Transcript Control Strategies - University of Detroit Mercy

Control Strategies
Shuvra Das
University of Detroit Mercy
Topics




Feedback Control Systems
Bang-Bang Control
PID Control
Digital Control
Control System Components
Reference
Input
+
Error
Signal
Controller
_
Feedback
Signal
Controller
Output
Actuators
Actuators
Sensors
Sensors
Control
Inputs
Plant
Plant
Outputs
Plant
• Plant is the system whose performance we wish to
control.
• Such a system may have multiple inputs and
outputs.
• The essence of control is to determine which
control inputs affect the performance in which we
are interested, and to produce those inputs which
cause the plant to exhibit the desired performance,
as observed in the outputs of the system.
Controller
• The controller is the heart of the control system.
• The control engineer determines some way to
provide inputs to the plant, which will cause the
plant to behave as desired.
• The derivation of this strategy, called the control
law, is the primary focus of the control engineer.
• Implementation of control often takes place in
electronic circuitry, which performs mathematical
operations of integration, differentiation,
multiplication, addition and subtraction.
Controller
• The same operations can be accomplished through
computer code for a digital controller, which can
be as simple as a single chip processor, or as
complex as a high-end Pentium workstation.
• The error signal is the difference between the
desired (reference input) and the measured
outputs. A controller uses this error signal to
determine the appropriate control action.
• The larger the error, the more control effort will be
needed to achieve the desired performance.
Control System Components
Reference
Input
+
Error
Signal
Controller
_
Feedback
Signal
Controller
Output
Actuators
Actuators
Sensors
Sensors
Control
Inputs
Plant
Plant
Outputs
Actuators
• Actuators convert the controller’s output
signal (usually an electrical signal) into a
signal that has physical relevance to the
system we wish to control. Some examples
of actuators include motors, hydraulic
pistons, and relays.
Sensors
• Sensors are designed to convert some observed
physical quantity to a signal that can be processed
by the controller. For example, a potentiometer
(variable resistance) can be used to sense the
orientation of an antenna. A sonar sensor can be
used to sense the distance of an autonomous
material-handling robot from an obstacle in its
path. To measure temperature in a furnace used
for the heat treating of metals, a thermocouple can
be used.
Advantages of Feedback
 Providing the controller with information about
the plant's actual behavior allows for automatic
adjustments to maintain performance within
acceptable limits.
 Decreases sensitivity to variations in parameters
and to external disturbances
 Caution: feedback can produce instability
feedback can introduce instability
Feedback Control Concepts:
Input
Output
Controller
Actuator
Actuators
Plant
Plant
• Open loop control
• No feedback
• Controller receives no information about whether
or not it is providing the correct information
Open-loop control
Electronic control
unit
Motor
0
30
0
30
0
25
0
0
• Open-loop control of
the position of a robot
arm.
• The desired angular
position is set using a
dial or other input
device.  denotes the
actual arm position.
Open-loop control
• The control unit produces a voltage needed to
drive the motor (actuator) for an amount of time
dependent only on the input setting.
• There is no way to automatically correct for error
in the arm position.
• If someone accidentally disturbed the robot such
that its zero position was offset by a few degrees,
the controlled system would exhibit the same
offset error.
Closed-Loop/Feedback Control:
• In a closed-loop system there is feedback.
• The output is monitored by a sensor.
• The sensor measures the system output and
converts this measurement into an electrical
signal, which passes back to the controller.
• The feedback allows the controller to make any
adjustments necessary to keep the output at or near
its desired value.
• Closed-loop control is also known as feedback
control.
Closed-loop control
Control unit
Set
point
(300)
Error
Motor
+
_
300
00
Figure 4
Pot
• This time a potentiometer
(a.k.a. “pot”) has been
connected to the motor
shaft. As the shaft turns,
the pot resistance
changes. The resistance
is converted to a voltage
and then fed back to the
controller. Thus, we
have a measurement of
the actual arm position
Closed-Loop control
• To command the arm to an angular position of
30°, a set-point voltage corresponding to 30° is
sent to the controller. This is compared to the
measured arm position, and the controller drives
the motor in a direction to reduce the error.
• Feedback decreases a system’s sensitivity to
disturbances. Suppose the arm is bumped and it
comes to rest at 35 instead of 30 degrees. With a
closed-loop system, the effect of the disturbance is
measured and is passed back to the controller,
which compensates for the error.
Closed-loop control
Inlet
Valve
Sensors
Sensors
Inflow
Tank
Level
Outflow
Figure 5
• To maintain the level in the vessel, we have to
monitor the level itself and adjust the inlet valve if
the level deviates from the desired value.
• Such a feedback strategy is error driven in that the
control effort is a function of the difference
between the required level and the actual level.
Control Law
• The relationship between the error and the
control effort is called the control law.
Feedback control can provide regulation
against unmeasured disturbances.
An Application of Feedback
Control: Regulation
• A control system for maintaining the plant output
constant at the desired value in the presence of
external disturbances is called a regulator.
• Disturbances will cause the plant output to deviate
and the regulator must apply control action or
control effort to attempt to maintain the plant
output at the reference value with minimum error.
A good regulator will minimize the effects of
disturbances on the plant output.
Regulation
Disturbance, w
Compensation
e
r
+
Plant
+
D(s)
-
G(s)
+
1
Regulation
• As an example, consider a temperature control
system for a furnace. The goal is to maintain a
constant temperature equal to that specified as the
reference input. Opening the furnace door creates
a disturbance - a rush of cool air entering the
chamber. The performance of the system is
related to how quickly the system is able to
compensate for this disturbance.
Stability
• Simply and imprecisely, a system is unstable if its
output is out of control. Goal of control system
design is to cause the controlled system to possess
a desired output characteristic, an unstable system
is undesirable.
• If the plant is inherently unstable, then the
controller must stabilize the system. If the plant is
naturally stable, then the controller is to enhance
some characteristic of the system response without
causing instability. Note that closing the feedback
loop can affect the stability of a system.
Stability
• Picture an overhead crane with a wrecking ball
attached to the end of its chain. If the wrecking
ball is given an initial push and allowed to swing
freely, it will eventually come to rest at its
equilibrium point.
• Now consider the problem of balancing a
broomstick in an upright (or inverted) position.
This is an example of an unstable equilibrium
position.
Stability
• Even if we place the broomstick at this position
initially, once we let go, the broomstick will not be
able to maintain the desired position without some
kind of control effort. If you were trying to
balance the broomstick on your palm, you would
need to make continuous adjustments to keep it
from falling. A special kind of apparatus called an
inverted pendulum allows us to design and test
control laws that allow for the balancing of the
pendulum without human intervention.
Robustness
• When we design control systems, we often do not
have a perfect mathematical model of the plant.
Some of the parameters of the system may be
uncertain. Robustness is the property that the
dynamic response (including stability) is
satisfactory not only for a nominal plant transfer
function used for the design but also for the entire
class of mathematical models that express the
uncertainty of the designer about the dynamic
environment in which the real controller is
expected to operate.
Transient Response
• The overall response of any dynamic system will
consist of two distinct parts. The transient
response is the part of the total response that
normally diminishes as time proceeds without any
subsequent sudden changes in inputs or
disturbances to the system. The steady-state
response is what is left when the transient has
indeed died away to zero. Note that for stable
systems, the transient response always approaches
zero as time approaches infinity.
Response
Steady-stateresponse
Transient
Figure 7
Response
Overall response
Steady-state response
Transient response
Figure 8
Steady State Accuracy
• Steady-state accuracy refers to how well the
output, y, tracks the reference input, r, once the
initial transients of the system shown in Figure 9
die out. The difference between r and y is called
the system error, e. As time goes on (in the
absence of further disturbances or abrupt changes
in the reference input - steady-state), this error
should at best, decrease to zero, but should at least
approach some acceptable finite constant value.
Steady State Accuracy
Compensation
y
r +
e
D(s)
G(s)
-
1
Frequency Response
• When a sinusoidal signal is the input to a linear
dynamic system, the output will be a sinusoid of
the same frequency, but most likely of differing
magnitude and phase (Fig. 10). Furthermore, the
magnitude and phase of the output may vary with
the frequency of the input signal. Collecting this
frequency response data and plotting them give
the control engineer insight as to the behavior of
the system, and approaches to designing
appropriate compensation.
Acos(t)
Bcos(t+)
Linear System
BANG-BANG CONTROL
• There are many different strategies for designing
feedback control for a dynamic system.
Depending on the knowledge (or lack thereof) of a
model for the system we want to control, we may
choose different strategies.
• Bang-bang control refers to the operation of
actuators in a control system. Also known as "onoff" control, this strategy is used when a smooth
system response is not critical.
BANG-BANG CONTROL
• Consider, for example, the cooling system in your
automobile. A temperature sensor (thermostat)
monitors the temperature of the engine coolant.
When the temperature exceeds the desired
operating point, the corresponding signal from the
thermostat initiates the opening of a valve to allow
coolant to re-circulate, drawing cool liquid from
the reservoir to keep the engine temperature at the
desired level. The valve is either on or off, thus
the name "on-off" or "bang-bang" control.
BANG-BANG CONTROL
• In the absence of a precise mathematical model for
the plant, bang-bang control is sometimes utilized
to provide gross control of movement.
• A third mode for each of the motors will be "stop".
(I suppose this makes the problem one of bangbang-bang control…)
PID CONTROL
• PID stands for Proportional-Integral-Derivative
and a PID controller can be useful in providing a
level of control more precise than the gross control
provided by a bang-bang strategy.
• Electronic components called operational
amplifiers (or op-amps) can be configured to
perform the following operations on an electrical
signal: integration, differentiation, and
multiplication by a proportional gain factor.
PID CONTROL
• Thus op-amps can be used to implement a
differential equation electrically. This allows a
control engineer to modify the basic response of a
dynamic system. The output of the electronic
controller is a control signal, which drives the
actuators in such a way as to provide the desired
plant output.
• A PID controller consists of a proportional gain
element, an integrator and a differentiator, all
working together
PID CONTROL
 Proportional control: Increasing proportional gain
usually improves steady-state accuracy at the cost
of less stable transient response dynamics.
 Integral control: Improves steady-state accuracy,
at the cost of undesirable transient response
characteristics (slow settling time, less stable)
PID CONTROL
 Derivative control: Controller output proportional
to rate of change of actuating error signal. Must
always be used with proportional control. PD
allows for controller with high sensitivity, but is
susceptible to noise. Improves stability, because it
kicks in before actuating error gets too large.
 PID: combines effects of all three. Designer
determines what values to set for the three gain
parameters - not as easy as it sounds. Control
theory gives the designer some strategies for
picking these values.
PID vs. Bang Bang
– MATLAB Demo…. PID Controller
– Compare PID to bang-bang:
 Discuss the ND cart steering.
• Jerky, as opposed to PID smooth.
Digital Control
• In many applications, computers of some kind are used to
control devices and systems. In fact a network of op-amps
configured to implement differential equations is called an
analog computer, which came before the digital
computers with which we are all familiar. Today's digital
computers operate on discrete pieces of information, rather
than on a continuous electrical signal. Such computers are
used to implement difference equations, the discrete-time
counterpart to differential equations. In digital
computers, the control design is implemented
using algorithms and code, rather than electronic
hardware.
Digital Controls-Advantages
 Less complex hardware (assuming the computer is
there already)
 Flexibility (change software, not hardware)
 Parameters don't drift with temperature, age
 Accuracy - digital signals have more noise
immunity (1's and 0's - e.g., CD audio vs. vinyl)
 Reliable - no wires, parts to go bad
Project
• In the project, you will be using a STAMP2
single-board computer as the controller. The
sensor will feed back to the computer information
about the distance from the wall, and will use that
data to decide how to adjust the direction (or
position in the case of the sensor) of each of the
servomotors. Part of your job is to decide on a
strategy for the decisions made by the computer
and then generate the code to accomplish this.
(Talk about the need for D/A and A/D when using
a computer.)