Abstract
This work is part of a research initiative that aims at increasing the overall gas turbine efficiency by means of constant volume combustion (CVC). For that purpose, flow control in the compressor becomes important, since unsteady combustion effects that may occur in a CVC are very likely to affect stability and efficiency of the compressor negatively due to flow disturbances.
Active Flow Control (AFC) often has to deal with uncertain flow conditions, e.g., due to turbulence, varying operating ranges, or simply environmental effects. By that, system parameters such as gain or time constants of the system model also become uncertain, making it difficult for control algorithms to ensure optimality or even stable behavior. Robust control in the sense of ℋ∞ control tackles these problems using an uncertainty description and a nominal model of the system. In this contribution, robust control applied to a linear stator cascade is addressed when only a binary control output from solenoid valves is available. Moreover, a surrogate control variable is proposed, describing the extent of the velocity deficit. By means of a principal component analysis, this control variable is reconstructed from a single measurement input.
AFC is realized via trailing edge blowing. In comparison to proportional valves, solenoid valves are cheaper and offer faster switching times with the drawback of a restricted range of the control output to integer or even binary values. Since the ℋ∞ controller, as well as most other control algorithms, results in a real-valued signal u(t) ∈ ℝ, a sum-up rounding strategy is applied to the controller output, forming a binary control output ub (t) ∈ {0, 1}. Although it is impossible for the two outputs to completely match, unless both are integer-valued, there is proof that the difference of real-valued to binary output is bounded in its integral value. The investigations show that a switching frequency of the valves of 100 Hz is sufficient to ensure that the control error via binary control matches its expected equivalent via real-valued control for the presented system.