Due to the short duration of impulsive impact of an aircraft during touchdown, a traditional landing gear can only achieve limited performance. In this study, a magnetorheological (MR) absorber is incorporated into a landing gear system; an intelligent control algorithm, a human simulated intelligent control (HSIC), is proposed to adaptively tune the MR absorber. First, a two degree-of-freedom (DOF) dynamic model of a landing gear system featuring an MR absorber is constructed. The control model of an MR damper is also developed. After analyzing the impact characteristic during touchdown, an HSIC is then formulated. A genetic algorithm is adopted to optimize the control parameters of HSIC. Finally, a numerical simulation is performed to validate the proposed damper and the controller considering the varieties of sink velocities and sprung masses. The simulations under different scenarios show that the landing gear system based on the MR absorber can greatly reduce the peak impact load of sprung mass within the stroke. The biggest improvement of the proposed controller is over 40% compared to that of skyhook controller. Furthermore, HSIC exhibits better adaptive ability and strong robustness than skyhook controller under various payloads and sink velocities.
The very important design issue of landing gear systems with an adaptive ability of impact energy mitigation and simultaneous generation of minimal deceleration on the protected aircraft structure is an intensive research topic. To compass all impact scenarios (i.e., a wide range of flight parameters such as ground friction coefficient, aircraft overall weight, attitude, and sink velocity), a traditionally passive landing gear has to be employed to meet the requirement of the most heavy dynamic excitation or harsh environmental loading. As a result, it cannot avoid the highly redundant structure and trade-off performance. To attenuate the landing impact transmitted to aircraft, some active or semiactive types of landing gear systems have been suggested in aircrafts. One of the most attractive candidates to formulate an adaptive landing gear is to use magnetorheological (MR) fluid absorber because of its fast response characteristic to magnetic field, compact size, and, hence, wide control bandwidth [
The MR technology brings us salient features in alleviating the underdesirable impact load on aircrafts and pilots, on one hand. On the other hand, the significant hysteresitic nonlinearity of the MR absorbers as well as dynamic model uncertainties of the landing gear system (e.g., variable sink velocities and payloads) and especially short time impact (typically a touchdown ranging from 50 and 200 ms) provides yet a significant challenge in choosing a suitable control strategy.
So far, many control methods have been investigated by many researchers in recent years through numerical simulations or simple experimental studies to deal with the challenge. There are two types of control strategies. One is that control strategy is formulated based on energy balance. For example, Mikułowski and Jankowski [
The other type is the nonlinear control strategies, considering the nonlinearity and uncertainty of the system. Choi and Wereley [
Consequently, the main purpose of this study is to find a simple and effective control strategy to improve the ride comfort and stability of landing gear system; simultaneously, the control can potentially be employed in a practical case. In the prior work [
To accomplish this goal, a two-DOF dynamic model of aircraft incorporated with an MRF-based landing gear is firstly constructed to simulate the course of touchdown. After analyzing the response of a classic touchdown, the HSIC is then proposed. Subsequently, the numerical simulation is performed to validate the effectiveness of the control strategy under different sink speeds and masses. In comparison, the skyhook control is also formulated. Finally, a great deal of numerical simulations considering variable masses and sink velocities are performed to evaluate the effectiveness of the proposed control algorithm.
In the work [
Schematic diagram of an MR absorber [
Typically, the damping force of an MR absorber can be expressed as a combination of viscous damping force and coulomb damping force [
To formulate control strategy, a suitable dynamic model needs firstly to be constructed. In this study, one of two DOF dynamic models of a landing gear system is adopted in Figure
Dynamic modeling of an MR landing gear.
In this figure, the sprung mass
The motion equations of the landing gear system can be written as
If the state of the landing gear is set as
In (
The HSIC algorithm, inspired by the excellent control experience of an expert, is proposed by Zhou and Bai early in 1983 [
Generally speaking, the design procedure of applying the theory includes the analysis of controlled plant to obtain the desired phase portrait and the design of controller. In the following, the two steps will be discussed in order.
As a helicopter landing on ground, a classic acceleration time history of sprung mass is shown in Figure
A classic acceleration time history of sprung mass.
For the first control task, it is helpful to consider the man’s reaction to a jump. To avoid the injure caused by the big impact from the land, a person has to bend his leg as soon as possible, which inspires us to make full use of stroke of MR absorber. Moreover, a human body is more sensitive to acceleration, which means that it is better for maintaining a constant deceleration.
For the initial sink velocity,
The desired phase portrait of displacement and velocity of sprung mass.
The calculated or estimated desired deceleration is very important for improving control performance. Considering the nonlinearity and uncertainty of landing gear system, the method cannot be used anymore. In this study, we give an effective and simple method to estimate the infimum of desired acceleration if assuming that the desired deceleration can be guaranteed and the effective stroke equals the maximum stroke of the MR absorber. The desired deceleration can be calculated from (
As mentioned earlier, the main control purpose is to maintain a constant deceleration during touchdown. Therefore, we can divide the course of touchdown into two phases in time domain. One is to reduce the maximum impact acceleration; the other is to avoid a big overshoot. It is obvious that different control modals are desirable for the two control phases. Considering the effectiveness and potential application, the acceleration feedback control is applied for reducing maximum impact acceleration whereas the skyhook control is adopted for reducing a big overshoot, because skyhook control is very effective in vibration attenuation in semiactive vibration control. Two control modes needs only to sense the acceleration and velocity signal, which is easily applied in practical case.
According to the above discussion, it is found that the acceleration feedback control and skyhook control may be effective in different phases. How to coordinate them and optimize control parameters will be discussed in the following.
Since the HSIC theory was proposed, the theory has advanced by Li and Wang [
It is an intelligent module which can be formulated by an agent’s repeated learning and accumulating control experiences, and its structure is shown in Figure
In this figure, the input information set
Structure of sensed schema.
Similar to mankind’s reaction to itself state or external environment, the input information will be sensed and sent to the block of characteristic identification. The function of the block of characteristic identification is to classify the sensed input information. The outputs of the block of characteristic identification are some characteristic elements, which will classify the state space into different control regions. The set of all characteristic elements are named as characteristic primitive set
Combining the elements of the characteristic primitive set
The final output is the characteristic model set and can be gotten as
It is a stereotype embraced control strategy based on outside information of system and itself inner states, and its structure is shown in Figure
The input information of the motion schema is the same as that of sensed schema. The physical sense of the motion schema is in the fact that it simulates how to adopt some actual control modes according to the sensing information like mankind. The function of the block of construct is to adaptively select the required feedback signal of the control mode.
Structure of motion schema.
The selection of control modes is dependent on the control tasks. Usually, there are some traditional control modes such as proportional control primitive
The block of fusion operation is to logically combine the control modes. There is an operation relation between the control mode primitive set and the control mode set:
For brevity, the motion schema can be formulated as a five-element group with order:
It is used to coordinate the relation between sensed schema and motion schema, which simulates human being’s intuition reasoning and decision process. The structure is shown in Figure
In this figure, once the sensed schema and motion schema are obtained through the block of computation, the function mapping relation among the characteristic mode set and control mode set is determined by the block of intuition reasoning and decision making. The physical sense is that one mankind has a double mapping when doing something. He firstly needs to judge qualitatively the object and then adopts quantitatively control behavior. The output of the block of intuition reasoning and decision making is some logic values, which will activate the corresponding the control mode if the logic switch is true.
Structure of associated schema.
Generally, the function of the association schema is to obtain production rules “IF…Then…”. The process can be expressed as
It is obvious that the HSIC with the fixed control parameter cannot be able adaptively to meet the requirement of all impact scenarios of landing gear system. Therefore, the control parameter
After designing the sensed schema, motion schema and associated schema, the entire control structure of HSIC can be combined as a three-element group with order (which is shown in Figure
The HSIC controller structure-based SMIS for MR landing gear system.
According to above discussion, the final control law can be simply written as in Algorithm
IF IF Else Else IF Else End
Control parameters of the HSIC that need to be determined initially include
The optimal procedure of control parameters.
The real number encoding is adopted in this paper. The length of chromosome is determined by the number of the control parameters. If
To improve control performance, the fitness function is chosen as the maximum impact deceleration. The crossover operators used here are one-cut-point crossover by convex crossover. The mutation operator used in this paper is convex combination. The parameters used in the simulation of the genetic algorithm are population size = 50, mutation probability = 0.3, and crossover probability = 0.1. As an illustration, Figure
The convergent procedure of fitness value with generations.
To determine the specific function relations between desired deceleration or acceleration feedback gain and sink velocity as well as sprung mass, many simulations are performed considering all kinds of combinatorial sink velocity as well as sprung mass. The results are shown in Figures
The relation of desired deceleration with sink velocity and sprung mass.
The relation of desired deceleration with sink velocity and sprung mass.
To reduce the complexity of computation, the linear surface fitting method is adopted in this study. The simple specific function relations can be evaluated and expressed as follows:
The relation of fitted ideal deceleration with sink velocity and sprung mass after surface fitting.
The relation of fitted acceleration feedback gain with sink velocity and sprung mass after surface fitting.
To evaluate the control performance and adaptive ability of MR landing gear system, we constructed the numerical model based on Matlab/Simulink. The system and control parameters employed in this study are given in Table
System and control parameters.
Quantity | Symbol | Value | Units |
---|---|---|---|
Mass of sprung mass |
|
800 | kg |
Mass of unsprung mass |
|
15.3 | kg |
Spring stiffness of coil |
|
80,000 | N/m |
Damping constant of MR absorber |
|
4,500 | Ns/m |
Maximum controllable damping force of absorber |
|
5,000 | N |
In order to figure out the sensitivity of the desired deceleration value on the control performance, thirteen different deceleration values are applied in the control numerical experiment. The results are shown in Figure
Sensitive analysis of desired deceleration on the control performance.
To simulate the different scenarios of touchdown, the mass of sprung mass can be increased or reduced, so does the sink velocity of landing gear system. For comparison purpose, the skyhook control law is also adopted, and its control gain is also optimized by the genetic algorithm. Consider
Once the set value of desired deceleration equals or falls into a small region nearby the optimal deceleration, the control performance of HSIC will be significantly improved compared to that of acceleration feedback control, skyhook control or passive, which is shown in Figure
The control performance comparison with sink velocity of 2 m/s and mass of sprung mass of 800 kg.
Vibration acceleration of sprung mass (
Vibration acceleration of unsprung mass (
Displacement of MR absorber (
Controllable damping force
Relation of impact force and stroke
There are two gains of skyhook applied in this study. One is the 1200 Ns/m which is chosen to make both skyhook control and HISC keep almost the same stroke value so that they can compare to each other in terms of the improvement of impact acceleration. The corresponding results are shown in Figure
Maximum acceleration reduction compared to passive case.
Sprung mass | Strategy | Sink rate | |||
---|---|---|---|---|---|
1 m/s | 2 m/s | 3 m/s | 4 m/s | ||
500 kg | Skyhook | 5.66% | −2.91% | −6.19% | −7.71% |
HSIC | 27.15% | 11.19% | 7.07% | 5.03% | |
700 kg | Skyhook | 9.04% | 2.85% | −0.05% | −1.54% |
HSIC | 38.79% | 17.88% | 11.53% | 8.21% | |
800 kg | Skyhook | 8.08% | 8.08% | 7.89% | 7.74% |
HSIC | 17.97% | 11.86% | 9.32% | 7.44% | |
900 kg | Skyhook | 9.97% | 5.20% | 2.63% | 1.24% |
HSIC | 41.59% | 20.94% | 12.93% | 9.27% | |
1100 kg | Skyhook | 10.18% | 6.34% | 4.03% | 2.73% |
HSIC | 41.43% | 21.91% | 13.61% | 9.87% |
The control performance comparison with different sink velocities and masses.
Maximum impact acceleration
Maximum stroke of MR absorber
The comparison results of different sink velocities and masses are demonstrated in Figure
Maximum stroke reduction compared to passive case.
Sprung mass | Strategy | Sink rate | |||
---|---|---|---|---|---|
1 m/s | 2 m/s | 3 m/s | 4 m/s | ||
500 kg | Skyhook | 9.54% | 9.26% | 8.95% | 8.75% |
HSIC | 13.29% | 7.89% | 6.29% | 5.38% | |
700 kg | Skyhook | 8.49% | 8.43% | 8.20% | 8.04% |
HSIC | 17.72% | 11.13% | 8.97% | 7.28% | |
800 kg | Skyhook | 9.65% | 4.25% | 1.53% | 0.09% |
HSIC | 41.10% | 19.76% | 12.42% | 8.90% | |
900 kg | Skyhook | 7.73% | 7.78% | 7.62% | 7.48% |
HSIC | 18.88% | 12.30% | 9.22% | 7.47% | |
1100 kg | Skyhook | 7.15% | 7.27% | 7.15% | 7.03% |
HSIC | 17.71% | 12.42% | 9.27% | 7.62% |
In this study, the semiactive control of a landing gear system featured with a MR absorber during touchdown has been investigated. An intelligent control strategy, human simulated intelligent control (HSIC), is proposed. The genetic algorithm is employed to optimize the control parameters of HSIC. Numerical simulations considering the variety of sink velocities and masses have been performed to check the effectiveness and adaptive ability of the proposed control algorithm. It can be concluded from the numerical results that compared to passive or based skyhook control system landing gear system, the control strategy can effectively reduce the maximum impact acceleration and maintain the minimum change of acceleration during touchdown, simultaneously mains minimum stroke; the control strategy performs very well and exhibits strong robustness in different situations such as variable sink velocities and sprung masses; the control strategy can easily be applied in practical landing gear system.
In the future, the more precise model of MR absorber will be incorporated, and then experimental research will also be performed to check the actual control performance.
This research is supported financially by the National Natural Science Foundation of China (Project nos. 51275539 and 60804018), the Fundamental Research Funds for the Central Universities (CDJZR12110058 and CDJZR13135553), and the Program for New Century Excellent Talents in University (NCET-13-0630). Dr. Y. T. Choi and Professor N. M. Wereley in University of Maryland provided the data of the MR shock absorber and gave some helpful suggestions in improving the paper. These supports are gratefully acknowledged.