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An active tendon, consisting of a displacement actuator and a co-located force sensor, has been adopted by many studies to suppress the vibration of large space flexible structures. The damping, provided by the force feedback control algorithm in these studies, is small and can increase, especially for tendons with low axial stiffness. This study introduces an improved force feedback algorithm, which is based on the idea of velocity feedback. The algorithm provides a large damping ratio for space flexible structures and does not require a structure model. The effectiveness of the algorithm is demonstrated on a structure similar to JPL-MPI. The results show that large damping can be achieved for the vibration control of large space structures.

In general, large flexible space structures contain cable elements [_{infinity} optimality and H_{2} optimality to control the vibration of buildings with the soil-structure interaction (SSI) effect. Nudehi

Most control schemes are based on an accurate model of the structure. However, when the model of the structure is not precisely defined or some active tendons fail, the performance of those control schemes deteriorates and can even cause instability of the control system. As a result, some studies have adopted decentralized schemes, which consist of independent controllers to activate specific tendons with only local feedback information. The decentralized schemes are useful for high dimensional large space structures, and can also be adapted to address the failure of some active tendons. Magana

This study presents a differential force feedback algorithm to suppress structure vibrations. The algorithm can introduce large active damping to structures. The kernel idea of the control algorithm is velocity feedback, so the stability of the control system can be guaranteed. The control algorithm is simple, and also, no structural model is required.

The paper is organized as follows: in Section 2, the governing equation of the structure is presented and the differential force feedback strategy is addressed. In Section 3, the stability and effectiveness of the control algorithm are discussed for when there are discrepancies between the actual axial stiffness of the tendon and the stiffness used for control law design. In Section 4, a simulation is demonstrated on a free-free structure similar to JPL-MPI [

The mass of an active tendon in a large space structure is usually small compared with the mass of the truss structure. As a result, the dynamics of the active tendon can be restricted to the tension in the tendon in the vibration control and its interaction with the structure. A multi-tendon system is considered in the following deduction, where the number of tendons is _{i}^{th} tendon, and _{i}^{th} tendon. The amount of damping on the large space structure is low, so it is neglected in the equation. Here, the mass of the tendon is small and neglected in the governing equation [^{th} tendon is derived from the structure vibration and the tip displacement of the active tendon as follows:
_{ci}^{th} active tendon, _{i}^{T}^{th} tendon on the space structure; and _{i}_{i}

The control algorithm is the differential force feedback:
_{fi}^{th} active tendon. After eliminating the tension caused by the active displacement, the residual tension on the tendon is proportional to the vibration displacement. Therefore, the active displacement in ^{th} tendon can be expressed as follows:

Eliminating _{i}

Substituting

Obviously, if the feedback coefficient _{fi}_{fi}

The differential force feedback algorithm (_{fi}_{ci}_{ci}_{ci}_{ci}_{ci}

Eliminating _{i}

Substituting

If Δ_{ci}

The free-free truss was adopted to assess the accuracy of the differential force feedback algorithm (

The preloaded tendons are installed on the tips of the structure. The natural frequencies of the three cables are greater than the control frequencies after adjustment of the preloaded tension. The integral force feedback, the PI control algorithm and the differential force feedback are adopted to control structure vibrations. The stiffness error of the active tendon is Δ_{ci}_{ci}_{i}_{fi}

In order to compare the control effectiveness of the three control algorithm in the frequency region, a typical frequency-response function between the force applied in the middle of the truss and the displacement response on the top of arm 3 is shown in _{i}_{f}_{c}_{i}_{fi}^{−5} and the stiffness error is set to Δ_{ci}_{ci}, i

In order to compare the control effectiveness in the time region, the three control algorithm is adopted to attenuate the truss vibration under the same while noise excitation in the middle of the truss. The coefficients of three control algorithm are selected as same as the coefficients on frequency-response curve. The displacement response on the top of structure is shown in

The differential feedback can suppress effectively the structure vibrations for both lower order modes and high order modes. In order to obtain a high suppression rate, the large active displacement _{fi}

Because Δ_{c}_{c}_{c}/k_{c}_{c}/k_{c}

When the differential force feedback coefficients are set to _{fi}^{−5}, the curve of the achieved damping ratio and the resulting error is shown in _{c}/k_{c}

A differential force feedback algorithm to attenuate the vibration of large space structures was presented. The algorithm was based on the velocity feedback. The control algorithm did not require the structure model and the stability of the control system was guaranteed. The proposed control algorithm could achieve high damping ratios for structures. The effectiveness and stability of the differential force feedback algorithm was investigated accounting for discrepancies between the actual stiffness of the tendon and the stiffness used for the design of the control law. The simulation results for a free-free structure show that the proposed algorithm can provide more damping for the vibration suppression of a space structure.

This work was supported by National Science and Technology Major Project of China Grant No. 2009ZX04014-033 and National Natural Science Foundation of China Grant No. 50905004. The authors are grateful to other participants of the projects for their cooperation.

Guyed truss structure.

Mode shapes of the structure.

Root locus with three control strategies (

Root locus with three control strategies (

Frequency-response functions with three control strategies.

Displacement responses on the top of arm 3.

Active displacements on the cable 3.

Root locus with different Δ_{c}/k_{c}

Relationship between damping ratio and error Δ_{c}/k_{c}

Parameters of the space structure.

Dimension of bays on arm 1 | 0.9 m × 1.1 m × 0.5 m |

Dimension of bays on arm 2 | 0.9 m × 1.1 m × 0.5 m |

Dimension of bays on arm 3 | 0.9 m × 1.1 m × 0.7 m |

Diameter | 10 mm |

Thickness | 1 mm |

Density | 2,700 kg/m^{3} |

Young's Modulus | 70 GPa |