An innovative computer-assisted teaching technique is proposed as an effective way to help in the assessment of undergraduate courses in classical control theory. Using an iterative Matlab/Simulink ...based algorithm, the task of identifying an unknown linear system from its frequency response is given to the students. At each step, the student improves his/her approximation to minimize the frequency response of the mismatch and decides whether the estimate is sufficient. The proposed self-evaluation task gives the students a means to analyze Bode diagrams and system identification techniques, nontrivial issues in introductory courses in control systems theory
Management of cardiovascular disease in intensive care would benefit from improved methods for data from clinically available, information rich arterial pressure waveforms. This paper explores the ...feasibility of using the transfer function between the aortic and femoral pressure waveforms as a diagnostic tool, over an experimental cohort including the progression of sepsis. Transfer functions appeared as physiologically expected, with Bode plot peaks near breathing and heartbeat frequencies. The Bode plot response to clinical interventions and disease progression also matched physiological expectations, with peaks increasing in magnitude in response to fluid infusion and attenuating in response to the progression of sepsis. While there are clear potential diagnostic benefits to the approach, further work is needed to make this information easier to rapidly interpret in a clinical environment, and to evaluate the specificity of the transfer function responses presented here to the progression of sepsis.
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.
In learning undergraduate controls, one of the most abstract and confusing concepts is that of phase margin (PM). One frustration is the difficulty in conceptualizing what physical process could ...produce the pure phase shift referred to in the definition of PM. Another frustration occurs when simple second-order formulas given for PM do not work in practice. Finally, when resonances occur, there may be multiple gain-crossover frequencies, and which one to use to compute the PM may be unclear. This paper offers visualizations and explanations that students have found helpful in learning about PM-both its evaluation and its application. The phase-root locus (PRL) plot reveals the effect of adding phase in the same way that conventional gain root locus shows the effects of adding gain. The PRL ultimately leads to a definition of PM involving phase shifting that results in physical (real-coefficient) systems, unlike the usual abstract Nyquist plot rotation. This definition of PM suggests a simple, effective compensator design method for improving PM via phase shifters, a solution illustrated by numerical examples. These materials can either be presented in lectures or assigned as supplementary readings and may inspire student projects.
This paper illustrates how pole-zero phase maps can help students to determine the phase of a transfer function from a plot of the poles and zeros. This visualization of the phase of L(s) helps ...students develop s-plane intuition and facilitates the introduction of the analytical tools of classical control, such as Bode plots, Nyquist diagrams, and Evans root-locus plots.
A detailed understanding of the gain and phase characteristics of discrete-time zeros and poles is obtained. This new knowledge extends and complements previous results available in the control ...systems and digital signal processing literature. The results introduced in the paper also substantiate the view that discrete-time zeros and poles have much more intricate frequency domain features than their continuous-time counterparts. A simple loop-shaping example is used to illustrate the feasibility of discrete-time control system design developed entirely in the
z-plane.
System identification theory provides powerful theoretical tools for the control system design and analysis. Using the ARX model estimation and the system response to a pseudo-random binary sequence ...the transfer function and the frequency response characteristics are determined for a partially known system.
This chapter focuses on the stability of feedback control systems. It utilizes the transfer function modeling and an approach similar to the one of Chapter 7, which introduces the concept of ...stability applied to open-loop (uncontrolled) dynamic systems. The closed-loop transfer function is employed for single-input, single-output (SISO) systems, and the closed-loop transfer function matrix is used for multiple-input, multiple-output (MIMO or multivariable) systems to determine the pole position in the complex plane and to establish stable, marginally stable, or unstable behavior of feedback systems. The state-space model is also applied to determine the stability behavior of dynamic control systems. Analytical or MATLAB methods can be used to solve the characteristic equation related to the closed-loop transfer function or the closed-loop transfer function matrix when such solutions are available. The Routh–Hurwitz test or criterion is the analytical tool of choice for designing control systems with parameters, such as gains, that are originally undetermined. The method is illustrated by several examples. The root-locus method and the Nyquist criterion are introduced here to monitor the closed-loop pole migration between the left-hand complex plane and the right-hand complex plane for feedback system with a variable gain by analyzing the poles and zeros of the open-loop transfer function. For the same purpose, the Bode plots are utilized, as well as the phase and/or gain margins.
In this paper, the problem of finding the set of Proportional Integral Derivative (PID) controllers that can robustly stabilize a system based on its frequency response has been solved. The model of ...the system is not necessary for this problem. A band of uncertainty is assumed in the frequency response of the plant. The controller is so designed that it can robustly stabilize this plant in the entire range of its uncertainties. Interval coefficient linear inequalities are used to arrive at the final result.
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