Simulation(Take class notes)Why simulation?• It is often very useful to have a model for a system and to see the effects of different inputs or gains (for the case of feedback control) by simulating the response on a computer• For simulation, it is usually best to obtain the state equation for the system and to use numerical integration- This works for both linear and nonlinear systems- It usually avoids long hand derivation of time functions (as in HW 7 for the DC motor)• State equations for the U12M4T motor: / ; = / ) = ) = State Equations (1)• Let• One could have a state-space equation from (1)In which = (1) 01 0n: number of state variablesm: number of inputsm=1n=2For the motor:State Equations (2)0,, = • For simulation, we use numerical integration• It is an rectangular integration (Euler integration) ΔΔΔ Runge Kutta: for higher order integration – more accurate 22Δ/6 , ) , ∆ ∆2, ∆2 ∆2, ∆2Estimates of derivative half way acrossEstimates of derivative at endAn example0106005.7v t01.78Static friction∆ ∆Use the above two equations, you can calculate the state at t = 0, 1ms, 2ms, …. when the input is 1 V at t =0Time State Variable Derivativesms 0 0 0 0 5.7 rad/sec21 0 5.710-3rad/sec 5.710-33.578234How small t should
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