# Experimental validation of generalized predictive control for active flutter suppression

Abstract: This paper presents a status report on the experimental results of the transonic wind-tunnel test conducted to demonstrate the use of generalized predictive control for flutter control of a subsonic airfoil. The generalized predictive control algorithm is based on the minimization of a suitable cost function over a finite prediction horizon. The cost function minimizes the sum of the mean square output of the plant predictions using a suitable plant model, weighted square of control increments, and the term which incorporates the input constraints. The characteristics of the subsonic airfoil are such that its dynamics are invariant to low input frequencies. This results in a control surface that drifts within the specified input constraints. An augmentation to the cost function that penalizes this low frequency drift is derived and demonstrated. The initial validation of the controller uses a linear plant predictor model for the computation of the control inputs. The generalized predictive controller based on this model could successfully suppress the flutter for all testable mach numbers and dynamic pressures in the transonic region. The wind-tunnel test results confirmed that the generalized predictive controller is robust to modeling errors. The simulation results that were used to determine the nominal ranges for control parameters before wind-tunnel testing are also included. The wind-tunnel test results were in good agreement with the results of the simulation.

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### Cites background from "Experimental validation of generali..."

...Haley and Soloway (1996) have made an experimental investigation in a transonic wind-tunnel to demonstrate the use of the generalized predictive control for flutter suppression of a subonic airfoil....

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...The idea is old and it was first tested in 1973 on a B-52-E aircraft that achieved flight velocity above the specified limit, besides some problems with model accuracy and robustness, (Garrick, 1976)....

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##### References

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### "Experimental validation of generali..." refers methods in this paper

...This controller is also robust with respect to modeling errors, over and under parameterization, and sensor noise [ 4 ]....

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...GPC was introduced by Clarke and his co-workers in 1987 and it belongs to a class of Model-Based Predictive Control (MBPC) [ 4 ][5][6]....

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329 citations

106 citations

### "Experimental validation of generali..." refers background or methods in this paper

...' For more information on the software implementation and timing specifications see [ 7 ]....

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...Equations (4) and (5) should be added to the Jacobian and Hessian equations of [ 7 ] for a complete solution to the GPC control input....

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...The computational issues of Newton-Raphson are also addressed in [ 7 ]....

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...To include this filter in the derivation of the CFM iterative solution found in [ 7 ], the Jacobian and the Hessian of the filter are needed....

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90 citations