In this section we will look at the solutions for the response of various differential equation forms to step input changes. The step input is the only input we shall consider in this course.
All the equations in this section are linear and are in deviation variables - this greatly simplifies the solution. A step input, defined as a deviation variable, starts at zero and then at a time equal to zero rises to the value of the step. Since we are solving the equations for times greater than zero, the step simply appears in the equations as a constant input with a value equal to the height of the step.
In all the solutions in this section the symbol 'y' represents the process output and 'u' the process input.