Analysis

Analysis of the robustness of a SISO control system can be performed in the frequency domain, considering the system's transfer function and using Nyquist and Bode diagrams. Topics include phase margin and amplitude margin. For MIMO and, in general, more complicated control systems one must consider the theoretical results devised for each control technique: i.e., if particular robustness qualities are needed, the engineer must shift his attention to a control technique including them in its properties.

Constraints

A particular robustness issue is the requirement for a control system to perform properly in the presence of input and state constraints. In the physical world every signal is limited. It could happen that a controller will send control signals that cannot be followed by the physical system: for example, trying to rotate a valve at excessive speed. This can produce undesired behavior of the closed-loop system, or even break actuators or other subsystems. Specific control techniques are available to solve the problem: model predictive control, and anti-wind up systems. The latter consists of an additional control block that ensures that the control signal never exceeds a given threshold. (3000)

15. Make a list of terms from Text 15 and memorize them.

15. Read and translate Text 16 Text 16. Control Objectives

Generally speaking, the objective in a control system is to make some output, say y, behave in a desired way by manipulating some input, say u. the simplest objective might be to keep y small (or close to equilibrium point) – a regulator problem – to keep y – к small for r, a reference or command signal, in some set – a servomechanism or servo problem. Examples:

• On a commercial airplane the vertical acceleration should be less than a certain value for passenger comfort.

• In an audio amplifier the power of noise signals at the output must be sufficiently small for high fidelity.

• In papermaking the moisture content must be kept between prescribed values.

There might be the side constraint of keeping u itself small as well, because it might be constrained (e.g., the flow rate from a valve has a maximum value, determined when the valve is fully open) or it might be too expensive to use a large input. But what is small for a signal? It is natural to introduce norms for signals. Which norm is appropriate depends on the particular application.

In summary, performance objectives of a control system naturally lead to the introduction of norms.

15. Make a list of terms from Text 16 and memorize them

15. Give a short summary of Text 17 Text 17. Control Objectives

The use of automatic control systems permeates life in all advanced societies today. Such systems act as a catalyst for promoting progress and development. Control systems are an integral component of any industrial society and are necessary for the production of goods. Technological developments have made it possible to travel to the moon and outer space. The successful production of chemical components depends on the proper functioning of a large number of control systems used in lines for their production. As this fact is seldom apparent control engineering is often called a hidden technology.

Control engineering deals with the task of affecting a temporally changing process in such a way that the process behaves in a given way. Such tasks are not only found in technology, but also in daily life in very large number. For example the ambient temperature in a room must be held between given limits, despite temporal changes due to sun exposure and other influences. The grip arm of a robot must move along the edge of a workpiece or be led as fast as possible from one point to another in order to grip a workpiece. The same applies to the grip arm of a crane, which is to carry bricks to a certain place on the building site.

In all of these cases, a manipulated variable must be selected in such a way that the given goal is achieved. As this selection depends on how well the goal is reached, a control loop arises that consists of the given process and a new feature, the controller. In the first example, the room was the process and the thermal valve the automatic controller, which measures the current air temperature and lets more or less heat into the heater depending on the deviation from the target temperature. In the robot example the control equipment has the task of steering the grip arm on a given course and/or to a given point, whereby the control is based on information that is supplied by the sensors installed on the grip arm. In the third example, the automatic controller is the crane operator, who determines the current grip arm position by sight and steers the crane. (2200)