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Definitions and Terminology
Published in Jose A. Romagnoli, Ahmet Palazoglu, Introduction to Process Control, 2020
Jose A. Romagnoli, Ahmet Palazoglu
Furthermore, depending on how many output and input variables are considered for the control problem, we can distinguish two major control structures: Single-input single-output (SISO). There is a single-output variable (control objective) and a single-input (manipulated) variable is available to influence the process behavior.Multiple-input multiple-output (MIMO). There is more than one output variable (control objective), and more than one input (manipulated) variable are used to affect the process behavior.
Chapter 4: Transfer function matrix G (z)
Published in Zoran M. Buchevats, Lyubomir T. Gruyitch, Linear Discrete-Time Systems, 2017
Zoran M. Buchevats, Lyubomir T. Gruyitch
The transfer function G (z) of a SISO system is defined as the ratio of the Z—transform of the system output to the Z—transform of the system input under all zero initial conditions. It is well known that the transfer function is the Z—transform of the unit impulse response of the system under all zero initial conditions. By following that definition, the transfer function matrix of a MIMO system is defined as the matrix composed of the system transfer functions, which relates the Z—transform of the output vector to the Z—transform of the input vector under all zero initial conditions2, 6, 8, 14, 18, 41, 61, 80, 81, 89, 96, 101, 108, 110, 122. That definition expresses the physical sense of the transfer function matrix from the point of view of the transmission and the transformation of the input vector onto and into the output system response, respectively.
System Model Representation
Published in Ramin S. Esfandiari, Bei Lu, Modeling and Analysis of Dynamic Systems, 2018
As mentioned earlier, there is a transfer function for each I/O pair. A SISO system has therefore only one transfer function, whereas a MIMO system has several, one for each possible I/O pair. If a system has q inputs and r outputs, then there are a total of qr transfer functions, assembled in an r×q transfer function matrix (also known as a transfer matrix), denoted by G(s)=[Gij(s)] where i=1,2,…,r and j=1,2,…,q.
Discrete-time multivariable PID controller design with application to an overhead crane
Published in International Journal of Systems Science, 2020
Huiru Guo, Zhi-Yong Feng, Jinhua She
It is known that proportional-integral-derivative (PID) controllers are most commonly used in industrial control applications, and more than of the industrial controllers are of PID type (Tavakoli et al., 2006). A single-input single-output (SISO) PID controller has only three parameters to tune, i.e. the proportional, integral and derivative gains. There exist many simple rules for tuning the three parameters of an SISO PID controller (Åström & Hägglund, 2006). However, the tuning of a multi-input multi-output (MIMO) PID controller is much more difficult. This is because the three gains involved in an MIMO PID controller are no longer scalars but matrices. For a plant with n inputs and m outputs, it needs to tune parameters to design an MIMO PID controller (Boyd et al., 2016; Merrikh-Bayat, 2018). In industrial applications, most processes can be modelled as MIMO systems (Coughanowr & LeBlanc, 2008). When the interactions among different channels of a system are low or modest, one can decouple the system and design PID controllers in multiple SISO loops. However, when the interactions are significant, the system is highly coupled, and effective methods for designing multivariable PID controllers for coupled MIMO systems are highly needed.
Frequency domain integrals for stability preservation in Galerkin-type projection-based model order reduction
Published in International Journal of Control, 2021
We investigate the electric circuit of a low-pass filter in Figure 12. The circuit includes 21 physical parameters: seven capacitances, six inductances and eight conductances. A mathematical modelling generates a system of DAEs (1) for 14 node voltages and 6 branch currents (). The (nilpotency) index of this system is one. Furthermore, the system is asymptotically stable and strictly proper. The system is single-input-single-output (SISO), because a voltage source is supplied and the output is defined as the voltage at a load conductance.
Stable inversion of LPTV systems with application in position-dependent and non-equidistantly sampled systems
Published in International Journal of Control, 2019
Throughout, linear, single-input, single-output (SISO) systems are considered. Extensions to multi-input, multi-output (MIMO) systems follow directly. The focus is on discrete-time systems, since this is natural for sampled systems. Results for continuous-time systems follow along similar lines.