Feedback controllers frequency response analysis

Frequency response analysis is a useful tool for designing feedback controllers. It helps the designer ... 

In Chapters 17 and 18 we will study a new technique which is often used to design feedback controllers. Quite different from everything we have seen so far, it is called frequency response analysis. 

In previous chapters, Laplace transform techniques were used to calculate transient responses from transfer functions. This chapter focuses on an alternative way to analyze dynamic systems by using frequency response analysis. Frequency response concepts and techniques play an important role in stability analysis, control system design, and robustness analysis. Historically, frequency response techniques provided the conceptual framework for early control theory and important applications in the field of communications (MacFarlane, 1979). We introduce a simplified procedure to calculate the frequency response characteristics from the transfer function of any linear process. Two concepts, the Bode and Nyquist stability criteria, are generally applicable for feedback control systems and stability analysis. Next we introduce two useful metrics for relative stability, namely gain and phase margins. These metrics indicate how close to instability a control system is. A related issue is robustness, which addresses the sensitivity of... 

Part IV (Chapters 13 through 18) covers the analysis and design of feedback control systems, which represent the control schemes encountered most often in a chemical plant. Emphasis has been placed on understanding the effects which various feedback controllers have on the response of controlled processes, and on the selection of the most appropriate among them. The subject of controller tuning has been deemphasized, and as a consequence, the traditional root-locus techniques and frequency response tuning methods have been scaled down. 

Frequency response techniques are powerful tools for the design and analysis of feedback control systems. The frequency response characteristics of a process, its amplitude ratio AR and phase angle, characterize the dynamic behavior of the process and can be plotted as functions of frequency in Bode diagrams. The Bode stability criterion provides exact stability results for a... 

In this section we present an advanced control technique, time-delay compensation, which deals with a problematic area in process control—namely, the occurrence of significant time delays. Time delays commonly occur in the process industries because of the presence of distance velocity lags, recycle loops, and the analysis time associated with composition measurement. As discussed in Chapters 12 and 14, the presence of time delays in a process hmits the performance of a conventional feedback control system. From a frequency response perspective, a time delay adds phase lag to the feedback loop, which adversely affects closed-loop stabihty. Consequently, the controller gain must be reduced below the value that could be used if no time delay were present, and the response of the closed-loop system will be sluggish compared to that of the control loop with no time delay. 

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