Robustness analysis of an air heating plant and control law by using polynomial chaos
- University of São Paulo, Polytechnic School, LAC -PTC, São Paulo (Brazil)
- São Paulo State University - Sorocaba Campus, Sorocaba (Brazil)
- São Paulo State University - Rio Claro Campus, Rio Claro (Brazil)
This paper presents a robustness analysis of an air heating plant with a multivariable closed-loop control law by using the polynomial chaos methodology (MPC). The plant consists of a PVC tube with a fan in the air input (that forces the air through the tube) and a mass flux sensor in the output. A heating resistance warms the air as it flows inside the tube, and a thermo-couple sensor measures the air temperature. The plant has thus two inputs (the fan's rotation intensity and heat generated by the resistance, both measured in percent of the maximum value) and two outputs (air temperature and air mass flux, also in percent of the maximal value). The mathematical model is obtained by System Identification techniques. The mass flux sensor, which is nonlinear, is linearized and the delays in the transfer functions are properly approximated by non-minimum phase transfer functions. The resulting model is transformed to a state-space model, which is used for control design purposes. The multivariable robust control design techniques used is the LQG/LTR, and the controllers are validated in simulation software and in the real plant. Finally, the MPC is applied by considering some of the system's parameters as random variables (one at a time, and the system's stochastic differential equations are solved by expanding the solution (a stochastic process) in an orthogonal basis of polynomial functions of the basic random variables. This method transforms the stochastic equations in a set of deterministic differential equations, which can be solved by traditional numerical methods (That is the MPC). Statistical data for the system (like expected values and variances) are then calculated. The effects of randomness in the parameters are evaluated in the open-loop and closed-loop pole's positions.
- OSTI ID:
- 22390783
- Journal Information:
- AIP Conference Proceedings, Vol. 1637, Issue 1; Conference: ICNPAA 2014: 10. International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, Narvik (Norway), 15-18 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
AIR
APPROXIMATIONS
CHAOS THEORY
CLOSED-LOOP CONTROL
COMPUTER CODES
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
HEATING
MASS
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
POLYNOMIALS
PVC
RANDOMNESS
ROTATION
SENSORS
STOCHASTIC PROCESSES
TRANSFER FUNCTIONS
TUBES