# Structured Control Design for a Highly Flexible Flutter Demonstrator

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## Abstract

**:**

## 1. Introduction

## 2. ${\mathcal{H}}_{2}$-Optimal Input and Output Blending

#### 2.1. Modal Control of Linear Time-Invariant Systems

#### 2.2. ${\mathcal{H}}_{2}$-Optimal Blending Vector Design

## 3. Optimization-Based Control Design

`systune`routine based on non-smooth optimization techniques [9]. The software tools allow an intuitive definition of tuning requirements in the frequency domain (e.g., bandwidth) and in the time domain (e.g., rise time) as either minimization criteria (soft requirements) or as inequality constraint (hard requirements).

#### 3.1. Constant Controller Design

#### 3.2. Scheduled Controller Design

#### 3.3. Design Requirements

## 4. Application to the FLEXOP Demonstrator

#### 4.1. Baseline Controller

- (i)
**Direct Mode**: The direct mode allows the pilot on the ground to bypass the flight control system. The only part active in the flight control computer is the mapping from the received remote-control signals to the commanded surface deflections. The pilot controls the pitch, roll and yaw axis directly via the aircraft’s control surface deflections and its velocity via the thrust setting.- (ii)
**Augmented Mode**: The augmented mode switches on basic augmentation for the pilot [23]. Instead of directly controlling the surfaces the pilot inputs pitch- and roll-attitude commands. The side-slip angle is automatically regulated to zero, reducing the pilots need to control the yaw axis separately. Velocity control remains in direct control, i.e., the pilot controls the velocity via the thrust setting.- (iii)
**Autopilot Mode**: In this mode the pilot fully delegates the aircraft control to the flight control system. Altitude, course angle, velocity and side-slip angle are automatically controlled. To fly along the defined test pattern, reference commands based on the aircraft position are generated in a navigation module.

#### Parameter Tuning

#### 4.2. Flutter Suppression Controller

#### 4.2.1. Input-Output Blending

#### 4.2.2. Single-Input Single-Output Controllers

## 5. Verification

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Closed-loop interconnection of plant G with flutter suppression controller K, output blending matrix ${K}_{y}$, input blending matrix ${K}_{u}$, and controller C.

**Figure 4.**Control architecture for fully automated flight (mode (iii)), and augmented flight (mode (ii)), indicated in gray.

**Figure 6.**Bode-magnitude plots from virtual inputs to virtual outputs illustrating the decoupling of the unstable symmetric bending mode (

**a**) from the unstable asymmetric bending mode (

**d**) via the negligible contributions in the cross-coupling channels depicted in (

**b**,

**c**). The plots are shown for 52 m/s ( ), 54 m/s ( ), 56 m/s ( ), 58 m/s ( ), and 60 m/s ( ) indicated airspeed ${V}_{\mathrm{ias}}$.

**Figure 7.**Gain-scheduled SISO controllers ${W}_{1}\left({V}_{\mathrm{ias}}\left(t\right)\right)$ for the symmetric mode (

**a**) and ${W}_{2}\left({V}_{ias}\left(t\right)\right)$ for the asymmetric mode (

**b**) plotted from 30 m/s to 70 m/s airspeed.

**Figure 8.**Comparison of the closed-loop poles with baseline controller only in gray and the closed-loop poles with baseline and flutter controller (colored) in dependence of the indicated airspeed ${V}_{\mathbf{ias}}$. Only the positive imaginary axis is depicted for readability reasons.

**Figure 9.**Simulation results without flutter suppression controller for an acceleration scenario for indicated airspeed (

**a**), accelerations on the wing root (

**b**), angle of attack (

**c**), and accelerations on the wing tip (

**d**). The flight in the stable regime is indicated in gray ( ), the unstable situation in red ( ).

**Figure 10.**Simulation results with flutter suppression controller for an acceleration scenario for indicated airspeed (

**a**), accelerations on the wing tip (

**b**), angle of attack (

**c**), and accelerations on the wing root (

**d**). The flight in the stable regime is indicated in gray ( ), the unstable situation in red ( ).

**Figure 11.**Simulated aircraft position during three laps on the test track in (

**a**), reference and aircraft altitude in (

**b**), reference and aircraft velocity in (

**c**), and angle of attack in (

**d**).

**Figure 12.**Control surface activity during the simulated flight for the two left and two right ailerons controlling the roll motion in (

**a**), the two left and right ruddervators in (

**b**), and the two ailerons stabilizing the two flutter in (

**c**,

**d**) for the phases when the flutter suppression controller is activated.

**Table 1.**Summary of the control loops of the FLEXOP baseline flight control system with the inner loop functions (first part) and autopilot functions (second part).

Control Loop | Channel | Structure | Scheduling |
---|---|---|---|

Pitch Attitude Control | $({\mathsf{\Theta}}_{\mathrm{ref}}-\mathsf{\Theta})\to {\delta}_{e}$ | PI | 2nd-order polyn. in ${V}_{\mathrm{ias}}$ |

Pitch Damping | $q\to {\delta}_{e}$ | P | 1st-order polyn in ${V}_{\mathrm{ias}}$ |

Roll Attitude Control | $({\mathsf{\Phi}}_{\mathrm{ref}}-\mathsf{\Phi})\to {\delta}_{a}$ | P | 1st-order polyn in ${V}_{\mathrm{ias}}$ |

Roll Damping | $p\to {\delta}_{a}$ | P | 1st-order polyn. in ${V}_{\mathrm{ias}}$ |

Yaw Control | $\beta \to {\delta}_{r}$ | PID | 2nd-order polyn. in ${V}_{\mathrm{ias}}$ |

Autothrottle | $({V}_{\mathrm{ref}}-{V}_{\mathrm{ias}})\to {\delta}_{\mathrm{th}}$ | 2 DOF-PID | none |

Altitude | $({H}_{\mathrm{ref}}-H)\to {\mathsf{\Theta}}_{\mathrm{ref}}$ | PI | 2nd-order polyn. in ${V}_{\mathrm{ias}}$ |

Course Angle | $({\chi}_{\mathrm{ref}}-\chi )\to {\mathsf{\Phi}}_{\mathrm{ref}}$ | PID | 2nd-order polyn. in ${V}_{\mathrm{ias}}$ |

**Table 2.**Overview of the six defined optimization problems with the number of free parameters and optimization criteria within the model-based design procedure of the baseline controller.

Channel | Structure | Free Parameters | Criteria |
---|---|---|---|

Pitch Attitude Control | PI | 8 | Damping ration of 0.6 |

incl. Pitch Damping | P | Phase margin of 45 ${}^{\circ}$ | |

Roll Attitude Control | P | 4 | Response time of 1s, steady state |

incl. Roll Damping | P | Error of 0.1, phase margin of 45 ${}^{\circ}$ | |

Yaw Control | PID | 9 | Disturbance rejection gain |

Auto-Throttle | 2 DOF-PID | 5 | Model matching error |

Altitude | PI | 6 | Bandwidth criterion |

Course Angle | PID | 9 | Response time of 5 s |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Pusch, M.; Ossmann, D.; Luspay, T.
Structured Control Design for a Highly Flexible Flutter Demonstrator. *Aerospace* **2019**, *6*, 27.
https://doi.org/10.3390/aerospace6030027

**AMA Style**

Pusch M, Ossmann D, Luspay T.
Structured Control Design for a Highly Flexible Flutter Demonstrator. *Aerospace*. 2019; 6(3):27.
https://doi.org/10.3390/aerospace6030027

**Chicago/Turabian Style**

Pusch, Manuel, Daniel Ossmann, and Tamás Luspay.
2019. "Structured Control Design for a Highly Flexible Flutter Demonstrator" *Aerospace* 6, no. 3: 27.
https://doi.org/10.3390/aerospace6030027