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 • 2.3 From flow sheet to block diagram • Process • Control • Laboratory Process Dynamics and Control

7. 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

8. 2.4 Control strategies 2.4.1 Open-loop control • Example 2.3. Open-loop control of a static system. • Assume that the system output is given by . What control action causes to follow the setpoint ? • Clearly, the required control action is . • What control action is needed if , where is some function. Which is the general principle? • Exercise 2.2. Open-loop control of the liquid holdup in a tank. • Consider the liquid tank in the figure. • The flow rate of the incoming liquid • is held (approximately) constant by a • controller. • Derive the open-loop control law for , • which causes the liquid volume to • follow the setpoint . • Hint: How does depend on and ? • Process • Control • Laboratory Process Dynamics and Control

9. 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? • Exercise 2.3. Feedforward control of the liquid holdup in a tank. • Consider the same problem as in Exercise 2.2. Derive the feedforward control law for using the measurement of . • Note: This is simple! • Process • Control • Laboratory Process Dynamics and Control

10. 2. Basic control concepts • Process • Control • Laboratory Process Dynamics and Control