Process Dynamics and Control (419307), 7cr Kurt-Erik Häggblom 2 . Basic control concepts

1. Process Dynamics and Control (419307), 7cr • Kurt-Erik Häggblom • 2. Basic control concepts • 2.1 Signals and systems • 2.2 Block diagrams • 2.3 From flow sheet to block diagram • 2.4 Control strategies • 2.5 Feedback control • Process • Control • Laboratory Process Dynamics and Control

2. 2. Basic control concepts • 2.1 Signals and systems • A system can be defined as a combination of • components that act together to perform a • certain objective. Figure 2.1. A system. • A system interacts with its environmentthrough signals. • There are two main types of signals: • input signals(inputs) , which affect the system behavior in some way • output signals (outputs) , which give information about the system behavior There are two types of input signals: • control signals are inputs whose values we can adjust • disturbances are inputs whose values we cannot affect (in a rational way) Generally, signals are functions of time , which we can indicate by and . • Process • Control • Laboratory Process Dynamics and Control

3. 2. Basic control concepts 2.1 Signals and systems A signal is (usually) a physical quantity or variable. Depending on the context, the term “signal” may refer to the • type of variable (e.g. a variable denoting a temperature) • value of a variable (e.g. a temperature expressed as a numerical value) In practice, this does not cause confusion. The value of a signal may be known if it is a measured variable. In particular, • some outputs are (nearly always) measured • somedisturbancesmight be measured • control signals are eithermeasured or knownbecausethey are given by the controller A system is a • static system if the outputs are completely determined by the inputs at the same time instant; such behavior can be described by algebraic equations • Dynamic(al) system if the outputs depend also on inputs at previous time instants; such behavior can be described by differential equations • Process • Control • Laboratory Process Dynamics and Control

4. 2. Basic control concepts • 2.2 Block diagrams A block diagram is a • pictorial representation of cause-and-effect relationshipsbetween signals. • The signals are represented by • arrows, which show the direction of information flow. • In particular, a block with signal arrows denotes that • the outputs of a dynamical system depend on the inputs. • The simplest form a block diagram is a single block, illustrated by Fig. 2.1. • The interior of a block usually contains • adescriptionor the nameof the corresponding system, or • asymbol for the mathematical operation on the input to yield the output. • Figure 2.2. Examples of block labeling. • Process • Control • Laboratory Process Dynamics and Control

5. 2. Basic control concepts 2.2 Block diagrams The blocks in a block diagram consisting of several blocks are connected via their signals. The following algebraic operations on signals of the same type are often needed: • addition • subtraction • branching • Process • Control • Laboratory Process Dynamics and Control

6. 2. Basic control concepts • 2.4 Control strategies • 2.4.1 Open-loop control • In some simple applications, open-loop control without measurentscan be used. In this control strategy • the controller is tuned using a priori information (a “model”) about the process • after tuning, the control actions are a function of the setpoint only (setpoint = desired value of the controlled variable) • This control strategy has some advantages, but also clear disadvantages. Which? • Process • Control • Laboratory • Examples of open-loop control applications: • bread toaster • idle-speed control of (an old) car engine Process Dynamics and Control

7. 2. Basic control concepts 2.4 Control strategies • 2.4.2 Feedforward control • Control is clearly needed to eliminate the effect of disturbances on the system output. Feedforward control is a type of open-loop control strategy, which can be used for disturbance elimination, if • disturbances can be measured • we know how the disturbances affect the output • we know how the control signal affects the output • Feedforward is an open-loop control strategy because the output, which we want to control, is not measured. • Obviously, this control strategy has advantages, but it also hassome disadvantage. Which? • When feedforward control • is used, it is usually used in • combination with feedback • control. • Process • Control • Laboratory Process Dynamics and Control

8. 2. Basic control concepts 2.4 Control strategies • 2.4.3 Feedback control • Generally, successful control requires that an output variable is measured. In feedback control, this measurement is fed to the controller. Thus • the controller receives information about how a control action affects the output • usually the measured variable is the variable we want to control (in principle, it can also be some other variable) • Process • Control • Laboratory Process Dynamics and Control

9. 2. Basic control concepts • 2.5 Feedback control • 2.5.1 The basic feedback structure • Process • Control • Laboratory Process Dynamics and Control

10. 2. Basic control concepts 2.5 Feedback control • 2.5.2 An example of what can be achieved by feedback control • We shall illustrate some fundamental properties of feedback control by considering control if the inside temperature of a house. • The temperature inside the house depends on the outside temperature and the heating power according to some dynamic relationship. If we assume that • depends linearly (or more accurately, affinely) on • the dynamics are of first order • the relationship between the variables can be written • (2.1) • where is the static gain and is the time constant of the system. The system parameters have the following interpretations: • denotes how strong the effect of a system input ( ) is on the output ( ); a larger value means a stronger effect • denotes how fast the dynamics are; a larger value means a slower system • Process • Control • Laboratory Process Dynamics and Control

11. 2.5 Feedback control 2.5.2 An example of what can be achieved • In this case . The equation shows that in the steady-state ( ) • if • an increase of increases • an increase of increases • Thus, the simple model (2.1) has the same basic properties as the true system. We want • the inside temperature to be equal to a desired temperature • in spite of variations in the outside temperature • even if the system gain and the time constant are not accurately known. A simple control law is to adjust the heating power in proportion to the difference between the desired and the actual inside teperature, i.e, (2.2) • Process • Control • Laboratory Process Dynamics and Control