3 mass, 4 spring mechanical system: ode45 vs lsim simulation скачать в хорошем качестве

3 mass, 4 spring mechanical system: ode45 vs lsim simulation

This video continues the case study of a 3-mass, 4-spring system whose first-principle modeling was covered in the videos    • 3 mass, 4 spring mechanical system (s...   and    • 3 mass, 4 spring mechanical system: A...   with force balances and Newton's equations. Here, the equations dx/dt=Ax+Bu, derived in the referred materials, are entered in matrix form, simply by entering the constant matrices A and B by copying them from the theoretical modeling slides. The output equation y=Cx+Du is implemented so that only the three positions are part of the vector y. Once the model has been typed onto a Matlab script, a simulation is performed under certain initial conditions and a sinusoidal input profile (arbitrarily chosen). To compare the results and the computation time, the numerical integration is performed both with Matlab command "ode45" (a generic simulator, which can also simulate nonlinear systems) and with "lsim" (a simulator specialized in linear systems in the Control Systems Toolbox). The second case is, at least in this example, several times faster to execute; both simulations are coincident apart from numerical tolerances to the fifth or sixth decimal place. Animation to better apprehend how this system moves and vibrates will be discussed in the forthcoming video    • 3 mass, 4 spring mechanism animation ...   . The free response (zero input) properties are discussed in detail in the video {moll3freeEN_TODO}. ________________ PDF/code/notes at: http://personales.upv.es/asala/YT/V/m... #simulation #matlab #differentialequations #mechanicalengineering _________________ Antonio Sala, UPV, Spain Full collection of videos at: http://personales.upv.es/asala/YT/ind...