need a full lab report, should include introductions, calculations in details, discussion and conclusion , provide for you the code part
SOUTHAMPTON SOLENT UNIVERSITY WSMSE (AUTOMATION & CONTROL LABORATORY) CONTROL SYSTEM ANALYSIS USING MATLAB & SIMULINK (SIMLAB1) Aims: · To use MATLAB & Simulink to assist in the process of analysing an example of a control system. · In so doing, to become familiar with some of the basic functions of MATLAB & Simulink as applicable to control system analysis. Objectives: · Given a Control System Block Diagram, reduce to a single block, hence obtaining the associated closed-loop transfer function of the system. · Use Routh-Hurwitz analysis to find a range of values of the system gain constant K for which the system is stable, and, after selecting a value of K in the region of stability identified, confirm the system’s stability using MATLAB. · Use Simulink to find the time-domain transient behaviour of the system in response to a unit step input. · Use MATLAB to find the time-domain equation of the system output in response to a unit step input, and confirm this by taking the Inverse Laplace transformation of the s-plane system output equation. · Find the frequency-domain response of the system from the transfer function. · Use MATLAB to create a Bode plot for the system transfer function. · Comment on whether the system’s time-domain response, given a unit step input, represents an over, under or critically damped system. Method, Results & Analysis: The following is an example of a control system block diagram: The block diagram reduces to the following single block system: Task 1: Confirm the above by carrying out the block diagram reduction yourself. Task 2: Given the following functions for G1(s) , G2(s) , and G3(s) find the transfer function of the system: G1(s) = s G2(s) = K G3(s) = s + 2 You should arrive at the following transfer function: Task 3: Use Routh-Hurwitz analysis to find a range of values of the system gain constant K for which the system is stable. You should find that the system is stable for: K ≥ 0. Let: K = 1/3 ; Hence: Task 4: Confirm the system’s stability using MATLAB, by entering the above transfer function into MATLAB and using the following commands: num=[4 0] %Sets up a row vector corresponding to the coefficients of s in the numerator of the transfer function. den=[1 6 3] %Sets up a row vector corresponding to the coefficients of s in the denominator of the transfer function. F=tf(num,den) %Sets up the transfer function. zplane(num,den) %Gives a pole-zero plot of the system. Task 5: Use Simulink to find the time-domain transient behaviour of the system output in response to a unit step input by doing the following: Set up a system schematic as follows: Click the simulate button, and save the result. With a unit step input the s-plane equation for the output of the system is given by: Task 6: Use MATLAB to find the time-domain equation of the system output in response to a unit step input, by inputting the following commands: s=sym('s') %Sets up a variable ‘s’. F=4/((s^2)+(6*s)+3) %Sets up the s-plane output equation of the system in an appropriate format. f=ilaplace(F) %Finds the inverse Laplace transform and hence the corresponding time-domain equation of the system. Task 7 (Optional): Confirm the above by taking the Inverse Laplace transformation of the s-plane system output equation. Task 8: Find the frequency-domain response of the system from the transfer function. Task 9: Use MATLAB to create a Bode plot for the system transfer function, by entering the following commands: F=tf(num,den) %Re-initialises transfer function in appropriate format. bode(F) %Generates a Bode plot of the system frequency response. Conclusions: Comment on whether the system’s time-domain response, given a unit step input, represents an over, under or critically damped system. SSI&CSIMLAB119/01/12r.2