Second Order Systems: Response Analysis

This lecture covers second-order systems, focusing on the response analysis of these systems. It explains the characteristics of second-order systems, such as damping ratio and natural frequency, and how they affect the system's response. The lecture discusses the response of second-order systems to different inputs, including unit step inputs. It also delves into the different cases based on the damping ratio, namely overdamped, critically damped, and underdamped systems. The lecture further explores the pole-zero diagram visualization and the significance of pole locations in determining system behavior. Additionally, it examines the characterization of second-order systems, including peak time, percent overshoot, and settling time, with constraints and examples provided.

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Damping

Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples include viscous drag (a liquid's viscosity can hinder an oscillatory system, causing it to slow down; see viscous damping) in mechanical systems, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators.

Frequency response

In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations.

Settling time

In control theory the settling time of a dynamical system such as an amplifier or other output device is the time elapsed from the application of an ideal instantaneous step input to the time at which the amplifier output has entered and remained within a specified error band. Settling time includes a propagation delay, plus the time required for the output to slew to the vicinity of the final value, recover from the overload condition associated with slew, and finally settle to within the specified error.

Step response

The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from zero to one in a very short time. The concept can be extended to the abstract mathematical notion of a dynamical system using an evolution parameter.

Nyquist stability criterion

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