A Role For Simulink In A Continuous Time Signals And Systems Course

SimulinkTM, which runs on the MATLABTM engine, can be introduced in a course on Continuous-Time Signals and Systems. Graphical concepts similar to textbook block diagram examples can easily be illustrated without referring to any underlying of the computational concepts. Early on in a course on Continuous-Time Signals and Systems, students see causal linear time-invariant systems described by differential equations, including block diagram realizations using integrators 1 . This usually reinforces the exposure to differential equations seen in a circuit analysis course, where a differential equation represents a circuit with a forcing function. In the context of a continuous-time course, systems are treated as block diagrams and a system described by a differential equation can be easily built using SimulinkTM as illustrated in a textbook. This paper suggests a two-part exercise involving a second order system, initially given fixed coefficients, with a one-volt step function input. In the first part, the students are given a SimulinkTM file containing an implementation of the system as a cascade of a feed forward section with a feedback section; this construction is usually referred to as the Direct Form I realization of the differential equation. Using the principle discussed in the course the students reverse the cascade and observe no change in the output. The student should then observe the redundancy of integrators and construct the Direct Form II or Canonic Form for this system. The output of the model, with the pre-selected coefficients, is a decaying sinusoid with a steady state response of zero volts. Using the first part as a reference or starting point; the second part asks the students to modify the coefficients to generate a step function response which oscillates with a period which is increased by a factor of two, a time constant which is reduced by a factor of two and a steady state response of two volts. The suggested first step is the correlation of the response from the first part with the differential equation coefficients via a pole-zero plot.