I've found that slow systems and nonlinear systems can be best dealt with in a computer. A good example is an oven controller.
An oven is typically so slow, that analog components are not suited to the long time constants. In addition, people generally desire the oven to settle at temperature promptly.
Through utilizing a PID controller, one can get an oven tuned in, but it will either be slow or overshoot (or likely both). Through the magic of programming, you can change the nature of the control algorithm as the oven heats.
Start with open loop control and a maximum call for heat until the oven reaches a specific setpoint.
Switch in a PID loop with a reduced D coefficeint and a preset integrator value (such that you are targeting a sever overshoot). Continue this until you are quite close to the target setpoint and then...
Switch over to a PID loop with sufficeint D to ensure little overshoot and again preset the integrator.
Not an easy task in analag, but great for a computer. And, it has a practical application in that you can bake your brownies faster :D
- Mike