Tuning a Controller
When designing a controller, the following important points must be considered:
1. Stability
A central goal in control engineering is to avoid permanent oscillations in the system. Unstable systems oscillate with an ever-increasing peak value. At the stability limit, a system oscillates permanently with a constant peak value. A system whose oscillations decay is called a “stable” system. With decaying oscillations, the overshoot should be limited so that the components of the system are not damaged by too large an amplitude of the output quantity.
A controlled system is capable of oscillation if it contains at least 2 storage elements. An I controller or a D controller counts as an additional storage element. Since oscillation must be avoided with the highest priority, it is often helpful not to build storage elements into the controller if you can achieve the goals of control engineering without them.
By reducing the gain in the controller, you can often calm down an oscillating system.
2. Robustness
If you have set the parameters of a system so that it does not oscillate, you are only halfway there. The parameters of a real system change. A “robust” system remains stable even if its parameters change. You have to estimate how much the parameters can change. The following effects act on parameters:
Ageing: system parameters change over the service life. In a car, for example, the brakes get worse as they wear. In the engine, valves can wear and lead to a changed output torque. The output current of a solar panel decreases over the years for the same solar irradiance.
Unit-to-unit variation: if a manufacturer produces 1000 cars, they are not all identical. We call the difference between two vehicles of the same design unit-to-unit variation. It arises, for example, from manufacturing tolerances. The vehicles behave similarly, but not identically.
Dependence on environmental influences: many parameters depend on temperature, pressure or humidity. The load capacity of an electric car’s battery, for example, depends strongly on temperature. The characteristic of a valve can depend on pressure.
In practice, you should choose parameter settings that remain reliably stable even if the parameters change by 50 %. That is a robust system design.
3. Speed
In many applications, controlled systems should reach the final value quickly. They should also reach a steady state quickly and overshoot as little as possible. These goals contradict each other. You need a compromise. Note that robustness is always much more important than speed. A controller that oscillates after a few years in the field is always worse for the system than a slightly too long rise time.
Settings for robust and stable controllers
How must the controller parameters be set for a system to be robust and stable? There is no general rule for this, only approaches with which you are often right:
Few storage elements: a system’s tendency to oscillate increases the more storage elements it contains. That is why it can help to remove two storage elements in the controller from the system with kIR = 0 and kDR = 0.
Low gain: systems with high gain tend to oscillate more than systems with low gain. High gain tends to lead to a faster rise and stronger overshoot. So the controller parameters should tend to have small values.
Limits of systems
Many systems are limited. Their input and output quantities cannot take arbitrary values. One example is the bucket as a storage element. Its limits are the fill levels “empty” and “full”. It can happen that the controller drives the actuator in such a way that the bucket would have to be fuller than “full”. But it cannot be. A controller must cope with the system being limited. It must work in such a way that the bucket is never empty or full.
Anti-windup
If a system contains an I controller (or kIR > 0 in the PID controller), the control error is integrated (summed). If one of the quantities in the system cannot change freely (e.g. because of a limit), the control error may have large values over a longer period. If these are summed, the I component of the controller keeps growing. Afterwards, the I component only decreases when the control error again points in the other direction for a long time. This throws a controller out of step. To minimise this effect, the I component of a controller is often limited to a maximum value. This effect is difficult to describe; you will experience it in the lab.