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3.0: Prelude to Feedback Control System Models

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    Feedback, i.e., using observed outputs as another input to the system, is an important characteristic of automatic control systems. In particular, negative feedback permits precise control of the overall system gain, and can compensate for signal distortions and nonlinearities. Feedback makes the system robust against disturbance inputs and parameter variations.

    The design of a single-input single-output (SISO) feedback control system involves the use of a comparator to generate an error signal, \(e=r-y\) (Figure 3.0.1). The controller, \(K(s)\), suitably conditions the error signal before it is input to the process, \(G(s)\). A sensor, \(H(s)\), monitors the output and feeds it back to the input. Often a sensor gain \(H\left(s\right)=1\) is assumed.

    clipboard_e8cc252c116f72206bf800f33d679fb6d.png
    Figure \(\PageIndex{1}\): Feedback control system block diagram.

    A static, i.e., proportional gain controller, \(u(t)=Ke(t)\), serves as baseline controller in a SISO feedback control system. The static controller is simple to design and is effective in meeting the basic design objectives in output regulation and reference tracking problems.

    First-order phase-lead and phase-lag controller are used for transient and steady-state response improvements in feedback control systems. The phase-lead controller is characterized by positive phase contribution to the Bode plot of loop transfer function. The phase-lag controller, used for steady-state error improvement, adds negative phase to the Bode plot.

    A proportional-integral-derivative (PID) controller comprises three basic modes of control that include the proportional, the derivate, and the integral modes. The PID controller is popular in industrial process control for its ability to provide robustness in designs involving simple models of complex processes.

    The cascade controller design employs output feedback, which has a limited potential to affect the behavior of the closed-loop control system. Pole placement using state feedback is a more powerful controller design method that may be employed with state variable models of dynamic systems.

    Rate sensors, such as rate gyros and tachometers, are used in position control applications to enhance the controller design options. A rate feedback controller offers additional design flexibility and may be considered when static controller falls short in meeting design objectives.

    In this chapter, we will limit our discussion to the cascade and rate feedback controllers of the static and dynamic types. These controller are described below.


    This page titled 3.0: Prelude to Feedback Control System Models is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Kamran Iqbal.

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