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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.
1/39 Process Control Second Order Models and Response. Outline 1. Poles, zeros, response for di erent pole locations 2. Solution to second order systems ... critically damped ( = 1) and overdamped ( >1) systems 26/39 Process Control Second Order Models and Response. You should be able to derive all the previous expressions for y(t)
I will develop some insights into how these systems behave both in the time domain in response to a step input, and in the frequency domain (that is, in response to sinusoids at different frequencies). In Lab 3, you will be connecting a specially design board, called “Bulb Board”, to the Pybench.
As in the first-order system, τ has the dimension of time and represents a characteristic time of the system. We will take it to be positive; dimensionless ξ in the second-order system, however, we will allow to be positive or negative. Parameter ξ is called the damping coefficient, and the response depends markedly on its value.
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.
The response is referred to as a critically damped response, and the system is called a critically damped system, with a double pole: x1 = x2 = −b 2a x 1 = x 2 = − b 2 a. if Δ <0 Δ <0, there are two complex, conjugate roots, and the response is a sinusoid with an exponential envelope.
Under, Over and Critical Damping OCW 18.03SC.. . Example 3. Show that the system x + 4x + 4x = 0 is critically damped and . graph the solution with initial conditions x(0) = 1, x(0) = 0. Solution. Characteristic equation: s2 +4s + 4 = 0. Characteristic roots: (this factors) −2, −2. Exponential solutions: (only one) e−2t. General solution:
