# Model Identification and Control of a Buoyancy Change Device

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Prototype Description

^{3}and is able to dive up to 100 m. Its full length is 1285 mm with an outer radius of 200 mm. Its dry weight is 33 kg. Further details of the BCD can be found in [12].

## 3. Dynamic Model of the Vertical Motion of the Prototype

#### 3.1. Model Development

#### 3.2. Model Identification

## 4. Controller Development and Experimental Results

#### 4.1. Controller Structure

#### 4.2. Controller Experimental Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Identification results for experiments 1: (

**a**) u = −2.5 V, (

**b**) u = 2.5 V, (

**c**) u = −5 V, (

**d**) u = 5 V, (

**e**) u = −7.5 V, (

**f**) u = 7.5 V, (

**g**) u = −10 V and (

**h**), u = 10 V.

**Figure 8.**Identification results for experiments 2: (

**a**) x: 0 → 9 (mm), (

**b**) x: 0 → −9 (mm), (

**c**) x: 0 →13 (mm), (

**d**) x: 0 → −13 (mm), (

**e**) x: 0 → 17 (mm), (

**f**) x: 0 →−17 (mm), (

**g**) x: 0 →21 (mm), (

**h**) x: 0 → −21 (mm).

**Figure 10.**PI depth controller experimental results: z is the BCD depth, z

_{t}is the target depth and the dashed dot lines represent a ±5% band around z

_{t}.

**Figure 11.**PI control, step response to evaluate steady state error: z is the BCD depth, z

_{t}is the target depth and the dashed dot lines represent a ±5% band around z

_{t}.

**Figure 13.**PID depth controller experimental results: z is the BCD depth, z

_{t}is the target depth and the dashed dot lines represent a ±5% band around z

_{t}.

**Figure 14.**PID depth controller: integral action evolution over time of the trials shown in Figure 13.

C_{x} | C_{z} | ||

P | PI | PID | |

k_{p} | 15.44 [V/mm] | −9.71 [mm/m] | −9.71 [mm/m] |

k_{i} | − | −0.06475 [mm × s^{−1}/m] | −0.06475 [mm × s^{−1}/m] |

k_{d} | − | − | −32.27 [mm × s/m] |

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**MDPI and ACS Style**

Carneiro, J.F.; Pinto, J.B.; Almeida, F.G.d.; Cruz, N.A.
Model Identification and Control of a Buoyancy Change Device. *Actuators* **2023**, *12*, 180.
https://doi.org/10.3390/act12040180

**AMA Style**

Carneiro JF, Pinto JB, Almeida FGd, Cruz NA.
Model Identification and Control of a Buoyancy Change Device. *Actuators*. 2023; 12(4):180.
https://doi.org/10.3390/act12040180

**Chicago/Turabian Style**

Carneiro, João Falcão, J. Bravo Pinto, F. Gomes de Almeida, and N. A. Cruz.
2023. "Model Identification and Control of a Buoyancy Change Device" *Actuators* 12, no. 4: 180.
https://doi.org/10.3390/act12040180