Simulation-driven fixed-order controller tuning via moment matching

Abstract

We propose a controller tuning method based on the data-driven model reduction by moment matching theory. By selecting a reference closed-loop transfer function, a moment matching data-driven model reduction algorithm is used to synthesize a fixed-order controller, via the identification of a model of the inverse transfer function of the controller, i.e. the transfer function from the controlled input of the system to the mismatch error signal. The controller is finally obtained by inverting this transfer function. The fixed-order controller is guaranteed to match the steady-state behavior of the ideal controller at certain pre-selected frequencies. The effectiveness of the resulting design method is assessed on a control problem for the 48-th order model of the Los Angeles University Hospital building.

On Moment Matching for Stochastic Systems

“…Proof: Consider the matrix X t defined in (11). Multiplying this equation by Φ −1 t on the left and by Σ t on the right yields…”

“…Substituting these two expressions in (14) proves that X t , defined in (11), is the solution of the stochastic differential matrix equation (12). Now define the variable z t := x t −X t ω t .…”

“…in which the first equality holds because of (11) and the second equality holds because lim t→−∞ Φ −1 t X t Σ t = 0 almost surely. In fact, by Assumptions 1 and 2, lim t→−∞ Φ −1…”

Data-driven constrained optimal model reduction

“…for instance like in the case of power systems [31], wave energy converters [33] or data-driven controller tuning [34], then the constrained problem should be solved.…”

“…the system is required to minimize the frequency response error for all frequencies but it is not constrained to have zero steady-state error for pre-assigned input signals. The reason that justifies the interest in the constrained problem is that in many engineering applications, such as modeling of power systems and power converters [31,32], optimal control of wave energy converters [33] and data-driven controller tuning [34], the system is excited by a specific or desired class of input signals. It is then of primary importance that the steady-state error for this class of signals is identically equal to zero and just of secondary importance that the error with respect to other input signals is minimized.…”