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Learning Objectives. Learn to analyze a general second order system and to obtain the general solution. Identify the over-damped, under-damped, and critically damped solutions. Convert complex solution to real solution. Suspended “mass-spring-damper” equivalent system.
critically damped ( = 1) and overdamped ( >1) systems 26/39 Process Control Second Order Models and Response
4is the damping factor. It value is centred around 1. At 1, the system is known as critically damped (will be discussed later). If 4< 1, then the system will oscillate when “kicked” by a transient such as a step function. If 4> 1, then the system is behaving slower than it need be. K is the gain at zero frequency, which is the DC gain. 0/= 1(/)
This document discusses the response of a second-order system, such as the mass-spring-dashpot shown in Fig. 1, to a step function. The modeling of a step response in MATLAB and SIMULINK will also be discussed. Fig. 1. Single-degree-of-freedom mass-spring-dashpot system.
Critical damping is the amount of damping for a particular system which will cause it to reach the steady-state response in the minimum possible time. The function on the right-hand side of (1), f(t), is the forcing function—some input to the system which is driving its response. MASS-SPRING-DASHPOT SYSTEM.
Free Response of Critically Damped 2nd Order System For a critically damped system, ζ = 1, the roots are real negative and identical, i.e. ss12==−ζωn (15) The solution form X(t) = A e st is no longer valid. For repeated roots, the theory of ODE’s dictates that the family of solutions satisfying the differential equation is () n (12)
INTRODUCTION. This tutorial discusses the response of a second-order system to initial conditions, including initial displacement and initial velocity. The mass-spring-dashpot system shown in Fig. 1 is an example of a second-order system.
