Probabilistic control using H2 control design and polynomial chaos: Experimental design, analysis, and results

• Published in: Probabilistic engineering mechanics 2012-10, Vol.30, p.9-19
• Main Authors: Templeton, Brian A., Ahmadian, Mehdi, Southward, Steve C.
• Format: Article
• Language: English
• Subjects: [formula omitted] control; Applied sciences; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Exact sciences and technology; Experimental; Fundamental areas of phenomenology (including applications); LQR; Optimal control; Orthogonal polynomials; Parametric uncertainty; Physics; Polynomial chaos; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2012.02.003

This work presents an experimental investigation of recently developed design methods that combine polynomial chaos with H2 control. The experiment utilizes a mechanical oscillator with different amounts of mass added in order to create an experimental parametric uncertainty. The uncertain mass is described in the system model by a polynomial chaos representation of a probability distribution function (PDF). Four different controllers using different variance weightings, are optimized using the H2 and polynomial chaos technique. A comparable standard H2 design and open loop performance are presented for comparison. The motivation for the work includes validating the proposed technique as well as contributing an experimental investigation to the polynomial chaos literature, which is predominately limited to simulation studies. The paper covers the experimental design and setup. A practical overview of the control design method is given. Standard control analysis tools showing responses for a selection of parameter values allow visualizing some of the properties of the controllers. Further, the experimental results from the test allow better conceptualization of the effects of the method as well as illustrating practical limits. Of particular interest, the defined H2 norms used for designing the optimal controllers also provide an elegant way to quantitatively compare the theoretically expected performance with the obtained experimental performance. •We describe an experimental implementation of a new probabilistic control method.•A 2-DOF oscillator with a changing mass represented a probabilistic system.•Experimental trajectories, L2 norms, and H2 norms are compared to theoretical ones.•Successful controller designs as well as potential pitfalls are examined.