Model-Based Control - Real-Time Rendering: Computer Graphics with Control Engineering - page 70

Computing
environment

Disturbance, d Disturbance, d

Performance
objective, r

Error, e Output, y

u

Plant
(Rendering Process)

QoS
Evaluator

TD

Controller TD

C

Controller
Designer

Model Estimator

M

Controller Subsystem Plant Subsystem

FIGURE 5.4 (See colour insert.) Modular adaptive control system for real-time rendering.

5.2.2 c ontRol s ystem P eRfoRmance c oncePts

a PPlicaBle to R eal -t ime R endeRing

The value of incorporating control principles in real-time rendering would be better
appreciated by highlighting important concepts pertaining to control system design.
These performance objectives are the premises by which the control systems are vali-
dated for their effectiveness at the design level. Since exhaustive coverage of this topic
is beyond the scope of this chapter, we focus the discussion on certain characteristics.
Stability —A system is inherently stable if it is not easily perturbed by small
variations (disturbances) introduced when it is at equilibrium state. Stability is a
system property that may be best described by the bounded-input-bounded-output
(BIBO) signal processing nomenclature. One example is a rendering system
designed to run at a user-defined frame rate when the controller works in a way that
small load variations sent to the rendering process do not result in unstable frame
rates at the output end.
Controllability —In control theory, it is possible to consider state and output con-
trollability. For brevity and in the context of real-time rendering, we extract the basic
underlying concept—the ability to manipulate or steer the output based on an admis-
sible set of rendering inputs within a specific time window.
Observability —Observability and controllability are mathematical terms for the
same problem. The observability of a system refers to how well its internal states
may be inferred by knowledge of its outputs and inputs. In simpler terms, a system
is observable if the behaviour or current values of its states can be determined by
analysing its outputs and inputs. Both observability and controllability criteria
reinforce a system with clear requirements for stable operation.
Robustness —Not all systems can handle large and unpredictable plant fluc-
tuations. The robustness of a system is its ability to operate under such situations
to achieve its objectives or allow its performance to degrade gracefully without
catastrophic failure. Apart from resilience to fluctuating operating conditions, a
real-time rendering application generally does not incur significant cost or damage
to its environment even when it fails.