![]() State-space models can be implemented and simulated in Scilab as well, using the predefined functions syslin() and csim(). Scilab implementation of state-space models (systems) We can easily verify the results of the simulation by comparing them against the result explained in the article RL circuit – detailed mathematical analysis, in which we simulated the ordinary differential equation (ODE) of the system. Image: State-space model Xcos block diagram – electrical system current response The step input voltage E is set to give 12 V after 0.1 s of simulation.Īfter running the simulation for 2 s, we get the following graphical window: In order to simulate our electrical system, as a state-space model, we only need to update the definition of the state-space matrices in the model we’ve used: E = 12 Since we had only one state variable, our state-space matrices have turned into scalars. In order to check our state-space model parameters (matrices), we are going to use the same Xcos block diagram to simulate our dynamic system. The state equations has the general form: \[\dot The number of state variables is equal with the order to ODE describing the system. The state variables are exactly those variables for which initial conditions are required. The set of state variables is not unique and they may be defined in terms of physical variables which can be measured, or in terms of variables that can not be measured directly.įor a given state-space model, the number of state variables is equal with the number of initial conditions needed to completely solve the system model. State variables can also be defined as the smallest set of independent variables that completely describe the system. The numbers of state variables of the state-space model is equal with the highest order of the ODE describing the dynamic system. The internal variables of the state-space model are called state variables and they fully describe the dynamic system and its response for certain inputs. If a dynamic model is described by a higher order ODE, using state-space, the same model can be described as a set of coupled first order ODEs. ![]() It solves many of the limitations of the classical control theory in which transfer functions were used to asses the behavior of a closed loop system.Ī state-space model describes the behavior of a dynamic system as a set of first order ordinary differential equations (ODE). State-space system representation lays the foundations for modern control theory.
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