Transfer Function Models of Dynamical Processes

Transfer Function Models of Dynamical Processes Process Dynamics and Control 1. Linear SISO Control Systems General form of a linear SISO control system: this is a underdetermined higher order differential equation the Function must be specified for this ODE to admit a well defined solution 2. Transfer Function Heated stirred-tank model (constant flow, ). Taking the Laplace transform yields: or letting Transfer functions 3. Transfer Function Heated stirred tank example +. +. +. The block is called the Transfer Function relating Q(s) to T(s). 4. Process Control Time Domain Laplace Domain Process Modeling, Transfer Function Experimentation and Modeling, Controller Implementation Design and Analysis Ability to understand dynamics in Laplace and time domains is extremely important in the study of process control 5. Transfer functions Transfer functions are generally expressed as a ratio of polynomials Where The polynomial is called the characteristic polynomial of Roots of are the zeroes of Roots of are the poles of 6.

15 Nonlinear ODEs Q: If the model of the process is nonlinear, how do we express it in terms of a transfer function? A: We have to approximate it by a linear one (i.e.Linearize) in order to take the Laplace. f(x 0) f(x)!! f x (x0) x x 0

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