Crisp Control Is Always Better Than Fuzzy Feedback Control

1
Crisp Control Is Always Better Than Fuzzy
Feedback Control

• MICHAEL ATHANS
• Professor of Electrical Engineering (Emeritus)
• MIT, Cambridge, Mass., USA
• and
• Visiting Scientist, Instituto de Sistemas e
  Robotica
• Instituto Superior Tecnico, Lisbon, PORTUGAL
• mathans_at_mit.edu or athans_at_isr.ist.utl.pt
• EUFIT 99 DEBATE WITH PROF. L.A. ZADEH
• Aachen, Germany, September 1999

2
Debating Points

• I like Fuzzy Logic as an alternative to
  probability theory, especially in applications
  involving man-machine interactions
• Fuzzy feedback control methods represent inferior
  engineering practice, often by people that never
  bothered to learn control theory and design
• Fuzzy feedback control is a vacuous technology
  for the design of high-performance control
  systems
• Fuzzy control methods are parasitic they
  simply implement trivial interpolations of
  control strategies obtained by other means
• Theological arguments about fuzzification,
  defuzzification, nonlinear control, and
  inherent robustness are simply nonsense
• Fuzzy feedback control has failed to capture and
  utilize alternative means in dealing with
  uncertainty using Fuzzy Sets and Fuzzy Logic
• Prof. Zadeh should communicate to his disciples
  the sorry state of affairs in fuzzy feedback
  control and tell them to shape-up

3
Crisp Vs Fuzzy Feedback Control

• Crisp control Normative - prescriptive
• Quantitative models of plant dynamics and
  disturbances
• Precise definition of performance specifications
• Modeling and environmental uncertainty accounted
  for
• Rigorous optimization-based design
• Fuzzy control Empirical - descriptive
• 1st generation (Mamdani). Ad-hoc interpolation
  of expert control rule-based system
• Vast majority of fuzzy applications use this
  method
• 2nd generation (Takagi-Sugeno). Ad-hoc
  interpolation of control strategies derived from
  crisp feedback control methodologies
  
• Fuzzy control has failed the noble goal of fuzzy
  logic in providing alternatives in dealing with
  uncertainty

4
The Joy of Feedback

• Measure system response, including effects of
  disturbances, using (noisy) sensors
• Compare actual system response to desired system
  response at each time
• Error signal(s) (Desired response)-(Actual
  response)
• Use error signals to drive compensator
  (controller) so as to generate real-time control
  corrections so as to keep errors small for all
  time
• FEEDBACK ESSENTIAL TO GUARANTEE GOOD PERFORMANCE
  IN THE PRESENCE OF UNCERTAINTY

5
Why Feedback?

• Automatic feedback control systems have been used
  since the 1930s to provide superior performance
  and higher fidelity than manual control systems
  requiring human operators
• The SCIENCE of Feedback Control was developed to
  allow engineering designs that deliver this
  superior performance, NOT to duplicate poor human
  control performance
• The performance payoffs are even more dramatic in
  the case of coupled multivariable systems, i.e.
  systems with many sensors and control inputs
• crisp control theory exploits the tight dynamic
  coupling
• humans are notorious in lacking ability to
  develop control rules for such multivariable
  systems
• Increased cost of feedback (sensors, actuators,
  processors,...) is justified by increased
  performance capabilities
• sensor/actuator hardware costs greatly exceed
  processing costs

6
Fixed Structure Feedback

• Compensator structure does not change (no
  learning)
• No change in digital processor algorithms that
  approximate the solution of compensator
  differential equations and gains
• Design methodologies available for general
  multivariable case using (crisp) robust-control
  theories and algorithms

7
Adaptive Feedback Control

• Uncertain plant parameters identified in
  real-time and compensator parameters are adjusted
  also in real-time

8
Fault-Tolerant Feedback

• Supervisory level monitors for failures
• Failure isolated and identified
• Compensator structure and algorithms modified

9
Crisp Mathematical Control

• Based upon analytical description of plant
  dynamics, model errors, environment, constraints,
  and performance objectives
• Optimal Control Theory
• Used to generate open-loop preprogrammed
  control and state variable trajectories as a
  function of time
• Feedback Control Theory
• Used to ensure precise command-following and
  disturbance-rejection performance, in the
  presence of uncertainty, using feedback of sensed
  variables
• stability guarantees are essential
• performance guarantees (in the presence of
  uncertain models) are desirable

10
Closed-Loop Stability

• Models have limitations, stupidity does not!
• Feedback control can result in superior
  performance
• Careless feedback strategies can cause
  instabilities
• Closed-loop stability must be guaranteed for
  family of plants (stability-robustness)
• stability guarantees for nominal plant and
  nominal plant simulations are not enough
• control engineers must be paranoid about
  closed-loop stability

11
Crisp Feedback Theory Status

• Start with global nonlinear dynamic model of
  plant (nonlinear differential or difference
  equations)
• Using linearization establish a collection of
  linear models in vicinity of operating conditions
• Generate linear multivariable dynamic compensator
  with guaranteed stability-robustness and
  performance-robustness properties for each linear
  model
• Use gain-scheduling of the parameters of the
  linear compensator collection to derive a single
  global nonlinear dynamic compensator for the
  global nonlinear plant

12
Linearization, Gain-Scheduling
13
Robust Feedback Control Design

• Start with nominal state-space model of linear
  MIMO dynamic system
• Define bounds on model errors (class of legal
  errors)
• parametric uncertainty upper and lower bounds
  for key coefficients
• unstructured uncertainty worst size of dynamic
  errors as a function of frequency (bending modes,
  torsional modes, actuator/sensor errors, ....)
• Model exogenous signals (a key requirement for
  superior performance)
• power spectral densities of commands,
  disturbances and sensor noise
• Quantify robust-performance specifications in the
  frequency domain

Design is meaningless unless performance specs
are quantified
14
Robust MIMO Feedback Design

• LQG or H2 method
• performance goal minimize RMS errors of
  stochastic performance variables
• H