Computer Control of Manufacturing Processes
The availability of a mathematical description of a manufacturing process provides a quantitative basis for process control that is understood as maintaining the desired status of the process in spite of many external and internal disturbance effects. The
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Computer Control of Manufacturing Processes
The availability of a mathematical description of a manufacturing process provides a quantitative basis for process control that is understood as maintaining the desired status of the process in spite of many external and internal disturbance effects. The desired status is defined by the set points, also known as reference signals that represent the desired numerical values of controlled variables of the process. The control task implies that the difference between the actual and desired process variables (error) is determined, and on the basis of this difference and according to the control law, the control efforts are defined and applied to the process. The manner in which the control effort drives the system from its actual state to the desired state, and the allowable discrepancy between the actual and the desired states are quite important. They are dependent on the control law and are explicitly defined by the design specifications along with the discrete time step (or clock frequency). Modern computer systems facilitate every function of the control task; process monitoring, specification of the set points, extraction of the errors, implementation of the control law, and the application of control efforts.
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S- and Z-Domain Transfer Functions
An s-domain transfer function, defined as a “Laplace transform of the output signal over Laplace transform of the input signal under zero initial conditions” presents the most common technique for the mathematical description of linear, dynamic, single-input-single-output systems. In the case of a multi-input-multi-output linear dynamic system, transfer functions of particular channels could be easily assembled into a transfer matrix. Transfer functions enable us to address the rigors of linear differential equations through simple algebra. Control engineers commonly use s-domain transfer functions for the analysis and design of continuous-time control systems. The situation changes when a discrete-time control system is to be developed, which is a very typical case in our computer-dominated environment. © Springer International Publishing Switzerland 2016 V.A. Skormin, Introduction to Process Control, Springer Texts in Business and Economics, DOI 10.1007/978-3-319-42258-9_3
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3 Computer Control of Manufacturing Processes
Although discrete-time control synthesis requires the use of z-domain transfer functions, the material of this chapter allows students to utilize their experience with s-domain transfer functions to the fullest. A z-domain transfer function, defined as a “Z-transform of the output signal over Z-transform of the input signal under zero initial conditions”, is used for mathematical description of linear, dynamic, single-input-single-output systems operated by a discrete-time controller. The output of such a controller is a “number sequence” i.e. a sequence of real numbers, u*(k), k ¼ 1,2,3,. . ., generated at the clock frequency, fCL, of the computer implementing the control law. The purpose of
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