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# Instrumentation and Control Lab

### Ex 8: Modelling and Control of a Magnetic Levitation System

#### 8.1 Objective:

(i) To model the magnetic levitation system
(ii) Design a controller to control the position of a steel ball in magnetic field

#### 8.2 Apparatus:

(i) Magnetic levitation apparatus with the steel ball, (ii) Data acquisition card (iii) PC with Matlab and Simulink software etc.

#### 8.3 Procedure and Experimental Results:

(i) Write down the equation of motion of a steel ball under the magnetic and gravitational field. Find out the point of equilibrium.

(ii) Note that the equation governing the motion is nonlinear in nature. Linearise the equation of motion at equilibrium point. You may take the equilibrium current and positions are 0.8A and 0.009m respectively. Now find out the open loop transfer function (take voltage as input and position of the steel ball as output). Now derive the close loop transfer function with unity gain feedback.

(iii) Find out the pole zero locations of the transfer function. Also draw root locus and bode plot of the system. Is the system is stable?

(iv) Implement the above system in Simulink. Observe the step response of the system.

(v) Now add a transfer function in the form of (KP + KDS). Take some initial guess of KP and KD.

(vi) Plot the root locus and find out the values of KP and KD from desired root location. Also study frequency response and find out the gain margin and phase margin of the system.

(vii) Write down the closed loop transfer function of the overall system. Also draw block diagram of the system.

(viii) Implement the system with controller in Simulink and observe the step response as well as response for square wave set point.

(ix) Now instead of adding a transfer function in the form of (KP + KDS), add the transfer function in the form of (KP +KI/S + KDS). Repeat the steps (vi) to (viii).