Rajeev Control Lab Report

8/13/2019 Rajeev Control Lab Report

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INDIAN INSTITUTE OF SPACE SCIENCE AND TECHNOLOGYThiruvananthapuram

Control SystemsLab(Report)

By:

Rajeev VermaSC11B041

AEROSPACE

ROLL:35


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Lab Session 1Defining 's' in MATLAB:The mat lab code tfis used to define a transfer in mat lab directory s=tf('s'),Writing a transfer Function in mat lab:First we need to define susings=tf('s'),thenH=(s^2+s+2)/(s^3+s+3)ora=[1 1 2]b=[1 0 1 3]H=tf(a,b)can also be used to define transfer functionTo make step responseInitially defined a transfer function H(s)sstep response can be simply found out by using the mat labcommandstep(H)To make bode responseSimilarly the bode response of a transfer function can be simply defined using the command bode (H)bode(H)

Lab Session 2BlocksSourcesStep-It has three parameters step time i.e. time from which we need to step change the input commandInitial value, Final ValueConstant-to give a constant input, it only has one parameter the value of constantRamp-ramp command, we need to give slope, start time and initial output.Sine-to give sine command with parameters amplitude frequency and initial phase.Clock-Just counts the time.


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Sink-to workspace saves the output as a variable in workspaceContinues

Integrator-its the transfer function '1/s'Transfer function-used to define transfer function

Discontinuesused in case of non linearity's like coulomb function saturation back lash etc.

Math's Operations

Add-Add some inputs and give one outputGain-Multiply input with a constantProduct-Multiplies some input commands and give one output

LTI Viewerltiview when invoked without input arguments, initializes a new LTI Viewer for LTI system responseanalysis.Command is

ltiview(H)In case of simulink window go to control design linear analysis select plot type and click linearise modelCreate the complete simulink chart with source block, transfer functions and outputs to workspaceNow select any part of the system and right click on it and select create sub system, to create thesubsystem.To edit the mask, select edit mask in edit menu in the simulink window with subsystem


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Lab Session 3Proportional + rate feedback:

Here K1 and K2 are control Parameters. K1 is called proportional gain and K2 is called Feedback gain.Parameter definition for the simulation is:KT=0.181KB=0.181Jm=1.1694*10^-4JL=12.753NmNL=1/398Bm=2.943*10^-4BL=58.86Ra=8.6Kp=0.36KTG=0.1

Wb=5*2*piZai=0.6J=Jm+((NmNL)^2)*JLB=Bm+(KT*KB/Ra)+(BL*(NmNL)^2)K=KT/RaK1=(Wn^2)*J/(Kp*K)K2=(2*Zai*Wn*J-B)/(K*KTG)B1=B-KB*KT/Ra

The K1 and K2 are set in above to get standard 2nd order transfer function.Now to the system behavior we perform linear analysis of the system and calculate the :

a)3 dB bandwidth 4.97Hzb) M peak- .351dBc) Peak Overshoot for step response 9.47%d) Rise time 06mse) Settling time- 217ms


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Proportional+Integrator +rate feedback:Apply a integrator + a gain of K1/10 parallel to the proportional gain.


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a) 3 dB bandwidth 4.9815Hzb) M peak 0.378dbc) Peak Overshoot for step response 9.98%d) Rise time .67.6mse) Settling time 223ms


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Proportional + Integrator + Differentiator :When Tacho Generator is unavailable then to KTG=0 . So feedback loop os not possible. So in thesimulation we remove the rate feedback connection and apply a proportional Differentiator of(K2*KTG/Kp)s/(1/300*s + 1) in parallel to proportional gain K1.

a) 3 dB bandwidth 5.49Hzb) M peak .589dbc) Peak Overshoot for step response 10.7%d) Rise time 58.4mse) Settling time 202ms


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SESSION 4(a)Step response:

Step command is input at 100%,50%,10%and 5% of maximum amplitude of 4*398*p/180rad for 100% motor shaft deflection. The disturbance signal is kept to be zero.

100%

50%

10%5%


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Rise Time are:a.b.c.d.

100% command amplitude - .202sec50% command amplitude - .117sec10% command amplitude - .093sec5% command amplitude - 1.658 sec

Disturbance Response:Input command is kept zero and a disturbance torque is given to the moter torque o/p. forsimulation the magnitude of this step disturbance be .1*KT*Vs/Ra.(Vs=28). Finding theshaft deflection after 10sec for varing integrator gain as 0, K1/10, K1/5.

0

K1/10

K1/5


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For Ki=0 the value of o/p torque after 10sec is 0.3987.For Ki=K1/10 the value of o/p torque after 10sec is 0.1503.For Ki=K1/5 the value of o/p torque after 10sec is 0.05365.


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Lab Session 4(b)Part1The frequency response of a non-linear system is a function of input command amplitude. This can beevaluated by taking the ratio of the amplitude of fundamental harmonic of system output to the inputsinusoidal command amplitude and the phase lag of fundamental harmonic of system output w.r.t theinput sinusoidal command. A mat-lab program is developed to carry out the above task. The first part isto generate a sinusoidal sweep command of the specified amplitude and frequency range and thesecond part is to extract the fundamental harmonic amplitude ratio and phase lag. The mat-labsubroutines sweep.m and dtfa.m are developed to implement these tasks. The Simulink model used forfinding the non-linear system frequency response is shown in fig.

TheoryThe non-linear SIMULINK block diagram representation of electro-magnetic engine gimbal controlsystem using PI plus rate feedback controller. The non-linear elements are-:1) Actuators stroke limit-: We simulate this by limiting the final integrator generating the motordeflection variable by (4 *398*pi/180)2) Supply voltage limit-In the simulation we limit the supply voltage as 28V. Itsrepresented by Vs3) Integrator output limit-: Effective saturation limit of +- 13V is put on integrator controller output.


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4) Coulomb Friction-: The value of coulomb friction is 0.06 N-m w.r.t. motor shaft.

Graph of Sweep Command


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5%

10%


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50%

100%


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CommandAmplitude-3dBBandwidth(Hz)-90 Bandwidth(Hz)

5%-8.995-16.66dB

10%-13.53-14dB

50%-11.626-13.8dB

100%-11.65-20.2dB

Part 2The graph is obtained as follows of the speed torque characteristics and load focus.

Firstly start the lab6_1.m then Lab3_1.m then Simulink patch up file Lab6_3.mdl and then the filelab6_4.m and then we get the final graph.Typical command profiles are 100% sinusoidal command and 10% sinusoidal command with 5 Hzfrequency. The former will force the motor to operate to operate along its speed-torque saturation


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boundary whereas the latter will be within the motor capacity limits. The speed torque characteristics ofthe motor can be plotted using the following mat-lab commands.plot([Vs/KB 0],[0 KT*Vs/Ra])hold onplot([-Vs/KB 0],[0 -KT*Vs/Ra])plot(Speed_Torque(:,2),Speed_Torque(:,1))grid on

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Rajeev Control Lab Report