1、Add Your Company SloganChapter 9:Control Systems BasicsControl Systems Basics2In this chapter,it:Introduces the fundamental concepts of control systems engineeringIntroduces the terminology of control system designDescribes the steps of designing and testing a controllerShows how to interpret block
2、diagram representations of systemsAfter reading this chapter,you should be able to understand the feedback principles,the plant characteristics,the controller structure design,the parameter specification,and the system stability.Text A:Concepts of Control System39.1 IntroductionA control system(also
3、 called a controller)manages a larger systems operation so that the overall response approximates commanded behavior.In years past,mechanical or electrical hardware components performed most control functions in technological systems,sometimes human participation of the control loop was necessary.A
4、well-designed embedded controller can provide excellent system performance under widely varying operating conditions.To ensure a consistently high level of performance and robustness,a control system must be carefully designed and thoroughly tested.Many of the techniques of control system engineerin
5、g rely on mathematical manipulations of system models.Text A:Concepts of Control System6Open-Loop Control and Feedback Control:In many control system designs,it is possible to use either open-loop control or feedback control.Feedback control systems measure the system parameters being controlled and
6、 use that information to determine the control actuator signal.Open-loop systems do not use feedback.All the systems described in Table 9.1 use feedback control.Example 9.1:Consider a home heating system consisting of a furnace and a controller that cycles the furnace off and on to maintain a desire
7、d room temperature.This type of controller could be implemented with open-loop control and feedback control.Text A:Concepts of Control System7Open-Loop Control:For a given combination of outdoor temperature and desired indoor temperature it is possible to experimentally determine the ratio of furnac
8、e on-time to off-time that maintains the desired indoor temperature.An open-controller implementing this algorithm will produce the desired results only so long as the system environment remains unchanged.Feedback Control:A feedback controller for this system measures the indoor temperature and turn
9、s the furnace on when the temperature drops below a turn-on threshold.The controller turns the off when the temperature reaches a higher turn-off threshold.We focus on control systems that use feedback because feedback controllers,in general,provide superior system performance in comparison to open-
10、loop controllers.Text A:Concepts of Control System8As the applications of embedded computing expand,an increasing number of controller functions moving to software implementations.To function as a feedback controller,an embedded processor uses one or more sensors to measure the system state and driv
11、es one or more actuators that change system stateThe sensor measurements are inputs to a control algorithm that computes the actuator commands.The control system design process encompasses the development of a control and its implementation in software along with related issues such as the selection
12、 of sensors,and the sampling rate.Text A:Concepts of Control System99.3 Plant CharacteristicsIn the context of control systems,a plant is a system to be controlled.From the controllers point of view,the plant has one or more outputs and one or more inputs.Sensors measure the plant outputs actuators
13、drive the plant inputs.At the beginning of a control system design project,it is helpful to identify a number of plant characteristics relevant to the design process.Linear vs.nonlinear systems:a linear system produces an output that is proportional to its input.Text A:Concepts of Control System10Re
14、al-world systems are never precisely linear.Various factors always exist that introduce nonlinearities into the response of a system.For example,some nonlinearities in the automotive control discussed earlier are:The force of air drag on the vehicle is proportional to the square of its speed through
15、 the air.Friction(a nonlinear effect)exists within the drive train and between the tires and the road.The speed of the vehicle is limited to a range between minimum and maximum values.But the linear idealization is extremely useful as a tool for system analysis and control system design.Text A:Conce
16、pts of Control System11Several of the design methods in the following chapters require a linear plant model.This immediately raises a question:If you do not have a linear model of your plant,how do you obtain.The approach usually taught in engineering courses is to develop a set of mathematical equa
17、tions based on the laws of physics as they apply to the operation of the plant.These equations are often nonlinear,in which case it is necessary to perform additional steps to linearize them.Linear plant models are sometimes available from system data sheets or by request from experts familiar with
18、the mathematics of a particular type of plant.Another approach is to perform a literature search to locate linear models of plants similar to the one of interest.Text A:Concepts of Control System12System identification is an alternative if none of the above approaches are suitable.System identificat
19、ion is a technique for performing semi-automated linear plant model development.This approach uses recorded plant input signal u(t)and output signal y(t)data to develop a linear system model that best fits the input and output data.Simulation is another technique for developing a linear plant model.
20、You can develop a nonlinear simulation of your plant with a tool such as Simulink and derive a linear plant model on the basis the simulation.Perhaps you just dont want to expend the effort required to develop a linear plant model.With no plant model,an iterative procedure must be used to determine
21、a suitable controller structure and parameter values.In this situation,we can apply and tune PID controllers.PID controller tuning is carried out with the results of experiments performed on the system consisting plant plus controller.Text A:Concepts of Control System13Time Delays:Sometimes a linear
22、 model accurately represents the behavior of a plant,but a time delay exists between an actuator input and the start of the plant response to the input.Example:controlling the temperature of a showerMany industrial processes exhibit time delays.Control system design methods that rely on linear model
23、s cant directly work with time delays,but it is possible to extend a linear plant model to the effects of a time delay.The resulting model is also linear and captures the approximate effects of the time delay.Linear control system design methods are applicable to the extended plant model.Text A:Conc
24、epts of Control System14Continuous vs.Discrete Time Systems:A continuous-time system has outputs with values defined at all points in time.The outputs of a discrete-time system are only updated or used at discrete points in time.Real-world plants are usually best represented as continuous-time syste
25、ms.An embedded computing system measures its inputs and produces its outputs at discrete points in time.The embedded software typically runs at a fixed sampling rate,which results in input and output device updates at equally spaced points in time.Two basic approaches are available for developing co
26、ntrol algorithms that run as discrete-time systems:perform the design entirely in the discrete-time domain.perform the control system design in the continuous-time domain followed by a final step to convert the control algorithm to a discrete-time representation.Text A:Concepts of Control System15Nu
27、mber of Inputs and Outputs:The simplest feedback control system,a single-input-single-output(SISO)system,has one input and one output.In a SISO system,a sensor measures one signal and the controller produces one signal driving an actuator.Control systems with more than one input or output are called
28、 multiple-input-multiple-output(MIMO)systems.Because of the added complexity,fewer MIMO system design procedures are available.The pole placement and optimal control design techniques are directly suitable for MIMO systems.In many cases,MIMO systems can be decomposed into a number of approximately e
29、quivalent SISO systems.The critical factor that determines whether a MIMO system is suitable for decomposition into a number of SISO systems is the degree of coupling between inputs and outputs.When too much coupling exists from a plant input to multiple outputs,there is no but to perform a control
30、system design with the use of a MIMO method.Text A:Concepts of Control System169.4 Controller Structure and Design ParametersThe two fundamental steps in designing a controller are to:specify the controller structuredetermine the value of the design parameters within thatThe controller structure ide
31、ntifies the inputs,outputs,and mathematical form of the control.Example:root locus methodLike engineering design in other domains,control system design tends to be an iterative process.It might turn out that no combination of parameter values for a given controller structure results in satisfactory
32、performance.When this happens,the controller structure must be altered in some way that performance goals will be met.Text A:Concepts of Control System179.5 Block DiagramsA block diagram of a plant and controller is a graphical means of representing the structure of a controller design and its inter
33、action with the plant.Figure 9.1 is a block diagram of an elementary feedback control system.Each block in the figure represents a system component.The solid lines arrows indicate the flow of signals between the components.Text A:Concepts of Control System18In block diagrams of SISO systems,a solid
34、line represents a single scalar signal.In MIMO systems,single line can represent multiple signals.The circle in the figure represents a summing junction,which combines its inputs by addition or subtraction depending on the+or-sign next to each input.The contents of the dashed box in Figure 9.1 are t
35、he control system components.The controller are the reference input(or set point)and the plant output signal(measured by the sensor),which is used as feedback.The controller output is the actuator signal that drives the plant.A block in a diagram can represent something as simple as a constant value
36、 that multiplies the input or as complex as a nonlinear system with no known mathematical representation.Text A:Concepts of Control System19Linear System Block Diagram Algebra:It is possible to manipulate block diagrams containing only linear components to achieve compact mathematical expressions re
37、presenting system behavior.The goal of this manipulation is to the system output as a function of its input.The expression resulting from this exercise is useful in various control system analysis and design procedures.Each block in the diagram must represent a linear system expressed in the form of
38、 a transfer functions.Figure 9.2 is a block diagram of a simple linear feedback control system and lowercase characters identify the signal transformations in this system.Text A:Concepts of Control System20In Figure 9.2:r is the reference input.e is the error signal,computed by subtracting the senso
39、r measurement from the referencey is the system output,which is measured and used as the feedback signal.The blocks in the diagram represent linear system components.Each block can represent dynamic behavior with any degree of complexity as long as the requirement of linearity is satisfied,for examp
40、le:Gc is the linear controller algorithm.Gp is the linear plant model(including actuator dynamics).H is a linear model of the sensor,which can be modeled as a constant(1,for example)if the sensor dynamics are negligible.Text A:Concepts of Control System21The fundamental rule of block diagram algebra
41、 states that the output of a block equals the block multiplied by the block transfer function.Applying this rule twice results in Eq.Eq 9.1 says the system output y is the error signal e multiplied by the controller transfer function Gc,and multiplied again by the plant transfer function Gp.The sens
42、or measurement is the system output y multiplied by the sensor transfer function H.This relationship appears in Eq 9.2:Substituting Eq 9.2 into Eq 9.1 and rearranging algebraically results in Eq 9.3:Text A:Concepts of Control System22Eq 9.3 is a transfer function giving the ratio of the system outpu
43、t to its reference input.This form of system model is suitable for use in numerous control system analysis and design tasks.By employing the relation of Eq 9.3,the entire system in Figure 9.2 can be replaced with the equivalent system shown in Figure 9.3.Remember that these manipulations are only va
44、lid when the components of the block diagram are all linear.Text A:Concepts of Control System239.6 Performance SpecificationsOne of the first steps in the control system development process is the definition of a suitable set of system performance specifications.Controller performance specifications
45、 can be stated in both the time domain and in the frequency domain.Time domain specifications usually relate to performance in response to a step change in the input.Time domain specifications include,but are not limited to,the following parameters:l tr is the rise time from 10 to 90 percent of the
46、commanded value.l tp is the time to peak magnitude.l Mp is peak magnitude.This is often expressed as the peak percentage by which the output overshoots the step input command.l ts is the settling time to within some fraction(such as 1 percent)of the step input command value.Text A:Concepts of Contro
47、l System24Examples of these parameters appear in Figure 9.4,which shows the response of a hypothetical plant plus controller to a step input command with an amplitude value of 1.0.The time axis zero location is the instant response of application of the step input.The step response in Figure 9.4 rep
48、resents a system with a fair amount of overshoot(in terms of Mp)and oscillation before converging to the reference input.Text A:Concepts of Control System25Tracking error is the error in the output that remains after the input function has been applied for a long time and all transients have died ou
49、t.It is common to specify the steady-state controller error characteristics in response to different commanded input functions such as steps,ramps,and parabolas.The following are some example specifications of tracking error in response to different input functions:zero tracking error in response to
50、 a step input,less than X tracking error magnitude in response to a ramp input,where X is a nonzero value.Text A:Concepts of Control System26Performance specifications also can be stated in the frequency domain.The controller reference input is usually a low-frequency signal,while the noise in the s
