MECH 350 Introduction to Mechatronics Lab 1: Step response of RC circuit system: Experimental and Simulation Analysis Objectives The objectives of this lab are to 1) Introduce students to experimental

analysis and study of first-order RC circuit dynamic system. 2) Perform step response on the first-order RC circuit system through an experiment in the lab. 3) Perform step response on the first-order RC circuit system through a computer simulation using MATLAB and SIMULINK. Introduction: Computer simulation and experimental study are the main methods used by scientists and engineers to verify, study and analyze dynamic systems, in addition to the analytical solution. In this lab, an RC circuit model will be used to study step response of such representative first order dynamic system, which was analytically introduced in the lecture. The study will be performed both experimentally and via simulation using MATLAB and SIMULINK. Consider the RC circuit shown in Figure 1. In the lecture the following first order differential equation was derived for this circuit. Vin = vo + RC Vin R ww dvo dt Vout Figure 1: An RC Circuit (1) Task 1: Experimental step response of RC circuit Instruments Used in this task: ● Function Generator ● Oscilloscope Measure and record the value of the components given (including the resistor and capacitor). Construct the RC circuit as shown in Figure 1 using a breadboard. The input signal Vin which comes from the function generator that will be set to output a square wave with a frequency of 50.0 Hz, an amplitude of 1.0 V and a DC offset of 0.5 V. This will result in a square signal with a min value of 0 and a max value of 1 V. This signal represents a repeating unit step function every 20 milliseconds. Display both the input and output signals on the oscilloscope Channel 1 & 2. You need to use a splitter on the function generator output. Collect and store the data from the oscilloscope on the desktop. Use the collected data to plot the response using MATLAB and to determine the steady state amplitude of the output signal, the gain and the time constant. Task 2: MATLAB Simulation of step response of RC circuit Use the MATLAB simulation function 'ode45' to simulate the system. You will need first to write a MATLAB function that compute the derivative term from Equation (1) assuming that the input vin and the output vo are known. Let us call the derivative term dvodt and use it as the output of the fucntion. In the function you need to define vin and give it a value and to use it with the value of vo that will be supplied as input to the function with the time t. function dvodt = 10e3; 0.1e-6; 1; с = vin dvodt Components Used in this task: Capacitor C=0.1 µF (Qty:1) Resistor R=10 KN (Qty:1) Breadboard = = = RC circuit (t, vo) 1/ (R*C) * (vin >> [t, y]=ode45('RC_circuit',[0 .01], 0); Now you are ready to plot the result. >> plot(t,y) - vo); Assuming that we saved the function using the name "RC_circuit.m”, we can use the MATLAB built-in function "ode45", as indicated, below to generate the simulation data y and t. Use the plotted response to determine the steady state amplitude of the output signal, the gain and the time constant. Task 3: SIMULINK Simulation of step response of RC circuit Here we will use the same function 'ode45' but through the graphical simulation interface SIMULINK. There are a number of methods to do the simulation in SIMULINK. However, we will use the method that utilize the transfer function block. To do that convert the differential equation given by Equation (1) into a transfer function that relate Vo(s) to Vin(s). RC circuit_simulation - Simulink classroom use Model Browser SIMULATION FILE LIBRARY PREPARE a w↑ □ Ready DEBUG Stop Time 0.01 Normal Fast Restart RC circuit_simulation MODELING RC_circuit_simulation Step Back ▾ SIMULATE R*C₁s+1 out.time FORMAT 100% Run vo(s) Vin (s) APPS out.y = 1 RC s +1 X Step Stop REVIEW Forward auto(ode15s) Property Inspector (1) Figure 2: SIMULINK simulation model of RC circuit with a step response Build the SIMULINK model shown in Figure 2 and use it to simulate the response for 0.01 seconds. Task 4 Analysis Plot the response as given by the analytical solution for t = 0 to t = 0.01 seconds. Comment on the results obtained from the four tasks. To what extent the results match the analytical predictions, in terms of time constant and steady state amplitude of the output signal from the RC circuit.