The following are comments by Aptronix engineers on the
     differences between designing with traditional PID
     control versus fuzzy logic control.  There is an
     assumption that you understand the classic control
     problem of balancing an inverted pendulum.  For more
     details please see the Aptronix Quick Start Quide, User
     Manual and Reference Manual.
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                         Fuzzy Control Systems
                                   
                            Aptronix, Inc.
                                   
                                   
                                   
     1. For Non-linear, Dynamic System.
     
     
        As is well known, the conventional linear model-based
     controllers can be designed according to some optimal
     criteria, and the optimality and stability can be proved.
     However, it is difficult to design a optimal or stable
     controller for a nonlinear, dynamic, and ill-understood
     process, which is common in the real world. One practical
     method is to simplify and linearize the non-linear model.
     After the simplification, the optimality and stability are
     only for the simplified model. For an ill-understood
     process, its model is unknown and it is impossible to use
     conventional methods to design a controller.  In these cases,
     human experience should be utilized.
     
        For example, in the designing of a controller for an
     inverted pendulum, one must first simplify the real process
     model by linear equations and then design an optimal
     controller for the simplified model.
     
        Fuzzy logic controllers utilize human knowledge by
     describing the control strategies by linguistic rules. For
     the inverted pendulum example, a basic control strategy will
     be `if the pendulum declines to the right Fast, then move
     the cart to the right Fast'. The fuzzy term `Fast' can be
     represented by a fuzzy set. By considering the cases more
     carefully, we can fine tune these rules.
     
        Such kind of knowledge exists in many industrial control
     processes. Clearly, the control rules are model-free: no
     matter how (mathematically) difficult the process is, an
     experienced operator can still give some control rules.
     
        Fuzzy logic controllers are suitable for non-linear,
     dynamic, and ill-understood processes.
     
     
     2. Robustness
     
         PID (Proportional-Integral-Derivative) control is the
     major practical technology that is widely used in
     industries. However, the performance of PID controllers
     depends heavily on the operating parameters of the system.
     If there is any change in the system, a significant amount
     of time is required to tune the controllers. As a result,
     the average industrial plant operator ends up running over
     50% of his PID loops in manual mode.
     
         For example, if the length of the pendulum changes, the
     parameters of the linear controller should be changed
     accordingly.
     
         Fuzzy controllers are more robust. If the length of the
     pendulum changes in a certain range, the control rules and
     fuzzy sets need not change. Physical demonstrations have
     proven this robustness in several international conferences
     of fuzzy systems.
     
     
     
     3. Short Development Period
     
     In the design of a linear controller, one should do
     the following steps after selecting th