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Performance oriented antiwindup for a class of neural network controlled systems. SWAN 2006  Automation and Robotics Research Institute, UTA. G. Herrmann M. C. Turner and I. Postlethwaite. Control and Instrumentation Research Group University of Leicester. Motivation
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SWAN 2006 
Automation and Robotics Research Institute, UTA
G. Herrmann
M. C. Turner and I. Postlethwaite
Control and Instrumentation Research Group
University of Leicester
Antiwindup for a class of neural network controlled systems
Linear
Controller
+
+
+

Unknown
Nonlinearity
Adap
tation
NN
compen
sation
MotivationLinear
Plant
Linear control performance in combination with NNcontrol – Examples of practical validation:
G. Herrmann, S. S. Ge, and G. Guo, “Practical implementation of a neural network controller in a hard
disk drive,” IEEE Transactions on Control Systems Technology, 2005.
——, “A neural network controller augmented to a high performance linear controller and its
application to a HDDtrack following servo system,” IFAC 2005 (under journal review).
AntiWindup (AW) Control  a possible approach to overcome controller saturation
G. Grimm, J. Hatfield, I. Postlethwaite, A. R. Teel, M. C. Turner, and L. Zaccarian, “Antiwindup for stable linear
systems with input saturation: An LMI based synthesis,” IEEE Trans. on Autom. Control, vol. 48, no. 9, pp. 1509–1525, 2003.
Alternative for NN:
W. Gao; R.R. Selmic, "Neural network control of a class of nonlinear systems with actuator saturation Neural
Networks", IEEE Trans. on Neural Networks, Vol. 17, No. 1, 2006.
NNControl Examples :
S. S. Ge, T. H. Lee, and C. J. Harris, Adaptive Neural Network Control of Robotic Manipulators. World Scientific, Singapore, 1998.
Y. Kim and F.L. Lewis, HighLevel Feedback Control with Neural Networks," World Scientific, Singapore, 1998.
Antiwindup for a class of neural network controlled systems
+
Linear
AWCompen
sator
Motivation: Principle of antiwindup compensationLinear
Controller
Linear
Plant
Antiwindup for a class of neural network controlled systems
Stable, minimumphase, strictly proper with matched nonlinear disturbance f(y)
Antiwindup for a class of neural network controlled systems
The disturbance is continuous in y and bounded:
so that it can be arbitrarily closely modelled by a neural network approach:
 neural network basis function vector,
 neural network modelling error
 optimal (constant) weight matrix
The plantAntiwindup for a class of neural network controlled systems
is assumed to be Hurwitz stable
The linear controller component defines the closed loop steady state:
and the controller error:
The Nominal Controller – Linear Control Componentd  exogenous demand signal
Antiwindup for a class of neural network controlled systems
discontinuous sliding mode component  compensates for modeling error e
estimate 
compensates
for nonlinearity
is a design parameter
Estimation algorithm:
is symmetric, positive definiteLearning Coefficient Matrix
 Estimation error
The Nominal Controller – NonLinear Control ComponentAntiwindup for a class of neural network controlled systems
can asymptotically track thesignal yd so thatthe controller error:
becomes zero.
Theestimation error
remainsbounded.
The Nominal ControllerAntiwindup for a class of neural network controlled systems
+
Linear
AWcomp.
+

+
+
NN
compen
sation
Unknown
Nonlinearity
Non
linear
Algorithm
Controller conditioningLinear
Controller
Linear
Plant
Adap
tation
Antiwindup for a class of neural network controlled systems
Symmetric Multivariable Saturation Function:
The Deadzone  Counterpart of a Saturation Function:
Controller conditioning  PreliminariesMultivariable Saturation Function:
Antiwindup for a class of neural network controlled systems
Controller
+
+

+
Unknown
Nonlinearity
Adap
tation
Disturbance Limit
NN
compen
sation
The controller amplitude is large enough to compensate for the unknown nonlinearity.
Permissible Range of Tracking Control System
small design parameter
Controller conditioning  AssumptionsLinear
Plant
Saturation Limit:
We do not assume that the transient behaviour has to satisfy this constraint.
Antiwindup for a class of neural network controlled systems
is a small design dependent constant
NNcontrol is used
The NNcontroller is cautiously disabled
and replaced by a high gain controller. The NNestimation algorithm is slowed down.
Controller conditioning – Nonlinear Control ElementAntiwindup for a class of neural network controlled systems
compensation signals
compensation
in practice 0
AWcompensator:
to be designed
Closed Loop:
Note that
The control limits are satisfied
Controller conditioning – Linear Control ElementLinear controller
Antiwindup for a class of neural network controlled systems

+
w
NN
compen
sation
Non
linear
Algorithm
Controller conditioning – AWCompensator Design TargetDesign target for linear
AWcompensator:
Minimize g for
where
is a designer chosen performance output
Linear
AWcomp.
Linear
AWcomp.

+
d
Linear
Plant
+
Linear
Controller

+
y
+
+
Unknown
Nonlinearity
Adap
tation
This L2gain optimization target ensures recovery of the nominal controller performance.
Antiwindup for a class of neural network controlled systems
+
NN
compen
sation
Non
linear
Algorithm
Controller conditioning – AWCompensator Design TargetDesign target for overall AWcompensator:
The conditioned linear control uL term operating in connection with the constrained NNcontroller uNL, will track asymptotically any permissible steady state.
The NNweight estimates will remain bounded.
Linear
AWcomp.

+
d
Linear
Plant
+
Linear
Controller

+
y
+
+
Unknown
Nonlinearity
Adap
tation
Antiwindup for a class of neural network controlled systems
The nominal model used for linear controller design
Other
parameters:
A Simulation ExampleHsieh & Pan (2000) [12]:
6th order model to include issues of static friction, i.e. the presliding behaviour:
[12] Hsieh & Pan (2000)
Simulation for a direct drive DCtorque motor
Assume both angle position x1 and angle velocity x2 are
measurable
Antiwindup for a class of neural network controlled systems
Nominal NNController:
Gaussian Radial
Basis Function
A Simulation ExampleAntiwindup for a class of neural network controlled systems
Conditioning of NNController:
Linear AWCompensator design:
A Simulation ExampleAntiwindup for a class of neural network controlled systems
Position signal
Control signal
Antiwindup for a class of neural network controlled systems
Position signal
Control signal
Antiwindup for a class of neural network controlled systems
Performance similar for un/conditioned controller
Antiwindup for a class of neural network controlled systems