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BIBO Stability
Published in Hitay Özbay, Introduction to Feedback Control Theory, 2019
Formally, a system F is said to be bounded input-bounded output (BIBO) stable if every bounded input u generates a bounded output y, and the largest signal amplification through the system is finite. In the abstract notation, that means BIBO stability is equivalent to having a finite system norm, i.e., ║F║ < ∞. Note that definition of BIBO stability depends on the selection of input and output spaces. The most common definition of BIBO stability deals with the special case where the input and output spaces are U=Y=ℒ∞[0,∞). Let f(t) be the impulse response and F(s) be the transfer function (i.e., the Laplace transform of f(t)) of a causal LTI system F.
Force-System Resultants and Equilibrium
Published in Richard C. Dorf, The Engineering Handbook, 2018
Stability definitions relate either to the zero-input response (internal stability) or to the zero-state response (external stability). The latter is called external because performance depends on the external input as it influences the external output (internal performance is ignored). TABLE 104.2 contains two commonly used stability definitions: asymptotic stability relates to zero-input (internal) stability, whereas the bounded-input, bounded-output (BIBO) stability relates to zero-state (external) stability.
Laplace Transform
Published in Richard C. Dorf, Circuits, Signals, and Speech and Image Processing, 2018
Richard C. Dorf, David E. Johnson
A circuit is defined to have bounded input–bounded output (BIBO) stability if any bounded input results in a bounded output. The circuit in this case is said to be absolutely stable or unconditionally stable. BIBO stability can be determined by examining the poles of the network function (Equation (6.14)).
Stability Analysis of General Takagi-Sugeno Fuzzy Two-Term Controllers
Published in Fuzzy Information and Engineering, 2018
We have developed models of four different classes of general Takagi-Sugeno fuzzy PI/PD controller using modified rule base, algebraic product/minimum t-norm, bounded sum/maximum t-co-norm, CoG defuzzifier, unequal number (at least three) of fuzzy sets on the inputs, and different UoDs for the inputs. The greatest advantage of the proposed approach is that it has only parameters to tune in comparison to parameters in [18]. Tuning becomes relatively easier as the number of parameters in the rule consequent reduces. The proposed models are equally applicable to triangular membership functions case () where and in the model expressions. The model expression reveals that the developed fuzzy controller is a nonlinear PI/PD controller with variable gains. The bounds on gain variation are found, and the three-dimensional plots of gain provide an insight into the nature of gain variation. A sufficient condition for BIBO stability of the feedback control system having one of the proposed models in the loop is established.
Vibration control of cantilever beam using poling tuned piezoelectric actuator
Published in Mechanics Based Design of Structures and Machines, 2023
Kamalpreet Singh, Saurav Sharma, Rajeev Kumar, Mohammad Talha
A system is dynamically stable if the output is finite for every bounded input, called BIBO stability. The amplitude of the controlled displacement response in a stable system approaches zero as time approaches infinity (Kozioł and Cupiał 2020), as shown in Figure 13(a). The phase plot of a disturbed system under the action of a fuzzy logic controller demonstrates the stability of a smart cantilever beam as illustrated in Figure 13(b).