17/10/2016To perform a block diagram reduction using MATLAB | Matlab Examples Matlab Examples Do You Speak Matlab? To perform a block diagram reduction using MATLAB It’s not convenient to derive a complex transfer function for a complex control system, therefore, the transfer function of each element of a control system is represented by a block diagram and the concerned system mentioned in the block represents the transfer function of the element. This symbolic representation in short form gives a pictorial representation relating the output and the input of a control system based on cause and e桨敡ect approach. Simple Block Diagram Block diagram shown above. Here G1(s) and G2(s) represents the transfer function of the individual elements of a control system. The system given is a feedback system or can also be called a closed loop system. The output signal C(s) is fed back to be compared with the input R(s) , the di桨敡erence E(s)=[R(s)– C(S)] is actuating signal or error signal. Problem: To reduce the given block diagram using sumblk and 䤀Ind impulse,step and ramp response. https://matlabexamples.wordpress.com/2013/11/29/toperformablockdiagramreductionusingmatlab/ 1/5 G4 = 100/(s+1). G3. As shown % below. G2. G2 = 2/((s^2) + (5*s) + 100). Using these defined input output we will be using sumblk ‐‐‐‐‐‐‐‐‐ G1. Why?? https://matlabexamples.OutputName = 'y'. G4.com/2013/11/29/toperformablockdiagramreductionusingmatlab/ 2/5 . G1. G3 = 10/((2*s) +1). %‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % Now we are required to define all the blocks input and output. G2. %‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % Note: Now we are required to relate all these inputs and outputs. G3.OutputName = 'ym'.OutputName = 'ug1'.wordpress.17/10/2016 To perform a block diagram reduction using MATLAB | Matlab Examples Given Block Diagram Matlab Program %‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % Experiment 2 ‐ Block Diagram Reduction % By Siddharth Kaul %‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % % Reduce the given Block Diagram using sumblk function.InputName = 'u'. G4.OutputName = 'ug2'. G1 = 1/(s+1).InputName = 'e'.InputName = 'ym'.InputName = 'r'. % [see the image attached] % % Given ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ s = tf('s'). '+‐').outputResp). [outputResp.1:10]. % Step Response ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ inputTime = [0:.%. time] = lsim(OutputTF.G2.3). % e = r ‐ y sum2 = sumblk('u'.wordpress. inputTime).sum1.G4. title('Step Response'). % u = ug1 + ug2 % Rest is pretty simple ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % we have to find the relationship between r and ym for our output transfer % function.17/10/2016 To perform a block diagram reduction using MATLAB | Matlab Examples % Because there are two summing points in our block diagram.1:10].'r'.1. % ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % End of Program. % You can notice ym is our output and its not attached to any summing point % hence it is not included in the summing.'ug1'. plot(time. subplot(3.com/2013/11/29/toperformablockdiagramreductionusingmatlab/ 3/5 . % Ramp Response ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ inputTime = [0:. A generalised form has been given % below. Others can also be included. xlabel('Time ‐‐>'). xlabel('Time ‐‐>').1). [outputResp.G3.1:10]. inputTime).'ym'). plot(time. %‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ sum1 = sumblk('e'. subplot(3. This way % matlab will be able to relate the transfer fuction with each other. inputSignal. Responses taken into account are step and % ramp. ylabel('Magnitude ‐‐>'). subplot(3. outputResp). xlabel('Time ‐‐>'). ylabel('Magnitude ‐‐>'). inputSignal = 1*inputTime. %‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % First Impulse ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ inputTime = [0:. [outputResp.2).sum2.'r'.1. inputSignal.outputResp). title('Ramp Response'). title('Impulse Response').'ug2'). time] = step(OutputTF). Created By Siddharth Kaul % ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Output: https://matlabexamples. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ OutputTF = connect(G1. ylabel('Magnitude ‐‐>').1.'y'. inputTime). time] = impulse(OutputTF. inputSignal = ones(size(inputTime)). plot(time. %‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % Calculating responses. com/2013/11/29/toperformablockdiagramreductionusingmatlab/ 4/5 .MyClassBook Asim https://matlabexamples. 2013 [https://matlabexamples. 4 thoughts on “To perform a block diagram reduction using MATLAB” Pingback: E桨敡ects of addition of poles and zeros to closed loop transfer function | MyClassBook Pingback: Addition of poles and zeros to the forward path transfer function – MATLAB Program | MyClassBook Pingback: E桨敡ects of addition of poles and zeros to closed loop transfer function .wordpress. Matlab Programming on November 29.17/10/2016 To perform a block diagram reduction using MATLAB | Matlab Examples Given Block Diagram’s Output Response This entry was posted in State Space Modelling and tagged Block Diagram.wordpress.com/2013/11/29/to-perform-ablock-diagram-reduction-using-matlab/] . Block Diagram Reduction. wordpress. https://matlabexamples. 2016 at 6:44 am Very Good Example.com/2013/11/29/toperformablockdiagramreductionusingmatlab/ 5/5 .17/10/2016 To perform a block diagram reduction using MATLAB | Matlab Examples April 2.
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