# Active Shock Absorber Control Based on Time-Delay Neural Network

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## Abstract

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## 1. Introduction

## 2. Methodology

## 3. Time Delay Neural Network Controller Design

#### 3.1. Active Shock Absorber Description

- The currents on the solenoid valves of the compression and rebound strokes ${i}_{C},{i}_{R}$, whose values lie in the range 0…1.8 A. Applying the current value to the valve changes its capacity. The values of the force on the shock absorber rod and the values of the speed of the rod always have the same sign. Thus, a shock absorber controlled only by the currents on the valves works as semi-active. The set of a dynamic dissipative characteristics of the shock absorber for different values of currents is shown in Figure 2. In Figure 2 and Figure 3, the following notation in used: $F\u2014\text{}$ force on the rod, $v$—velocity of the rod, $i$—control current, $Q$—hydraulic pump flow rate.
- The hydraulic pump flow rate Q lies in the range of −24…24 l/min, where the sign determines the direction of the fluid flow. The set of dissipative characteristics obtained for different values of Q are presented in Figure 3. A pump is essentially an external source of energy in the system, and thus it becomes possible to generate forces on the rod opposite to the direction of the movement of the rod. This is how the “active” property of the shock absorber is realized.

#### 3.2. Neural Network Training

- Displacement of the shock absorber rod $x$ was defined as the product of two chirp signals, with a frequency varying from 0.01 to 2 Hz, and from 1 to 4 Hz. The gain of the multiplication is 0.03 m.
- The velocity of movement of the rod $v$ was defined as the time derivative of the displacement.
- Electrical currents and volumetric flow rate of a hydraulic pump were also defined as the product of two chirp signals, with frequencies variable for ${i}_{R}$ from 1 to 1.2 Hz, for ${i}_{C}$ from 1 to 1.3 Hz, and for $Q$ from 1 to 1.3 Hz, with amplitudes in the range of their possible values.

- Algorithm: Levenberg-Marquardt backpropagation
- NN performance criteria: mean squared error (MSE)
- Training epoch: 2000
- Maximum number of validation degradation checks: 10
- Data division: random, 60% for training, 20% for validation and 20% for testing

#### 3.3. Controller Design

## 4. Simulation Results

#### 4.1. Providing the Desired Force in the Form of a Wave Signal with Increasing Frequency

#### 4.2. Providing the Desired Force in the Form of a Wave Signal with Initial Time Delay

#### 4.3. Providing the Desired Force in the Form of a Sawtooth Signal

#### 4.4. Providing the Desired Force in the Form of a Step Signal

## 5. Implementation of the Developed Controller in the Quarter Vehicle Model

## 6. Conclusions and Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Active shock absorber dissipative characteristics set with different values of control currents ${i}_{C},{i}_{R}$.

**Figure 3.**Active shock absorber dissipative characteristics set with different values of the flow rate $Q$.

**Figure 11.**Desired force as a sine wave with increasing frequency. Top: velocity of the rod; bottom: force on the rod (red—desired, blue—actual).

**Figure 12.**Desired force as a delayed sine wave. Top: velocity of the rod; bottom: force on the rod (red—desired, blue—actual).

**Figure 13.**Desired force as a sawtooth. Top: velocity of the rod; bottom: force on the rod (red—desired, blue—actual).

**Figure 14.**Desired force as a step. Top: velocity of the rod; bottom: force on the rod (red—desired, blue—actual).

**Figure 17.**Desired force on the rod generated by the high level PID controller (red) and actual force on the rod (blue).

**Figure 18.**Vehicle body vertical accelerations using passive (red) and active shock absorbers with the developed low level controller (blue).

**Figure 19.**Desired force on the rod generated by the high level PID controller in the case of a sine excitation (blue) and actual force on the rod (red).

Parameter | Symbol | Value (Unit) |
---|---|---|

Mass of the body | ${m}_{b}$ | 375 (kg) |

Mass of the wheel | ${m}_{w}$ | 29.5 (kg) |

Suspension stiffness | ${k}_{s}$ | 20.58 (kN/m) |

Damping coefficient | ${c}_{s}$ | 772 (Ns/m) |

Tire stiffness | ${k}_{t}$ | 200 (kN/m) |

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**MDPI and ACS Style**

Alyukov, A.; Rozhdestvenskiy, Y.; Aliukov, S.
Active Shock Absorber Control Based on Time-Delay Neural Network. *Energies* **2020**, *13*, 1091.
https://doi.org/10.3390/en13051091

**AMA Style**

Alyukov A, Rozhdestvenskiy Y, Aliukov S.
Active Shock Absorber Control Based on Time-Delay Neural Network. *Energies*. 2020; 13(5):1091.
https://doi.org/10.3390/en13051091

**Chicago/Turabian Style**

Alyukov, Alexander, Yuri Rozhdestvenskiy, and Sergei Aliukov.
2020. "Active Shock Absorber Control Based on Time-Delay Neural Network" *Energies* 13, no. 5: 1091.
https://doi.org/10.3390/en13051091