Fundamentals

Controllers are at work everywhere in our everyday lives. The temperature of your body (internal core temperature) is kept at 37 °C by a biological controller. A cruise control in a car keeps the speed constant. A heating control system controls the temperature in a room. All these controllers are based on very similar principles, which control engineering deals with. Once you have internalised these principles and a few standard procedures, you can control a great many systems in the course of your technical career.

The goal of control engineering is for a quantity in the system (the “controlled variable”) to equal a setpoint. Using the example, this general formulation sounds like this: the body temperature should be 37 °C. The problem is that environmental influences act on the body temperature. To compensate for them, the body has to heat and cool. So it has to react actively to external influences.

What options does the body have? In the animal kingdom, an animal grows fur. With this, the body reacts to an environment that is too cold. There are also animals with a summer coat and a winter coat. These animals assume that, on average, it is much colder in winter than in summer. If that does not hold for once, the animal has a thermal problem. Changing the coat is a coarse intervention that at least moves the skin temperature in the right direction.

Some animals seek out thermally insulated places in their surroundings where they lose less heat. All of this is about minimising the effect of the outside temperature on the core temperature.

If that is not enough and the body becomes too warm or too cold, what can it do? It can heat or cool. Mammals heat by movement (e.g. shivering) or by increased metabolism. They cool by sweating and panting (dogs). Goosebumps, on the other hand, reduce heat loss.

The body’s reaction to a “wrong” temperature is limited in its effect. A lion cannot survive in the Arctic; its thermal means of intervention are too weak for that. With biological mechanisms, we can only ever compensate for slight deviations around the setpoint.

The control loop of human temperature regulation works as follows: the body knows the setpoint of its core temperature. The deviation is defined as setpoint minus actual value. The body can detect deviations upwards and downwards. It then reacts via one or more active interventions so that the deviation of the body temperature from the setpoint is as small as possible. Ideally it is 0; then the body temperature equals the setpoint.

The deviation “setpoint minus actual value” is positive when the body is too cold. The body then heats until the deviation disappears. If the body is too warm, the deviation is negative. The body then cools until the deviation disappears.

Let us look at a few terms from control engineering:

Terms

A setpoint is a specification that is often fed into the system from outside. It specifies what value the actual value should have. The setpoint is an input quantity. In the example it is the temperature value 37 °C. The reference variable is the official term for the setpoint in control engineering.

The controlled variable is changed by a control system so that it matches the setpoint as closely as possible. The controlled variable is an output quantity. In the example, the body temperature is the controlled variable.

The system is difficult to describe in general terms. The body is the system in which the temperature is controlled. The system is something in which the controlled variable (actual value) is present and that can accept a reference variable (setpoint).

A controller is a technical device – usually a piece of software – with which the goal of control engineering is to be achieved. It describes how to ensure that the controlled variable always matches the setpoint. The controller is added to the system for control. In the example of the body, parts of the brain and nervous system are responsible for control.

A disturbance variable influences the controlled variable unintentionally. It makes work for the controller, because the controller has to compensate for the effect of a disturbance on the controlled variable. Disturbances of body temperature control are, for example, the air temperature or the wind. If a person suddenly runs, their body heats up. The body reacts to this disturbance by sweating: it cools.

The actuator intervenes in the system so that the controlled variable changes. It is usually controlled directly by the controller. In the example, the actuator is the skin, through which sweating and goosebumps take place. The skin changes its behaviour so that the body temperature falls or rises. Another actuator is the metabolism, which provides more or less “heat production” in the body.

Further examples of controlled systems

The fill level of a water tank in a chemical plant should match a target level. The fill level of the tank is the controlled variable of the system. The target level is the reference variable. The tank is the system. It has an inlet with an adjustable valve, via which the inflow of water can be set. The inflow is the input quantity of the system. The valve is the actuator. Water is repeatedly drawn off from the tank, so that the fill level falls. This is the disturbance in the system. A controller has the task of ensuring that the fill level always matches the setpoint, no matter how much water is drawn off. To do this, the controller drives the actuator.

The speed (controlled variable) of a car (system) is controlled by a cruise control. The driver specifies the target speed (reference variable). The input quantity of the system is the accelerator pedal, which specifies the acceleration to the car’s control unit. The actuator is the engine. The controlled variable is the current speed of the car. Disturbances acting on the output quantity include the gradient of the road, headwind and friction. The cruise control is the controller. It ensures that the speed always matches the setpoint, no matter how large the disturbances are.

The three examples are greatly simplified to demonstrate the basic principle. To be able to analyse systems for control, we first convert them into a model. The model represents a real system as well as possible using mathematical equations.