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Digital Control Basics

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Oversampling

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Oversampling is the process of sampling a signal at a rate significantly higher than the Nyquist rate, which can help to reduce quantization noise and improve resolution in digital control systems.

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Feedback Control

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Feedback Control is the process of using a system's output to influence its input in order to maintain the output at a desired level. In digital control systems, the control algorithm is implemented in software.

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Z-Transform

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The Z-Transform is a mathematical tool used to represent discrete-time signals in the frequency domain, which is essential for the analysis and design of digital control systems.

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Aliasing

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Aliasing occurs when continuous-time signals are undersampled, causing different signals to become indistinguishable in the discrete-time domain which can lead to misrepresentation of the signal in digital control systems.

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Quantization

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Quantization refers to approximating the infinite range of amplitude levels in an analog signal with a finite range of discrete numerical values, which can introduce quantization error in digital control systems.

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Digital Controller

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A Digital Controller is a device that manipulates a process's control inputs based on digital algorithms using sampled data, aiming to drive a system towards its desired output.

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Dead Time

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Dead Time refers to the delay between the application of an input and the observable effect at the output. In digital control systems, it needs to be compensated for proper system dynamics.

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Nyquist Stability Criterion

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The Nyquist Stability Criterion is a graphical method used to determine the stability of a closed-loop control system by mapping the open-loop transfer function. In digital control, it ensures stability through the appropriate choice of sampling time.

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Pulse Transfer Function

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The Pulse Transfer Function describes the relation between the discrete-time output and input for linear systems. It is a z-domain representation used in digital control system analysis.

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State-Space Representation

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State-Space Representation is a mathematical model of a physical system as a set of input, output, and state variables represented by first-order differential or difference equations, used in both continuous and digital control system analysis.

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A/D and D/A Conversion

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A/D and D/A Conversion are processes that allow a digital control system to interact with the real world by converting analog signals to digital (A/D) and digital to analog (D/A) respectively.

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Stability Analysis

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Stability Analysis in digital control involves methods to ensure a system's output will settle to a steady value following a perturbation. Techniques such as root locus, bode plots, and Nyquist plots are used for this purpose.

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Discretization

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Discretization is the process of converting continuous-time control system models into discrete-time models, necessary when implementing digital controllers.

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Sampling

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Sampling is the process of converting a continuous-time signal into a discrete-time signal by taking measurements at discrete time intervals. This affects digital control systems by introducing the sampling period that must be managed to prevent aliasing and ensure system stability.

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Anti-Aliasing Filter

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An Anti-Aliasing Filter is a low-pass filter used before the sampling process to limit the bandwidth of a continuous-time signal to prevent aliasing in digital control systems.

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