7.1.  INTRODUCTION

Computer control is now the standard technique for implementing control
systems, mainly for two reasons. First is the exponential reduction in the cost
of computing; second is the versatility of implementing control laws in
software. Many developments in control systems are only practical with
computer control - for example, to implement the nonlinear and time-varying
control laws associated with adaptive control. Complicated computations
can be incorporated into the control loop - for example, when computer
vision is used to guide a robot.

Designing the software for such control systems is hard because the
systems are usually heterogeneous. They may include subsystems with very
different characteristics, such as hydraulic actuators and an inertial navigation
system. On the software side the situation is similar. The controller may
have several operational modes. The control law in each mode can be
specified by difference equations; the mode-switching logic can be specified
by a state machine. For vision guidance, complex image processing algorithms
need to be programmed.

For each of these subsystems and aspects of the software, formal models
that support its modeling, analysis, or programming have been developed.
For example, image processing algorithms can be programmed in various
dataflow models [1, 2]. Each formal model employs a computational mechanism
that dictates what are the components in the model, and how they communicate
and execute. Such a mechanism is called a model of computation.

Working with heterogeneous systems requires more than one model of
computation. This is evident from the trend of adding extensions to existing
tools and formal models. For example, both VHDL and Verilog, originally
designed for digital circuits and based on the discrete-event model, have
been extended to handle analog components [3, 4]. Simulink, a continuous-
time environment, has been extended with Stateflow [5] for modeling and
designing event-driven systems. Ideal switching elements, controlled by
finite-state machines, are added to bond graphs for modeling hybrid systems
w6x. However, most of these tools and formal models support just a few
models of computation and few choices in the way they can be combined.
Further extensions may be awkward or impossible due to the semantic
mismatch between the new model of computation and the existing infrastructure.

Ptolemy II [7] is a system-level design environment that supports component-
based heterogeneous modeling and design. Its model structure allows a
variety of models of computation to be implemented, and to be hierarchically
composed in heterogeneous models. This chapter presents Ptolemy II and
illustrates its application to control system design. We use several case
studies in Section 7.2 to elaborate the challenges in designing complex
control software. The Ptolemy II model structure is discussed next. Section
7.4 gives an overview of the models of computation that are useful in control
system design. The Ptolemy II modal model structure is presented in Section
7.5. An inverted pendulum controller is used to demonstrate how Ptolemy II
can be used in the modeling and design exploration of control systems. In the
final section we present conclusions and discuss our ongoing work.