# State space representation of electrical system

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Part III introduces dynamic elements and shows how to develop a state-variable model of a dynamic circuit. What’s different from what you learned in physics Modeling of electrical systems is best approached by thinking separately about the element laws and the interaction laws. Example: A State-Space Controller for DC Motor Position Control The electric circuit of the armature and the free body diagram of the rotor are shown in the following figure: For this example, we will assume the following values for the physical parameters. These values were derived by experiment from an actual motor in Carnegie Mellon's • The state of a system is a set of variables such that the knowledge of these variables and the input functions will, with the equations describing the dynamics, provide the future state and output of the system. • For a dynamic system, the state of a system is described in terms of a set of state variables. System u 1(t) u 2(t) y 1(t) y 2(t) In control engineering, 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 or difference equations. State variables are variables whose values evolve through time in a way that depends on the values they have at any given time and also depends on the externally imposed values of input variables. Part III introduces dynamic elements and shows how to develop a state-variable model of a dynamic circuit. What’s different from what you learned in physics Modeling of electrical systems is best approached by thinking separately about the element laws and the interaction laws.

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Difficulties going to State Space from System Diagram Contents. It is often quite easy to develop a state space model from a system diagram (see here for examples). However, there are several situations in which it is not entirely straightforward to develop a state space model from a system diagram. state-space mo dels. DT Mo dels The k ey feature of a state-space description is the follo wing prop ert y, w h i c e shall refer to as the state pr op erty. Giv en presen t v ector (or \state") and input at time t, w e can compute: (i) the presen output, using (7.2); and (ii) next state (7.1). It is easy to see that this puts us in a p osition ... robotics.itee.uq.edu.au 22.451 Dynamic Systems – System Representation State-Space Representation Another approach commonly used is to represent the system as a larger system of equations – The second order ODE with two variables to describe the “state” of the system rather than one variable The number of state variable depends on the robotics.itee.uq.edu.au