Transfer Function Vs State Space
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Transfer Function Model Transfer function models represent the systems in the classical approach to control system design. Transfer function model is defined in the s-domain. Transfer function model is defined under zero initial conditions. They are applicable to linear time invariant systems. Generally restricted to single-inputsingle-output (SISO) systems as it is cumbersome for multiple-inputmultiple-output (MIMO) systems. It reveals only the system output for a given input and provides no information regarding the internal state of the system The classical transfer function approaches provide the control engineer with a deep physical insight into the system and greatly aid the preliminary system design where a complex system is approximated by a more manageable model. Classical design approaches are generally trial and error procedures. In case of classical control, the Laplace Transform is applied for continuous systems while ztransforms are applied to discrete data systems. Under zero initial conditions, the transfer function of the system is the ratio of the Laplace transform of the output to the Laplace transform of the input.
State Space Model State space model is the basis for modern control theory and system optimization. State space model is a direct time domain approach State space model can be defined under non-zero initial conditions. State space models are applicable to linear time varying and invariant as well as non linear systems. Can be applied to both SISO and MIMO systems. State space models give an insight regarding internal state of the system also which is defined by the state variables. Modern state space approaches for complex systems are not easy to interpret and manage. Hence an insight of the system in preliminary system design is very difficult. Hence state variable approach cannot completely replace classical transfer function approach. State variable design approaches are based on accurate procedures. However in case of state variable approach, the state variable is applicable to both continuous and discrete systems. “The state of a dynamical system is a minimal set of variables (known as state variables) such that the knowledge of these variables at t=to together with the knowledge of the inputs for t>=to, completely determine the behavior of the system for t>to.” In state variable formulation of a system an n-th order differential equation can always be represented in terms of a set of n-first order differential equations.
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Transfer Function Model Transfer function models represent the systems in the classical approach to control system design. Transfer function model is defined in the s-domain. Transfer function model is defined under zero initial conditions. They are applicable to linear time invariant systems. Generally restricted to single-inputsingle-output (SISO) systems as it is cumbersome for multiple-inputmultiple-output (MIMO) systems. It reveals only the system output for a given input and provides no information regarding the internal state of the system The classical transfer function approaches provide the control engineer with a deep physical insight into the system and greatly aid the preliminary system design where a complex system is approximated by a more manageable model. Classical design approaches are generally trial and error procedures. In case of classical control, the Laplace Transform is applied for continuous systems while ztransforms are applied to discrete data systems. Under zero initial conditions, the transfer function of the system is the ratio of the Laplace transform of the output to the Laplace transform of the input.
State Space Model State space model is the basis for modern control theory and system optimization. State space model is a direct time domain approach State space model can be defined under non-zero initial conditions. State space models are applicable to linear time varying and invariant as well as non linear systems. Can be applied to both SISO and MIMO systems. State space models give an insight regarding internal state of the system also which is defined by the state variables. Modern state space approaches for complex systems are not easy to interpret and manage. Hence an insight of the system in preliminary system design is very difficult. Hence state variable approach cannot completely replace classical transfer function approach. State variable design approaches are based on accurate procedures. However in case of state variable approach, the state variable is applicable to both continuous and discrete systems. “The state of a dynamical system is a minimal set of variables (known as state variables) such that the knowledge of these variables at t=to together with the knowledge of the inputs for t>=to, completely determine the behavior of the system for t>to.” In state variable formulation of a system an n-th order differential equation can always be represented in terms of a set of n-first order differential equations.
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