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System dynamics is a methodology and mathematical modeling technique to frame, understand, and discuss complex issues and problems. Originally developed in the 1950s to help corporate managers improve their understanding of industrial processes, SD is currently being used throughout the public and private sector for policy analysis and design.
For example, if the dimension of the state space is greater than the dimension of the output, then there will be a set of possible state configurations for each individual output. That is, the system can have significant zero dynamics, which are trajectories of the system that are not observable from the output. Consequently, being able to ...
Differs from traditional system dynamics approaches in that 1) it puts much greater emphasis on probabilistic simulation techniques to support representation of uncertain and/or stochastic systems; and 2) it provides a wide variety of specialized model objects (beyond stocks, flows and converters) in order to make models less abstract (and ...
System dynamics is an approach to understanding the behaviour of systems over time. It deals with internal feedback loops and time delays that affect the behaviour and state of the entire system. [3] What makes using system dynamics different from other approaches to studying systems is the language used to describe feedback loops with stocks ...
Maximum overshoot is defined in Katsuhiko Ogata's Discrete-time control systems as "the maximum peak value of the response curve measured from the desired response of the system." [ 1 ] Control theory
Once a given system has been converted into the frequency domain it can be manipulated with greater ease. Modern control theory , instead of changing domains to avoid the complexities of time-domain ODE mathematics, converts the differential equations into a system of lower-order time domain equations called state equations , which can then be ...
Every control system must guarantee first the stability of the closed-loop behavior. For linear systems, this can be obtained by directly placing the poles. Nonlinear control systems use specific theories (normally based on Aleksandr Lyapunov's Theory) to ensure stability without regard to the inner dynamics of the system. The possibility to ...
The constraints on the system dynamics can be adjoined to the Lagrangian by introducing time-varying Lagrange multiplier vector , whose elements are called the costates of the system. This motivates the construction of the Hamiltonian H {\displaystyle H} defined for all t ∈ [ 0 , T ] {\displaystyle t\in [0,T]} by: