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Dynamic System Models and Basic Concepts
Published in Jitendra R. Raol, Girija Gopalratnam, Bhekisipho Twala, Nonlinear Filtering, 2017
Jitendra R. Raol, Girija Gopalratnam, Bhekisipho Twala
State space representation is very closely related to physical system behaviour and hence easily adaptable for dynamic system representation and is also very extensively used in modern control/system theory and applications. State variables in the state space representation are the dependent variables of the differential/difference equations. State space models are characterized by internal states and use I/O variables to describe a dynamic system. These are time domain models and could be used for representation of both continuous and discrete time linear and nonlinear single-input single-output (SISO) or multi-input multi-output (MIMO) systems. They are easily adaptable to problem solving in areas of control system design and analysis, optimization, system identification, parameter/state estimation/filtering and simulation. In general, the states of a system are not unique and can be described in several ways. This renders the state space model description of a system non-unique, unlike the transfer function model which is always unique for at least linear systems.
Vectors, Matrices, and Linear Systems
Published in Chee Khiang Pang, Frank L. Lewis, Tong Heng Lee, Zhao Yang Dong, Intelligent Diagnosis and Prognosis of Industrial Networked Systems, 2017
Chee Khiang Pang, Frank L. Lewis, Tong Heng Lee, Zhao Yang Dong
LTI systems in general can be represented by transfer functions (ratios of orders of Laplace operator “s” in continuous-time domain or z-transform operator “z”in discrete-time domain) in the frequency domain, or state-space representation using matrices in time domain. As such, a state-space representation is a mathematical model of a physical system as a set of inputs, outputs, and state variables, related by first-order differential equations and expressed as vectors in matrix form. The state space representation provides a systematic and convenient way to represent and analyze systems with multiple inputs and outputs.
Continuous-Time and Discrete-Time Systems
Published in Naim A. Kheir, Systems Modeling and Computer Simulation, 2018
The derivation of state-space models is similar to that of transfer functions, described earlier in the sense that differential equations describing the system are derived first. The key advantage of transfer functions is in their compactness, which makes them suitable for frequency-domain analysis and stability studies. However, the transfer function approach suffers from neglecting the initial conditions. Not only does state-space representation serve as an alternative to transfer functions, but also it is not limited to linear or time-invariant systems.
Fuzzy PD Plus I Control-based Adaptive Cruise Control System in Simulation and Real-time Environment
Published in IETE Journal of Research, 2019
G. Prabhakar, S. Selvaperumal, P. Nedumal Pugazhenthi
In this work, the FOPTD model of nonlinear ACC system [29] is taken into consideration. The system model is generally expressed as state-space representation. Instead of usual fuzzy PID controller, here fuzzy PD + I controller is introduced where the integral input to fuzzy inference system is replaced by incremental action. Then, the proportional signal and derivation signal of the conventional PID controller are modified with PD-type two-input fuzzy controller to include the varying gains. The transient response of the system has decided by the PD component of the controller. But the integral signal whose major role is to eliminate the steady-state error has fixed gain. Namely, the proposed controller is “fuzzy PD + linear I” type. To examine the performance of the fuzzy PD + I controller, a comparison is performed between the fuzzy PD + I, I – PD, PI – D and Linear PID in simulation. An effort is also made by the authors to ensure asymptotic stability for the considered system which is discussed in Section 2.1. Finally, all the simulated algorithms are tested with the prototype model in real time.
A Supervised Model of Multivariable Control in Quadruple Tank System
Published in Applied Artificial Intelligence, 2023
Aravindan M, Chilambuchelvan A, Tamilselvi S
A state-space representation is a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. State variables x(t) can be reconstructed from the measured input-output data, but are not themselves measured during an experiment. Output variables values depend on the values of the state variables. It is represented in the matrix form and it provides a convenient way to model and analyze systems with multiple inputs and outputs. The most general state-space representation of a linear system is written as