Undergraduate and Master courses on automatic control usually show students how to design control systems for stabilizing and regulating Linear Time-Invariant (LTI) systems, which are typically encountered when the physical continuous-time system to control is linearized around an equilibrium point. Typically, control system design for such LTI systems is taught first in the Laplace domain, using the notion of Transfer Function. Although simple, this formalism is limited to systems whose dynamics do not change with time, and with only one input and only one output. Advanced courses on automatic control extend to the State-Space Theory, which admits controlling systems with several inputs and/or outputs, as well as Time-varying systems. However, such courses usually remain limited to the time-invariant case, not showing the students the power of the State-Space Theory to tackle the control of Linear Time-Varying (LTV) systems.

Linear time-varying systems frequently appear when nonlinear systems are linearized about a trajectory rather than an equilibrium point, and their dynamics and control are quite different from those of their LTI counterparts, which makes them counterintuitive and difficult to understand even for students who have already mastered control of LTI systems. Usually, when studying and learning LTI systems, students make use of popular computer and software packages that allow them to simulate the responses of the control systems they design, helping them to understand concepts such as stability, zeros, poles and their relationship with the static and dynamic metrics of these responses. However, when shifting to the time-varying case, these software packages are scarce when not nonexistent.

For the above reason, this work presents a package for simulating and understanding LTV control systems on Matlab, which is one of the most widely used software environments for learning, analyzing and deploying control systems. The proposed software package allows students to define LTV systems, simulate their open-loop response, study their controllability, design and test their closed-loop control using two of the most popular techniques (namely, pole placement and optimal control), and visualize their point-wise poles and zeros along time. The developed package is useful for teaching and learning control of LTV systems in subjects of state-space and advanced control techniques, as a preparation for later subjects on nonlinear control.

Keywords: Educational software, linear time-varying, control, automation.