Magnetic Levitation [PDF]

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EXPERIMENT NO:03 MAGNETIC LEVITATION CONTROL EXPERIMENT MEX4243

NAME: J.B.S.THYRIAR REG.NO:211088830 GROUP: CLE-09-B DATE OF PERFORMANCE: 17/03/2014 DATE OF SUBMISSION: 02/04/2014 INSTRUCTOR:

AIMS :

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The first aim is to understand the dynamic behavior of SISO system.

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Then to design a PD controller and a PID controller to position the ball via the Maglev and to explain how PD and PID designs will affect the overall dynamic.

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And to understand the real-time application of control laws in a SISO plant.

OBJECTIVES :

To understand the dynamic properties of the system, obtain response plot from the nonlinear simulation and root locus plots from the linearized models. Carryout an identification experiment to obtain a model to describe the relations between the control voltage and the ball position. Obtain a root locus plot with a PD controller closing the loop around the ball position response and record performance parameters for different PID values. Obtain a root locus plot with a PID controller closing the loop around the ball position response and record performance parameters for different PID values.

APPARATUS: 1. Magnetic Levitation mechanical unit 2. Analog to Digital control unit 3. PID controlling software. 4. Magnetic levitation system and remote power control box. 5. PC with MATLAB software 6. Control system interfacing circuit

THEORY

INTRODUCTION :

The Maglev setup serves as a simple model of devices, which are becoming more and more popular in recent years i.e. Maglev trains and magnetic bearings. Maglev trains are recently tested and some lines are already available as for example in Shanghai. Magnetic bearings are used in turbines for the same reason as Maglev trains are being built, which is low friction in the bearing itself. Already many turbines are used commercially where the rotating shaft is levitated with magnetic flux. Some other magnetic bearings applications include pumps, fans and other rotating machines. The magnetic levitation systems are appealing for their additional possibility of active vibration damping. This can be done by various control algorithms implementations and without any modifications to the mechanical parts of the whole system. The Maglev unit allows for the design of different controllers and tests in a real time using Matlab and Simulink environment. 1. System setup and block diagram

Where k is a constant depending on the coil parameters. To present the full phenomenological model a relation between the constant voltage u and the coil current would have to be introduced analyzing the whole maglev circuitry.

However maglev is equipped with an inner control loop providing a current proportional to the control voltage that is generated for control purpose.

I=k1 . u

Exercise 01- Nonlinear Model Testing

TASK 

First, the response of the magnetic levitation model has set up.

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Then, the test was run with other value of control signal by changing the input value.

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The output signals were identified and its sing convention.

EXP :

The Matlab paths for the simulink system

Non- Linear Step response : when 0 step value was given

Output Signals for step 0 input (V)

Ball position (m) for 0 step input

Non-Linear Step response : for step input of 5

Output signal (V)

Ball positioning (m) (step 5)

Ans. Since there is no control voltage the ball initially tends to go downwards due to gravitational power. The stability is very low due to no feedback.

Exercise 2: Linear Model Testing

TASK 

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The model named MaglevIdent.mld was reached by the identification experiment

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Then it was executed in Simulink.

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In the work space we typed ‘ident’ and performed the identification.

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The model structure was specified, for example oe331 available to the workspace.

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The maglev transfer function T (z-1) was extracted using the following Matlab codes to write a ‘.m’ file to transform the model into the continuous from (use maglev.m file)

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sysd=filt(oe331.b,oe331.f,0.01);

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sysc=d2c(sysd,’zoh’);

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The following coding were used to perform the transformation from T(s) to G(s)

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PID=tf([0,2,4,2],[1 0]);

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G_Cont=sysc/(1-PID*sysc);

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The open loop poles were determined by obtaining a root locus plot.

EXP observation

The plant output signal

The root locus plot

Ans. According to the root locus plot there are poles in the positive part of the real axis. Which means the system isn’t stable. This will ultimately lead the system to an unstable situation so we could possibly say the system is unstable clearly.

Exercise 3: PD Control of ball position

Task 

Maglev root locus was opened using ‘rltool’ command in the workspace.

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PD controller was defined in the workspace and root locus was imported as the controller.

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PD parameter was changed and the results were examined.

Exp Observation

(P=4,D=0.2)

(P=4,D=3)

(P=8,D=0.2).

Root Locus and Bode plots.

Exercise 4- Real Time PD control of ball position

Task 

Sinusoidal and rectangular inputs were applied to the system.

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Examined the results.

Output of Ball position

Ans. The frequecies were Sine wave- 10Hz Square wave – 0.5 Hz

The real time system actually differs a lot from the simulation results. The system becomes stable after some time only. Mainly the stabilty of the system differs from the simulation part.Other than that the expected values were reached. The desired output was also somewhat lower than the real output.

Exercise 5- real Time PID control of ball position

Task

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The maglev unit was tested by the PID controller. (Used the Maglev_PID.mld).

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The error integration was turned on after 15 second in this exercise.

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Each parameter of the PID controller was changed and observed the change in responses.

Exp Observation

The Ball positioning output signal for (P=4, I=0.1, D=3)

Ans.

When using PID controller the output is more accurate and very much close to the desired output. When the PD controller was used output was similarly reduced and became stable, but in PID controller the system approaches the desired output and gives us the proper signal which very much appreciable. Therefore PID controller is better than just PD controller. The Integral part is useful in that case. Here the Errors were reduced more often.

Discussion We did the same practical with PD controllers and with PID controllers. By observing Fig 5 and 10 it is clearly obvious that Integral part is more responsible for the error reduction. The proportional term makes a change to the output that is proportional to the current error value. The proportional response can be adjusted by multiplying the error by a constant? ? , called the proportional gain. A high proportional gain results in a large change in the output for a given change in the error. If the proportional gain is too high, the system can become unstable. In contrast, a small gain results in a small output response to a large input error, and a less responsive controller. If the proportional gain is too low, the control action may be too small when responding to system disturbances. The contribution from the integral term is proportional to both the magnitude of the error and the duration of the error. Summing the instantaneous error over time gives the accumulated offset that should have been corrected previously. The accumulated error is then multiplied by the integral gain and added to the controller output. The integral term accelerates the movement of the process towards set point and eliminates the residual steady-state error that occurs with a proportional only controller. However, since the integral term is responding to accumulated errors from the past, it can cause the present value to overshoot the set point value. The rate of change of the process error is calculated by determining the slope of the error over time and multiplying this rate of change by the derivative gain Kd. The magnitude of the contribution of the derivative term to the overall control action is termed the derivative gain, Kd. The derivative term slows the rate of change of the controller output and this effect is most noticeable close to the controller set point. Hence, derivative control is used to reduce the magnitude of the overshoot produced by the integral component and improve the combined controller-process stability. However, differentiation of a signal amplifies noise and thus this term in the controller is highly sensitive to noise in the error term, and can cause a process to become unstable if the noise and the derivative gain are sufficiently large. Hence an approximation to a differentiator with a limited bandwidth is more commonly used. Such a circuit is known as a Phase-Lead compensator.

Proportional gain, Kp Larger values typically mean faster response since the larger the error, the larger the proportional term compensation. An excessively large proportional gain will lead to process instability and oscillation. Integral gain, Ki Larger values imply steady state errors are eliminated more quickly. The trade-off is larger overshoot: any negative error integrated during transient response must be integrated away by positive error before reaching steady state. Derivative gain, Kd Larger values decrease overshoot, but slow down transient response and may lead to instability due to signal noise amplification in the differentiation of the error.