Introduction

1.1 Introduction to Control Systems

Control engineering is the science of altering the behavior of a dynamic process in a beneficial way. By dynamic process, we mean a process whose output(s) change as a continuous, time-varying function of the input(s). A simple example is the temperature of a room controlled by a boiler and radiator. The input to the system is the desired room temperature and the manner in which the actual room temperature responds is a dynamic function dependent on the physical parameters associated with the boiler, room, and the external conditions.

Control systems are key components in a range of industrial areas and applications, including marine and mechanical engineering, industrial manufacturing, chemical and process engineering, aviation, space flight, and electrical systems. Control systems also surround us in everyday life, in applications such as thermostats (in, e.g., hot water tanks and refrigerators), washing machines, consumer electronics, traffic lights, car cruise controls, etc.

The use of a control system in a mechanism, device, or process may have many different objectives. Of highest importance is to ensure system stability, for example controlling the reaction rate in a chemical process to prevent it going out of control. Control systems may also be used to optimize the operation of a plant, such as the adjusting of fuel and air flow rates to an engine to maximize fuel efficiency and minimize emissions. The use of active roll stabilization in ships modifies the dynamic behavior of the vessel in order to improve passenger comfort. Control systems may also be used to improve inherent performance limitations of a system, for example, to speed up the dynamic response. An example of the latter is the control of modern fighter jets, where advanced control is used to stabilize the aircraft and provide improved high-speed manoeuvrability.

In addition to a controller, control systems also usually include other elements:

• Sensors are used to measure some physical property of the process or plant and thus provide information for the controller, e.g., a thermo-couple device to provide temperature data or an optical encoder to measure the rotation of a motor.

• Actuators transduce signals from the controller to provide the input to and cause a change in behavior of the process or plant, e.g., a hydraulic ram to rotate the rudder in a steering gear system, a heater, or an electric motor transmission to drive a link of a robotic arm.

It is important to keep in mind that these components may also influence the behavior of the overall control system, for example, if they have a slow response or provide inaccurate or noisy data.

1.2 History of Control Engineering

The field of control engineering has developed alongside the industrial revolution. The steam engine centrifugal governor, used by among others James Watt and illustrated in Figure 1.1, is often considered to be one of the first automatic controllers. The governor adjusts the steam supply to the engine according to the engine speed, ensuring stable operation under varying load conditions. (If the speed drops due to a load increase, the steam supply is increased, and vice versa.) These early control systems were developed by engineers in the mid-nineteenth century and were followed by a more formal mathematical analysis of dynamic systems by scientists such as James C. Maxwell and Oliver Heaviside.

What is currently considered to be standard techniques in feedback control systems design, including proportional-integral-derivative (PID) feedback control, root locus, and frequency response methods, were developed around 1920-1950 by engineers and scientists such as Walter R. Evans, Hendrik W. Bode, and Harry Nyquist. Evans developed the root locus method, a graphical method to determine the behavior of a system for variations in some design parameter, such as controller gain. Bode and Nyquist developed techniques to study the time-domain stability and behavior of a system based on its frequency-domain characteristics. We will use these tools later.

1.3 Control System Structure

Control systems can, in general, be classified as either open loop or closed loop. Let us look at what these terms mean, and what the structure of a control system looks like.

1.3.1 Open-loop systems

In open-loop systems, the output of a plant or process may be controlled by varying the input, but the actual output has no influence upon that input. This can be illustrated with a simple block diagram as shown in Figure 1.2.

An example of an open-loop control system is a room with a simple electric fire, illustrated in Figure 1.3. In this case, given an input (the mains supply switched on), the output (the room temperature) will eventually arrive at some constant level, i.e., the room temperature will become constant with time. The value of the output is dependent on the prevailing conditions or plant behavior, in this case the size of the heater and the heat losses from the room. If the rate of heat loss changes, for example, due to a change in outside temperature (external disturbance) or if someone opens a window (change in the plant), the room temperature will eventually settle at a new and different steady-state value. The open-loop control system does not know about the change in temperature and is therefore unable to correct for these external disturbances; when switched on the electric fire output is constant for all cases.

1.3.2 Closed-loop systems

In order for the system to be able to respond to external disturbances, variations in the input, or plant changes, and to achieve a desired output value, a closed loop (also known as feedback) system is required. Using a closed-loop control system, the actual output is continuously compared with the desired output value, in order that the controller can compensate for these system changes.

Consider the electric fire example from above: in a well-insulated room the temperature might rise to an uncomfortable level and the fire would have been switched off by someone sensing the room temperature. This situation is illustrated in Figure 1.4. Based on the “sensor signal” (the felt temperature), the person determines the action to be taken, i.e., acts as a controller, and switches the supply on or off. The actuator in this system is the heater, which is the component providing the heat energy input to the room. The controller adjusts the heater state, thereby modifying the flow of heat energy to the room. This type of control system is known as a closed-loop control system, or sometimes an error-actuated feedback control system.

1.3.3 System structure

In all closed-loop control systems, the output is measured and compared to the desired output (the setpoint). Any difference between the two (called an “error signal”) forms the input to the controller. Open-loop control systems do not have this feedback loop, and can therefore not compensate for errors resulting from changes in the plant, variations in the setpoint, or disturbances acting on the system in the way that closed-loop systems can.

The standard block diagram representation of a feedback control system is shown in Figure 1.5. In many cases, the actuator and the plant are represented by one block, since they are often closely integrated.

In the block diagram, the blocks represent components of the system, whereas the connecting vectors represent some system state or signal. In the room temperature example, if controlled by a thermostat, the room is the plant, with the output being the physical room temperature and the setpoint is an electronic signal representing the desired output temperature. The sensor, a component of the system, converts the actual temperature to a measured temperature signal. The difference between the setpoint and the actual output value, the error signal, is fed to the controller. The controller output...