The goal of this project is to model a system and analyze its performance. The system...
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The goal of this project is to model a system and analyze its performance. The system to be controlled is the ball-suspension system shown in the figure. The steel ball is suspended in the air by the electromagnetic force generated by the electromagnet. The control objective is to keep the metal ball suspended at the nominal equilibrium position by controlling the current in the magnet with voltage e(t). The resistance of the coil is R and the inductance is L(y) = L/y (depending on y). The force generated by the electromagnet is Ki²/y². 1) Model the system by deriving the state equations. 2) Draw the block diagram for the system 3) Suppose the Linearized state space model for the system is as follows: [Ax1] Ax2 Ax3 0 2kx32 mx 13 0 1 0 x3 x1² 0 -2kx3 mx1² Ax+ Au -R L With the following parameters e(t) = 10~15V, K = 1, R = 1-20, g = 9.8, m = 0.2~0.3Kg, L= 0.4~0.6H where dy dt M Ki a. Find the characteristic equation for the system b. Draw the root locus for the system c. Is the system stable? d. Simulate the system step response x1 = y, x₂ = = V, X3 = Mg i and u = e(t) Choose among these parameters and perform the following: R Steel Ball m L Electromagnet e(t) The goal of this project is to model a system and analyze its performance. The system to be controlled is the ball-suspension system shown in the figure. The steel ball is suspended in the air by the electromagnetic force generated by the electromagnet. The control objective is to keep the metal ball suspended at the nominal equilibrium position by controlling the current in the magnet with voltage e(t). The resistance of the coil is R and the inductance is L(y) = L/y (depending on y). The force generated by the electromagnet is Ki²/y². 1) Model the system by deriving the state equations. 2) Draw the block diagram for the system 3) Suppose the Linearized state space model for the system is as follows: [Ax1] Ax2 Ax3 0 2kx32 mx 13 0 1 0 x3 x1² 0 -2kx3 mx1² Ax+ Au -R L With the following parameters e(t) = 10~15V, K = 1, R = 1-20, g = 9.8, m = 0.2~0.3Kg, L= 0.4~0.6H where dy dt M Ki a. Find the characteristic equation for the system b. Draw the root locus for the system c. Is the system stable? d. Simulate the system step response x1 = y, x₂ = = V, X3 = Mg i and u = e(t) Choose among these parameters and perform the following: R Steel Ball m L Electromagnet e(t)
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To model and analyze the ballsuspension system well go through the steps youve outlined 1 Model the system by deriving the state equations Lets denote ... View the full answer
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