Control Strategies

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Control Strategies

• Shuvra Das
• University of Detroit Mercy

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Topics

• Feedback Control Systems
• Bang-Bang Control
• PID Control
• Digital Control

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Control System Components
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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.

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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.

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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.

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Control System Components
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Actuators

• Actuators convert the controllers 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.

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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.

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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

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Feedback Control Concepts

• Open loop control
• No feedback
• Controller receives no information about whether
  or not it is providing the correct information

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Open-loop control

• 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.

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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.

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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.

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Closed-loop control

• 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

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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 systems 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.

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Closed-loop control

• 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.

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Control Law

• The relationship between the error and the
  control effort is called the control law.
  Feedback control can provide regulation against
  unmeasured disturbances.

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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.

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Regulation
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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.

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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.

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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.

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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.

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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.

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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.

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Response
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Response
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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.

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Steady State Accuracy
Compensation
y
D(s)

e
G(s)
r
-
1
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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.

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Linear System
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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
  "on-off" control, this strategy is used when a
  smooth system response is not critical.

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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.

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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
  bang-bang-bang control)

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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.

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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

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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)

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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.

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PID vs. Bang Bang

• MATLAB Demo. PID Controller
• Compare PID to bang-bang
• Discuss the ND cart steering.
• Jerky, as opposed to PID smooth.

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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.

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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

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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.)