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The author developed two GUIs for asymptotic Bode plots and identification from such plots aimed at improving the learning of frequency response methods: these were presented at UKACC Control 2012. Student feedback and reflection by the author suggested various improvements to these GUIs, which have now been implemented. This paper reviews the earlier work, describes the improvements, and includes positive feedback from the students on the GUIs and how they have helped their understanding of the methods.

This technical note outlines an approach to the problem of synthesizing fixed-structure low-order controllers for systems whose mathematical models are unknown, but their frequency responses are available. Stability of the closed-loop system is guaranteed if the frequency response of the plant and the controller satisfy certain conditions at specific frequencies. It is shown that the relation between the rate of change of phase of the plant and the controller, at specific frequencies, characterizes the closed-loop system stability. We use this characterization in a systematic way to design fixed-structure low-order controllers such as PI and PID-controllers.

This paper presents a loop-shaping method for robust control design that can account for structured uncertainties using modifications of the classical Bode plot. By using this method, the robust performance criterion is explicitly translated into allowable and forbidden regions on Bode plot of a compensated SISO system. There is no need for transfer function-based models of the plant, the sensitivity function performance, or the uncertainty. As a result, the designed controllers are able to avoid excessive conservativeness that may lead to high-order controllers while improving the control performance. This paper shows utility of the proposed method by applying it to a head-positioning control system in a hard disk drive.

The paper deals with the frequency domain decentralized discrete-time controller design methodology to guarantee specified performance of the overall system. The underlying theory evolves from the stability conditions developed in the “Equivalent Subsystems Method” approach and applies closed-loop performance specification based on the relationship between phase margins of equivalent subsystems and maximum overshoot of the full system. To design local PI controllers for specified phase margin, Bode plots of discrete equivalent subsystems are used. Designed local continuous controllers are then converted to their discrete versions and implemented for the controlled plant. The design procedure is illustrated on the case study.

Actuators and Sensors, Implemented Solutions. The frequency response is undoubtly one of the basic methods of measure and characterization of systems. The knowledge of this technique and its application is essential in subjects such as Automatic and Electronic. In this paper a low cost circuit that allows to obtain, automatic or semiautomaticaly, the frequency response of a linear system is presented. This circuit, that responds to a specific design of the authors, will be called “bodemeter” due to its obvious application for drawing the Bode plot. The input and output of the system to study are directly connected to the bodemeter. This can be used with conventional instrumentation or it can be connected to a personal computer through a data acquisition card. The computer does not require any special characteristic as for speed, and it is solely recommendable to use a graphic output to visualize the plots; this characteristic is broadly overcome at present. The data acquisition card does not need special features either and any conventional low cost card can be used.

In this paper, a method for the auto-tuning of fractional order PIΛ Dμcontrollers using relay feedback tests is proposed. A design method for this kind of controllers is discussed, based on the magnitude and phase measurement of the plant to be controlled from relay feedback tests at a frequency of interest. Simple relationships among the parameters of the fractional controller are established and specifications such as the static error constant (kss), phase margin (ϕm) and gain crossover frequency (ωC) can be fulfilled, with a robustness argument by inspecting the flatness of phase Bode plot of the controller. An illustrative example of application is presented to show the reliability and effectiveness of the method.

In this paper, a method for auto-tuning of a fractional order lead-lag compensator using relay feedback tests is proposed. A design method for this kind of compensators is discussed, based on the magnitude and phase measurement of the plant to be controlled from relay feedback tests at a frequency of interest. Simple relationships among the parameters of this fractional controller are established and specifications such as the static error constant (kss), phase margin (φm) and gain crossover frequency (ωc) can be fulfilled, with a robustness argument by inspecting the flatness of phase Bode plot of the compensator. The auto-tuning method proposed can be taken as a first step for a latter generalization of these lead-lag compensators to the fractional PIΛDμ controllers.

In this paper, we show that the complete set of PID controllers that stabilizes a LTI plant and achieves prescribed performance levels, can be computed from knowledge of only the frequency response (Nyquist or Bode plot) of the plant and the number of RHP poles. The result is of practical importance in many situations where transfer function or state space models are not available and a design procedure that is free of analytical models is desired. The synthesis method also gives useful information on the frequency range over which accurate frequency response data on the plant is needed for PID design.

This paper presents a new limiting loop shaping technique for tuning the robust optimal LQ-PID regulators by the suitable weighting factors Q and R in order to satisfy the performance requirements. The technique is developed by pushing all two zeros formed by PID controller closely to a larger pole of the second order plant. As a result, an improved loop shaping is achieved in the high frequencies region on the Bode plot.

Recently a method has been introduced for finding the minimum bounds of the frequency response of a system with variable parameters on Bode gain/phase diagrams. The results are easily derived from classical control frequency response concepts and provide a simple way of introducing the concepts of control system design under parameter uncertainty to undergraduates. This paper describes the method and shows how it can be used for investigating stability and the design of simple classical compensators. Use of the method for interactive education is also discussed.

This paper analyses the dynamical properties of systems with nonlinear friction and backlash phenomena based on the describing function method. The dynamics is illustrated using the Nyquist and Bode plots and the results are compared with those of standard models

This work describes JBODE, a computer application developed in Java, HTML and ASP to study and understand the Bode diagram. This is achieved by means of Web theory pages for learning/refreshing basic concepts. Once the theory has been mastered the student can draw the real and asymptotic Bode diagrams of any transfer function. Also, there are on-line exercises for testing the understanding. The students' progresses are recorded in a database where the instructor can follow them. The final objective is to build a tool for learning basic control without using typical process control software.

Stability in presence of (possibly varying) time-delays in a control loop consisting of a continuous-time plant and a discrete-time controller is studied. A simple stability criterion is developed, consisting of a graphical test in a Bode plot of the closed loop system. The graphical test makes it very easy to design the controller for time-delay robustness.

A technique is developed which uses industrial feed composition data to predict distillation column closed-loop product variabilities. Signal processing techniques are used to obtain the frequency components of the feed composition signal. These frequency components are then combined with the closed loop Bode plot for disturbance rejection to predict closed loop product variabilities of the column. The prediction technique is illustrated using industrial propylene / propane (C 3 ) splitter feed composition data. Also, three different distillation configurations [(L,B), (L,V) and (D,V)] were analyzed using the proposed technique which indicate that this approach can be used for distillation configuration selection.

This paper deals with the frequency domain properties of an ellipsoidal family of rational functions, i.e. a family of rational functions whose coefficients depend affinely on an ellipsoidal parameter set. The problems considered are relevant to several recently developed techniques in the identification for control research area. The frequency plots of such a family are characterized and an efficient algorithm for computing the envelope of the Bode plots is devised. In particular, it is shown that the extremal values of the magnitude and phase of the value set at each frequency, which are in general non-convex optimization problems, can be computed via the solution of a sequence of Linear Matrix Inequalities (LMIs).

A quantitative approach to parametrically uncertain multivariable control is sketched within the context of Individual Channel Analysis and Design (ICAD). It is shown by way of an illustrative turbo-alternator example that there is advantage in superimposing relative parameter uncertainty on the inverse Nyquist diagram, where the uncertainty envelope does not vary with the controller. Further, the relative uncertainty envelope may be transferred to the Bode diagram to provide novel gain and phase robustness bounds. Unlike within ICAD, the specific turbo-alternator example chosen would present some difficulty for QFT.

Joint issues of modelling and control design are studied in a frequency domain setup. Stable systems with monotone Bode plots are chosen as the basis of the study presented in this work. Such dynamics is typical for plants in industrial process control. Adaptive information is considered and both open-loop and closed-loop experimental conditions are included. For systems with monotone Bode plots the information typically required for successful control design consists of a small part of the frequency response only. This can be exploited in experiment design.

A robust controller is designed to reduce the sensitivity of the frequency and the extraction steam pressure to the disturbance imposed on a cogeneration plant by using the LQG/LTR methodology. Natural frequency of generator swing is analyzed to determine the frequency band of the disturbance due to the variation in load and utilized as a design specification for the LQG/LTR controller. The singular-value Bode diagram of the sensitivity transfer function matrix is shaped to reduce disturbance effects on the power system frequency and steam pressure according to the design specification. The high order LQG/LTR controller is reduced to a low order controller and implemented in a nonlinear cogeneration plant model. Simulation shows the performance of the LQG/LTR controller in disturbance rejection.

The paper gives a special frequency domain interpretation of H∞ criteria which gives a useful and simple tool for sensitivity and robustness shaping techniques formulated on the Bode plot.

Techniques making use of genetic algorithms are proposed as a means of identifying the parameters of transfer functions. In particular, it is shown that the use of frequency-response data In the form of Bode plot information obtained from simple on-line tests using a relay, simple time-delayed control, and leading hysteresis, is all that Is required to implement the identification technique. The method is illustrated by genetically identifying a transfer functions using exact, over, and under parameterlsation.

This paper considers the problem to design a state feedback law for a linear multivariable system, which is completely determined by specifying poles and eigenvectors of the closed loop system. It is shown what rules the specifications of the desired poles and eigenvectors play in shaping Bode Diagram of the treated system. The robustness criterion is represented as the paticular shape of Bode Diagram of the return difference matrix. Based on the results, the procedure to design the state feedback law which yields the robust closed loop system is discussed.

A method is presented to determine simple transfer functions describing the input-output properties of continuous linear time-invariant systems. These transfer functions belong to a certain class of models including rational fractions and the transcendental function concerning time-lags. The evaluation of such models is based on the graphical representation of the logarithmic frequency plots (Bode-plots) of the given system in a fixed frequency range. The problem is then treated as an approximation problem in that sense that one fits the magnitude plot as well as the phase plot of the unknown model to the given plots in an interactive graphics dialog.

Measurements of impulse response, frequency response, step response and Bode diagram of linear systems by signal expansion and compression techniques are explained. This method uses special computer generated test signal, and all signal processings are performed by a microprocessor based measuring system. The S/N ratio can be improved immensely by several computer techniques. So this method is useful for measurements in noisy conditions. Since the test signal has flat power spectrum and constantly zero phase, equivalently, the frequency response function and the Bode diagram can be obtained directly. Applications for the measurement of heat conduction system, acoustic system and electrical second order system are described. When an impulse response of a wave propagation system is concerned, a direct wave and reflected waves can be separately analyzed. This method is also applicable for at least some kinds of nonlinear systems.

This paper describes a new computer simulation package for nonlinear dynamic systems that can be described by a block diagram and/or state space equations. Graphics routines are used to draw the block diagram for the system. Elements for the diagram are selected from a menu that includes transfer functions, summers, state space equations, and several nonlinearities such as dead zone, limiters, hysteresis, etc. Once the diagram is complete, the user activates the analysis package which can be used to generate transfer functions, root locus plots, Bode plots, and/or transient response plots. A unique feature of this simulation package is the automatic formulation of the state-space equations from the graphics image of the system.

In this paper the application of Quasi Classical Approach to the analysis of distillation columns with dual composition control is presented. The method relies heavily on a computer graphic package because it retains the basic fundaments of classical control theory such as Myquist and Bode plots. Firstly the main measurements and properties in which the methodology is based are briefly described. Then the advantages of using reserved frame controllers is discussed and through the example it is shown that they can handle the principal aspects of a control system. The experimental model of the| column, TOFA, has been chosen to show the applicability of the methodology.

Measurement errors corrupting the data of an empirical Bode plot of a causal system (log-amplitude and phase, versus frequency) can be minimized by taking into account the theoretical redundancy of such data in the ideal (noise-free) case, wherein each plot is the Hilbert transform of the other. An explicit closed-form analytical solution of the problem of least-mean-square fit of reciprocal Hibert-transform pairs to the measured data is derived, and illustrative examples are presented.