Modeling and Control of Distributed Parameter Systems
This area of research focuses on modeling and control of dynamical systems/processes described by partial differential equations (pdes) and time delays. Such systems/processes are referred to as distributed parameter or infinite-dimensional systems/processes. This terminology is intended to capture the significant complexity that distinguishes such systems/processes from their lumped-parameter or finite-dimensional relatives. To date, most of the classical and modern control research has focused on systems/processes described by ordinary differential equations (odes); i.e. systems/processes described by lumped-parameter or finite-dimensional models.
Relevant application areas include:
Relevant Control Challenges
- Aero-thermo-elasticity for flexible air-breathing hypersonic aircraft
- Servo-elastic effects for aircraft
- Flexible spacecraft and space structures
- Semiconductor thermal processes; e.g. chemical vapor deposition (CVD), active cooling of advanced microprocessor units
- Time delay compensation within distributed communication systems
- Time delays within digital (sampled-data) control system implementations
Relevant control challenges include:
Objectives and Goals
- uncertain nonlinearities (e.g. variable constraints),
- uncertain high frequency dynamics (i.e. unmodeled differential equations),
- parametric uncertainty,
- uncertain actuator and sensor dynamics,
- centralized versus decentralized control architectures,
- multiple time-scale dynamics; e.g. multiple measurement/actuation rates,
- selection of weighting function parameters for dynamical optimization,
- assessment of fundamental performance limitations and tradeoffs,
- following of varying (typically low frequency) reference commands,
- attenuation of (stochastic, typically low frequency) disturbances,
- attenuation of (stochastic, typically high frequency) measurement noise,
- state estimation,
- parameter and uncertainty estimation (system identification).
The main objective of this research is to develop systematic (finite-dimensional) methods for designing robust control systems for parameter systems and processes operating in the presence of significant nonlinearities and uncertainty. One relevant goal of this work is the development of a priori performance-dependent approximation/fidelity requirements.
Collaborators and Sponsors
- Classical pdes, delay differential equations, input-output operator theory, semigroup-based state space theory
- First principles and empirical (system identification) modeling
- Approximation of distributed parameter (infinite-dimensional) models by lumped-parameter (finite-dimensional) models that maintain essential physical attributes (relative to the target bandwidth and design specifications) while keeping the associated control design computationally manageable.
This work has been sponsored by the following organizations:
- National Science Foundation (NSF), DARPA, AFOSR, Intel, Honeywell, Boeing, NASA.