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Vibration Control
Published in Haym Benaroya, Mark Nagurka, Seon Han, Mechanical Vibration, 2017
Haym Benaroya, Mark Nagurka, Seon Han
where the degree of the first term is less than or equal to n - 1, and that of the second term is n, since D is a scalar. Hence, the transfer function will always be proper if D is nonzero and will be strictly proper if D = 0. In control theory, a proper transfer function is a transfer function in which the degree of the numerator polynomial does not exceed the degree of the denominator polynomial. A proper transfer function will never grow unbounded as the frequency approaches infinity. A strictly proper transfer function is a transfer function in which the degree of the numerator is less than the degree of the denominator. A strictly proper transfer function will approach zero as the frequency approaches infinity, which is true for all physical systems.
A New Analytical Approach for Set-point Weighted 2DOF-PID Controller Design for Integrating Plus Time-Delay Processes: an Experimental Study
Published in IETE Journal of Research, 2022
Sudipta Chakraborty, Jiwanjot Singh, Asim K. Naskar, Sandip Ghosh
Here, is chosen as where is used as a filter to make a proper transfer function. The selection of the tuning parameter λ is discussed later in this section. Now, with (35) and (36), one may obtain as where Now, using the Maclaurin series expansion of around s = 0, one may obtain the first three terms of (37) as a PID one and can be expressed as where Note that PID controller and its subsets are well utilized structure in the process industry due to its simplicity and easy implementation. While deriving the outer-loop controller, Maclauren series expansion is considered to shape the controller in to a PID one. For that the higher order terms of the expansion are not considered as it is having very minimal effect in system response. So, to attain a simple PID control structure from a higher order controller, this compromise is done.
Frequency domain integrals for stability preservation in Galerkin-type projection-based model order reduction
Published in International Journal of Control, 2021
A linear dynamical system (or its transfer function) is called strictly proper, if and only if the transfer function H satisfies A system of ODEs always exhibits a strictly proper transfer function. The transfer function of a general system of DAEs reads as, see Benner and Stykel (2017), with a strictly proper part and a polynomial part . The polynomial part either vanishes or represents a non-zero matrix-valued polynomial of degree at most with the index ν of the system. These properties also depend on the definition of inputs and outputs in each system.
Stabilising PID tuning for a class of fourth-order integrating nonminimum-phase systems
Published in International Journal of Control, 2019
The details of the proof for the theorem are available in Seer and Nandong (2017). Here, we only briefly present the basic assumptions underlying the proof. Consider a given process P(s) = N(s)/D(s) where N(s) = αmsm + α(m − 1)sm − 1 + ⋅⋅⋅α1s + α0 and D(s) = βnsn + βn − 1sn − 1 + ⋅⋅⋅β1s + β0 are polynomial equations with real coefficients of αi, i = 0, 1,… , m and βj, j = 0, 1,… , n. The system is assumed to be a proper transfer function, i.e. m ≤ n. Let us assume that the closed-loop characteristic equation with an ideal PID controller (5) can be written in the following form: