Controller Design, Matlab Analysis and Implementation Study
CONTROLLER DESIGN 1
ControllerDesign, Matlab Analysis and Implementation Study
ASSIGNMENT– PID CONTROLLER
Aplant is controlled as shown in the block diagram below:
s)
Theplant dynamics are represented by:
Part1: Theoretical compensating function
Determinea compensating function G_{c}(s)such that one of the poles is eliminated. Provide all calculations indetail with explanation. [10 marks]
PIDcontroller is determined by a combination of PI controller and PDcontroller
PIController
Accordingto Nise(2015), the controller function for a PI controller is given by
Assumingthe system is to be compensated such that I has a percentageovershoot of less than 5% and a zero steady state error due to step
ThePlant Transfer function is given by
Workingout for the damping ration
Asseen inNise(2015), the formula for calculating the damping ration is given by
Workingout for the natural frequency
But
Also
Sincea PI controller has a zero at
And
K=0.15
PDcontroller
Accordingto Khan(2012), thetransfer function of a PD controller is given by
Assumingthat the PD controller for percentage Overshoot<5%
Workingout for the damping ration
Assumingthat the Setting Time is set at 1 sec
Findthe desired closed loop (c.l) pole location
AccordingtoSilvaand Bhattacharyya (2005), the closed loop pole location is determinedby
Determineangle for PD controller
>>scl = 5.7142*exp( j*( piacos(0.7) ) )
scl=
3.9999+ 4.0808i
>>g=zpk([ ],[0,4],1)
>>theta=pi( angle( evalfr( g, scl) ) )
theta=
0.7754
>>a = 5.7142 * sqrt(10.7^2)/ tan(theta) + 4
a=
8.1633
>> k =1/abs(evalfr(tf( [1, a],1)*g,scl)) %
k=
3.9999
Compensatorzero
LoopGain
PIDcontroller design
Assumingthat the PID controller is design to meet a specification ofpercentage over shoot of less than 5% and SettingTime is set at 1 sec
PIDcontroller is determined by a combination of PI controller and PDcontroller
Accordingto calculations done above
Accordingto Khan(2012), combiningthe two Controller functions for PI and PD yields and PID controller
Part2: Computer simulation
Usingthe Matlab Control System Toolbox, provide the following items,providing documentation on your methods and commenting on yourresults.

Construct and document a model of the plant. [2 marks]

Construct and document the functions R(s) and C(s) for a step response and an impulse response on the input R(s). [4 marks]

Provide a Bode Plot. [5 marks]

Use an appropriate Matlab tool to determine the stability of the control system. [4 marks] Upload your Matlab code to WOLF in runnable form. This will be discussed in class.
Part3: Practical implementation study
Describein one paragraph each, two possible methods of realtime practicalimplementation of a control system. Choose from nonprogrammablecontrol systems hardware, programmable logic controller or robotics.Cite a practical commercial example of each. [5marks]
RealTimecontrol system can be applied in nonprogrammable control systems inapplications such as direct acting valve in LPG cylinders. Thesecylinders are designed to operate within a specified limit ofpressure. The directacting valve is used to regulate the pressure inthe LPG cylinder to protect the cylinder from exploding due to highpressure. The valve consists of a ball held exposed to the systempressure inwards and opposed by resistive spring force on theoutwards. During a fire outbreak, the increase in temperature leadsto a corresponding increase in pressure inside the cylinder thusexerting compressing force on the spring. When this force exceedsthat of the preset maximum system pressure limit, the spring willunset the ball and excess pressure will be released out of thecylinder. This is a safety precaution that protects the cylinder fromexploding which is more risky that fire resulting from leaking gas.
RealTimecontrol system can also be applied in programmable control system,where the output is regulated by preset computer codes that dictatethe output based upon the feedback provided by the system. Forexample, in a diesel power plant, the system is programmed toautomatically detect increased loading on the grid and the systemautomatically increases the output power by injecting more fuel tothe engine. When the loading on the power grid drop, the output poweralso gradually drops. Such a programmed system ensure there isminimal loss and production is tailored to meet the instantaneousdemand.
Conclusion
Theaim of this assignment was to design PID controller and implement thedesign in Matlab to confirm if it meets design specifications. Theassignment was also meant to test the understanding of the possiblereal life application of control system in our day to day lives. Theaims of the exercise were met as the theoretically calculated PIDcontroller function was confirmed and analyzed in Matlab. Though, theexercise had its fair share of challenges since the question did notspecify the parameters that were to be by the PID controller to bedesigned. Thus, assumption had to be made especially on the expectedpercentage overshoot (pOS) and Setting Time (Ts) so as to be able tocome up with a PID controller.
References
Khan,H. (2012). Pidcontroller. 1st ed. Saarbrücken:LAP, Lambert Academic Publishing.
Nise,N. (2015). Controlsystems engineering. 1st ed.Hoboken, NJ: Wiley.
Silva,G., Datta, A. and Bhattacharyya, S. (2005). PIDcontrollers for timedelay systems.1st ed. Boston: Birkhäuser.
No related posts.