real axis. This

constraint guarantees robustness and stability of the system with

the optimized PID controller.

−2 −1.8 −1.6 −1.4 −1.2 −1 −0.8 −0.6 −0.4 −0.2

−1

−0.8

−0.6

−0.4

−0.2

0.2

0.4

0.6

0.8

−1+j0

Robustness

Circle

Parabolic

Approximation

Nyquist

Curve

Real Axis

Imaginary Axis

Tom Boelen received his M.Sc. in agricultural engineering in

1997 from the Katholieke Universiteit Leuven. He was a

researcher in the field of biological process technology at the same

university. He joined ISMC in 1998 and is currently a project engi-

neer for projects in the chemical and petrochemical industry.

Peter Van Overschee received his M.Sc. degree in applied

sciences in 1989 at the Katholieke Universiteit Leuven, Bel-

gium. In 1990 he received his M.Sc. degree in electrical engi-

neering at Stanford University, California. In 1996 he received

the Automatica Best Paper Award. He is president of IPCOS

Belgium and is responsible for projects in the oil industry.

REFERENCES

[1] A. O'Dwyer, Handbook of PI and PID Controller Tuning Rules. London:

Imperial College Press, 2003.

[2] K. Aström and T. Hagglund, PID Controllers: Theory, Design and Tuning .

Research Triangle Park, NC: Instrum. Soc. Amer., 1995.

[3] L. Ljung, System Identification — Theory for the User. Englewood Cliffs, NJ:

Prentice-Hall, 1999.

[4] P. Van Overschee and B. De Moor, Subspace Identification for Linear Sys-

tems. Norwell, MA: Kluwer, 1996.

[5] Rapid, Robust advanced PID control. Course Control Theory Hands on Tuning

and Application, Leuven: IPCOS N.V., 2004.

[6] G.F. Franklin, J.D. Powell, and M.L. Workman, Digital Control of Dynamic

Systems. Reading, MA: Addison-Wesley, 1990.

[7] F.G. Shinskey, Process Control Systems, Application, Design and Tuning .

New York: McGraw-Hill, 1996.

[8] P.B. Deshpande, Multivariable Process Control. Research Triangle Park,

NC: Instrum. Soc. Amer., 1989.

[9] P. Friedman, Economics of Control Improvement. Research Triangle Park,

NC: Instrum. Soc. Amer., 1995.

[10] M. Morari and E. Zafiriou, Robust Process Control. Englewood Cliffs, NJ:

Prentice Hall, 1999.

he Atacama Large Millimeter Array (ALMA) (see Figure

1) is an international radio astronomical facility current-

ly under construction in Chile through the collaboration

of institutions in the United States, Canada, Europe, and

Japan [1]. When completed, the facility will consist of an

array of up to 64 12-m parabolic antennas that can detect mil-

limeter and submillimeter wavelength radio waves in the fre-

quency band between 31–950 GHz. The antenna will be

located at an elevation of 5,000 m on the Chajnantor plain in

the district of San Pedro de Atacama. At these wavelengths,

the radiotelescope array will be able to reveal the structure of

the cold regions of the universe, otherwise dark at visible

wavelengths, with unprecedented sensitivity and a resolution

of 10 milliarcseconds. This resolution is an order of magni-

tude better than the Hubble telescope or the very large array

operating in New Mexico.

ALMA achieves its exceptional resolution and sensitivity

by linking all of the 64 antennas into an interferometer array.

In this setup, the exact instant at which a radio wave reaches

each of the antennas is precisely recorded. Since the relative

position of each antenna is well known, the source of the wave

can be accurately pinpointed by comparing the timing (or

phase) of the wave arriving at any one antenna relative to the

other antennas using real-time correlator systems. The dis-

tance between two antennas is known as the baseline. A large

baseline causes signals to arrive at the antennas with a large

differential delay, and thus accurate angular resolution can be

achieved. The ALMA antennas can be moved into different

configurations like chess pieces using a specially designed

truck to achieve different combinations of resolution and sen-

sitivity. The maximum resolution is obtained with baselines

up to 18 km.

To accurately measure the phase of the sky signal over the

entire array or subarray, every antenna must receive a highly

stable common reference signal known as the local oscillator

(LO) reference. For ALMA, this LO reference signal is com-

posed of two optical waves sent through a single optical fiber

[2]. Both waves have a wavelength around 1.556

m to allow

transmission through conventional telecommunication optical

fiber with little loss. One optical wave is generated by a mas-

ter laser (ML), while the other is generated by phase-locking a

slave laser at a given frequency offset from the master. Both

Precision Timing Control for Radioastronomy

Maintaining Femtosecond Synchronization in the Atacama Large Millimeter Array

JEAN-FRANÇOIS CLICHE and BILL SHILLUE

FIGURE 1 Artist's rendition of the ALMA radiotelescope, which will

consist of up to 64 12-meter parabolic antennas spread over 18 km.

The array will receive cosmic signals from 31–950 GHz. Image

courtesy of NRAO/AUI and computer graphics by ESO.

FEBRUARY 2006

« IEEE CONTROL SYSTEMS MAGAZINE 19

... Performance criteria: To measure the performance of a PID controller, there have been some criteria defined as equations (11)-(14) (Oviedo et al., 2006) In this study, percent of overshoot and abovementioned parameters have been considered either separately or collectively when the cost function hits the minimum, to optimize performance of PID controller using metaheuristic algorithms. ...

Aim of this study is to present two optimal methods for adjusting parameters of PID controllers using Simulated Annealing (SA) and Particle Swarm Optimization (PSO) algorithms to achieve the desired goal intended for application of these controllers. Through adding intelligent techniques to the SA algorithm, it will lead to a higher speed and the reduction of the error in the PID controller. Available rules for setting PID parameters are commonly trial and error which involve various issues like being very time consuming, imprecise and facing a significant number of errors. Using performance measurement criteria and integrating them, an attainable method has been presented for setting these parameters which has a very high accuracy as wells as a significant speed, with a very low rate of error. Results obtained in this research demonstrate a considerable efficiency compared with that of other proposed methodologies

... Correspondingly, it has become more and more significant to boost the robustness of PID controller and also enhance its capacity of dealing with strong nonlinearities. In this regard, some relevant works can be found in [6,16,24] . Furthermore, considering the advantages of fuzzy logic, a nonlinear control law can be achieved in the fuzzy logic frame which has, in turn, inspired many researchers to combine PID control law with different fuzzy models, see e.g., [9,15,25,30,32] . ...

... It is estimated that approximately 90% of the current industrial controllers are of the PID type due to its simplicity, low cost and robustness (de Castro et al., 2016;Oviedo et al., 2006;Abdel-Geliel et al., 2014). However, for practical applications with nonlinearities or dead time, which are very common characteristics in industrial processes, the performance of regular PID controllers is not satisfactory. ...

This paper analyses anti-windup techniques applied to processes with presence of measurement noise.

... For an overview of the tuning methods the reader is referred to Aström and Hägglund (2005); Datta et al. (2000); Tan et al. (1999). It has been suggested that the reasons of poorly tuned parameters are the lack of knowledge among operators and commissioning personnel, generic tuning methods that do not match with the specific process needs and the large variety of PID structures, which leads to errors during the application of tuning rules (Oviedo et al. (2006)). One of the main problems is the tuning of the derivative term, which in 80% of the cases is switched off or completely omitted (Digest (1996)). ...

Guillermo P. Falconí
Jürgen E. Ackermann

In this paper an extension of the Matlab-tool PIDrobust is presented. This tool calculates the entire set of PID controllers that stabilizes a set of linear systems with time delay simultaneously. On this basis an iteratively algorithm is used to improve σ-stability in order to assist operators. At the end of the process the operator is able to judge the results and interactively choose a controller. This tool needs much less computational effort than other optimization methods and achieves similar performance. It is can also be used for tuning robust controllers by means of the parameter space approach.

Carlúcio Pereira Da Silva
Luiz Fernando Marquez Arruda
Diego Santos Greff

The proposal for this work deals with a technique for controlling a Boost-type DC-DC converter, called Instantaneous Adaptative Neural Network Controller (IANNC). The proposed control method uses a Perceptron neural network that seeks to maintain the voltage converter output. Through IANNC it is possible to establish the appropriate working cycle for the Pulse Width Modulation (PWM) control signal. The proposed method was confronted with a typical Proportional Integral (PI) controller aiming to validate the model. The results were obtained using the PSIM simulator, where, in particular, the stability of the converter's output voltage against an R load was considered. Resumo: A proposta para este trabalho trata de uma técnica para controle de um conversor CC-CC do tipo Boost, denominada Instantaneous Adaptative Neural Network Controller (IANNC). O método de controle proposto utiliza de uma rede neural do tipo Perceptron que busca manter estável a tensão de saída do conversor. Por meio do IANNCé possível estabelecer o ciclo de trabalho adequado para o sinal de controle Pulse Width Modulation (PWM). O método proposto foi confrontado com um controlador Proporcional Integral (PI) clássico objetivando validar o modelo. Os resultados foram obtidos por meio do simulador PSIM, onde, especialmente, considerou-se a estabilidade da tensão de saída do conversor frente a uma carga R.

Alexander A. Dyda
Nguyen Van Thanh Van Thanh
Ksenya N. Chumakova

The purpose of this work is to study the possibilities of improving the quality of the processes of controlling the movement of the vessel along the course by combining individual standard controllers. Of the known scientific directions devoted to the problem being solved, the closest is the theory of systems with variable structure, in which, due to switching, a unique useful property is achieved, which are not possessed by individual switched structures. The article is devoted to the approach to the construction of the ship course control system, which is based on the principle of switching regulators during the transient process. This makes it possible to improve the quality of control processes in the system by using the features of individual regulators, in particular, the application of the switching principle made it possible to significantly increase the speed of the system in comparison with systems without switching and ensure the desired monotonic nature of the control process. The proposed approach is illustrated based on switchable P-controllers. The results of modeling the developed ship course control system are presented and discussed.

Grid-scale electrical energy storage (EES) systems are enabling technologies to enhance the flexibility and reli-ability of electricity grids with high penetration of intermittent renewable energy sources such as solar and wind. They allow excess of generation to be stored for later use and can respond quickly to power fluctuations. Un-fortunately, there is no single type of EES technology that can effectively fulfill all the desired requirements. Hybrid EES (HEES), combining two or more EES, are an emerging, viable solution. While batteries have a higher energy density, supercapacitors (SC) have a higher power density and are characterized by a fast discharge rate. The combination of both technologies results in a HESS solution which can address the challenges associated with the large-scale deployment of distributed renewable energy sources and enhance the grid reliability. The goal is to design a power management strategy to enhance the performance of the HEES. This paper proposes various robust design methods for the control of the power electronics converters and enhance the performance of the power management of the HEES. These robust design strategies are based on pole placement, linear matrix inequalities (LMI), particle swarm optimization (PSO) and genetic algorithm (GA). The performance of these control schemes is compared in terms of the transient response time and robustness. The results obtained demonstrate the effectiveness of the power management strategy (PMS) for the photovoltaic (PV) system with HEES and the enhanced robustness of the controllers using GA and PSO-based tuning techniques.

Jun Qi
Yuanchao Li
Linlin Ou

Wide‐area damping control is able to improve the stability of inter‐connected power systems in case of low‐frequency oscillations. Nevertheless, the damping effect is closely related to the time delay of wide‐area control loops. The application potential of proportional‐integral‐derivative (PID) damper is explored in wide‐area power system damping control. First, the relative residue index based on dominant oscillation modes is employed to determine a suitable control loop. Then, the PID stability space is calculated numerically based on extended Hermite–Biehler Theorem. Finally, the damping‐robustness balance principle is discussed in the PID parameters selection. The proposed PID damper is tested by supplementing the generator excitation control in the two‐area four‐machine power system and the static var compensator control in the 16‐machine 68‐bus power system. Simulation results confirm that it is feasible to design a PID damper for the control loop with a larger relative residue index. The designed PID damper is able to enhance power system stability by inhibiting low‐frequency oscillations under considerable time delays, and it is robust to the changes of system operation state and time delay.

Yusen Li
Liying Cao
Ye Wang

The paper proposes a gas turbine flowmeter with adding the technology of automatic gain control (AGC). This design is using MSP430F169 chip. The main function modules and test results of this are given in the paper. This design can solve the disadvantage of signal degradation caused by the external environmental factors when using the gas turbine flowmeter in practical application. This gas turbine flowmeter has advantages of good precision, high rangeability, little environment influence, good stability and excellent reliability. The output signal can be adjusted according to the strength of the received signal so that it in certain dynamic range is realistic. The experimental results show that the quality of the output signal is improved by applying the technology of automatic gain control to the gas turbine flowmter in practical use.

In this Chapter we treat the subspace identification of purely deterministic systems, with no measurement nor process noise (vk ≡ wk ≡ 0 in Figure 1.4). We treat this problem for two reasons: Most of the conceptual ideas and geometric concepts, which will also be used in the Chapters to follow, are introduced by means of this simple identification problem. We treat the problem from a different point of view as in the literature, which makes it easier to assimilate it as a special case in the Chapters to follow. Similarities between the presented algorithm and the literature are pointed out.

Gene F. Franklin
J.D. Powell

This well-respected work discusses the use of digital computers in the real-time control of dynamic systems. The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude. MATLAB statements and problems are thoroughly and carefully integrated throughout the book to offer readers a complete design picture. Many of the figures in the book were created by Matlab files, which are available to download at the link below for interested readers.

W. Harmon Ray

A survey is provided of the state of the art in multivariable process control. Recent literature is organized and tabulated by topic to provide material for further study. The survey encompasses both linear and nonlinear multivariable systems, on-line estimation, adaptive control, distributed systems, and recent developments in computer-aided control system design. These developments together with recent applications provide the basis for predictions of the future evolution of the field.

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