A  Simulation  Toolkit  of Nonlinear PID Control on Scilab/Scicos (Sept. 2004)					

This documentation severs as a user guide for numerical simulations of nonlinear
PID controllers based on SCILAB/SCICOS, an “open-source” scientific software
developed by INRIA and ENPC of France.  The simulation toolkit, entitled
“NPID-PCA”, is developed by the author, and is distributed freely to publics. 
NPID-PCA is implemented following the so-called “Proportional Component
Ap-proach (or PCA)”. The significant feature of this approach is the selection
of proportional components as the nonlinear functions to synthesize nonlinear
PID controllers. Due to their simplest characteristics inherent by proportional
actions, the proposed NPID-PCA provides a better means for the design and
tuning of the nonlinearity of controllers. 
In the structures of NPID-PCA, we adopt the configuration of three independent
nonlinear proportional functions in connection to each gain loop. This scheme
is important when users desire to adjust the equivalent nonlinear gains
independently. NPID-PCA presents the most compatible structure with the
conventional, or linear, PID technique. A linear PID controller is conveniently
included as a special case for NPID-PCA.
A spline-based function, or Bézier curve, is used for forming nonlinear
proportional component functions. For each nonlinear curve, at most four
nonlinear parameters (or two control points in 2D) are used. The proposed
controller can provide four types of the simplest nonlinear curves to
approximate the nonlinear functions of the control output that are implic-itly
suggested by the process. The significant benefit is obtained by using Bézier
curves for the nonlinear design. Users are able to control and visualize the
nonlinear functions even without using a graphical means.
Specific attentions are made to the standardization in the implementation of
NPID-PCA controllers. All parameters are set within given ranges without lost
of generality. It will be helpful to reduce the optimization cost for the
design and tuning of controllers. A satura-tion element is included in the
structure of NPID-PCA. Therefore, an actual control force can be analyzed for
the control design. 
As the first version of NPID-PCA, this simulation toolkit only considers the
specifica-tion of high performance in process control. We include three case
studies with nine individ-ual demos. All cases below are taken from the
existing examples in the literature for compari-sons: 
CASE 1: Step response of first-order plant with or without time delay.
CASE 2: Step response of second-order plant with dead zone.
CASE 3: Step response of second-order plant with small damping.
The simulation results confirm the superior performances on the NPID-PCA
control-lers in comparing with linear PID technique. And, users can still
improve the performance by either manually tuning or optimization-tool using. 
To the author’s knowledge, NPID-PCA seems to be the first free toolkit
available in publics for the subject of nonlinear PID control. It is still in a
very preliminary stage, but the author wishes that the present toolkit is
useful for users to understand the theoretical funda-mentals as well as the
implementation and simulation of the NPID-PCA.