![image.png](/static/img/1a5d3f2a89bf06ab94bd0d3281444a04.image.webp)



```python
#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import numpy as np
import matplotlib.pyplot as plt


def IWP_Model_Controlled(u, X, h, J1, J2, l1, l2, c1, c2, m1, m2, Kb, Kt, Ra, g):
    theta, theta_dot, phi, phi_dot = X
    A = np.array([
        [m1 * l1 ** 2 + m2 * l2 ** 2 + J1 + J2, J2],
        [J2, J2]
    ])
    B = np.array([
        [c1, 0],
        [0, (Kt * Kb / Ra) + c2]
    ])
    C = np.array([
        -(m1 * l1 + m2 * l2) * g * np.sin(theta),
        Kt * u / Ra
    ])
    acceleration = np.linalg.inv(A).dot(-B.dot(np.array([theta_dot, phi_dot])) + C)
    dXdt = np.array([theta_dot, acceleration[0], phi_dot, acceleration[1]])
    next_X = X + h * dXdt
    return next_X


class ADRC:
    def __init__(self, dt, r, h, beta1, beta2, beta3, k1, k2, b0):
        self.dt = dt
        self.r = r
        self.h = h
        self.beta1 = beta1
        self.beta2 = beta2
        self.beta3 = beta3
        self.k1 = k1
        self.k2 = k2
        self.b0 = b0
        self.v1 = 0.0
        self.v2 = 0.0
        self.z1 = 0.0
        self.z2 = 0.0
        self.z3 = 0.0
        self.u_prev = 0.0

    def fhan(self, x1, x2, r, h):
        d = r * h
        d0 = h * d
        y = x1 + h * x2
        a0 = np.sqrt(d ** 2 + 8 * r * abs(y))
        if abs(y) > d0:
            a = x2 + (a0 - d) / 2 * np.sign(y)
        else:
            a = x2 + y / h
        if abs(a) > d:
            return -r * np.sign(a)
        else:
            return -r * a / d

    def TD(self, target):
        e = self.v1 - target
        fh = self.fhan(e, self.v2, self.r, self.h)
        self.v1 += self.dt * self.v2
        self.v2 += self.dt * fh
        return self.v1, self.v2

    def ESO(self, y, u):
        e = self.z1 - y
        self.z1 += self.dt * (self.z2 - self.beta1 * e)
        self.z2 += self.dt * (self.z3 + self.b0 * u - self.beta2 * e)
        self.z3 += self.dt * (-self.beta3 * e)
        return self.z1, self.z2, self.z3

    def NLSEF(self, v1, v2, z1, z2):
        e1 = v1 - z1
        e2 = v2 - z2
        return self.k1 * e1 + self.k2 * e2

    def control(self, y, target):
        v1, v2 = self.TD(target)
        z1, z2, z3 = self.ESO(y, self.u_prev)
        u0 = self.NLSEF(v1, v2, z1, z2)
        u = (u0 - z3) / self.b0
        self.u_prev = u
        return u


def iwp_adrc_discrete():
    J1 = 0.01186
    J2 = 0.0005711
    l1 = 0.1053
    l2 = 0.14
    c1 = 0.04
    c2 = 0.0001
    m1 = 0.826
    m2 = 0.583
    Kb = 0.0987
    Kt = 0.0987
    Ra = 1.5562
    g = 9.81

    dt = 0.001
    t_total = 3
    t_steps = int(t_total / dt)

    a = m1 * l1 ** 2 + m2 * l2 ** 2 + J1 + J2
    b0 = - (Kt / (Ra * (a - J2)))
    print(b0)

    r = 30
    beta1 = 300
    beta2 = 30000
    beta3 = 1e6
    k1 = 150
    k2 = 50

    adrc = ADRC(dt, r, dt, beta1, beta2, beta3, k1, k2, b0)

    theta0 = np.deg2rad(-10)
    theta_dot0 = 0.0
    phi0 = 0.0
    phi_dot0 = 0.0
    X = np.array([theta0, theta_dot0, phi0, phi_dot0])

    theta_ref = 0.0

    theta_history = np.zeros(t_steps)
    theta_dot_history = np.zeros(t_steps)
    phi_dot_history = np.zeros(t_steps)
    time_history = np.zeros(t_steps)
    control_history = np.zeros(t_steps)

    for i in range(t_steps):
        current_time = i * dt
        current_theta = X[0]
        Vm = adrc.control(current_theta, theta_ref)
        Vm = np.clip(Vm, -50, 50)
        X = IWP_Model_Controlled(Vm, X, dt, J1, J2, l1, l2, c1, c2, m1, m2, Kb, Kt, Ra, g)

        theta_history[i] = np.rad2deg(X[0])
        theta_dot_history[i] = X[1]
        phi_dot_history[i] = X[3]
        control_history[i] = Vm
        time_history[i] = current_time

    plt.figure(figsize=(12, 5))

    plt.subplot(1, 2, 1)
    plt.plot(time_history, theta_history, label='Pendulum Angle')
    plt.plot(time_history, np.zeros_like(time_history), 'r--', label='Target (0°)')
    plt.xlabel('Time (s)')
    plt.ylabel('Angle (°)')
    plt.title('Pendulum Angle Response (θ)')
    plt.grid(True)
    plt.legend()

    plt.subplot(1, 2, 2)
    plt.plot(time_history, phi_dot_history, label='Wheel Angular Velocity')
    plt.xlabel('Time (s)')
    plt.ylabel('Angular Velocity (rad/s)')
    plt.title('Wheel Angular Velocity Response (φ̇)')
    plt.grid(True)
    plt.legend()

    plt.tight_layout()
    plt.show()


if __name__ == '__main__':
    iwp_adrc_discrete()
```

ADRC算法平衡惯性轮倒立摆的代码

![image.png](/static/img/2f1466bf2f270287c78604a972d21c30.image.webp)



```python
import numpy as np
import matplotlib.pyplot as plt

# 倒立摆参数
M = 1.0  # 小车质量 (kg)
m = 0.1  # 摆杆质量 (kg)
l = 0.5  # 摆杆长度 (m)
g = 9.81  # 重力加速度 (m/s²)


# 倒立摆动力学模型
def pendulum_model(state, F):
    x, x_dot, theta, theta_dot = state
    sin_theta = np.sin(theta)
    cos_theta = np.cos(theta)

    # 计算theta''
    numerator = (M + m) * g * sin_theta - F * cos_theta - m * l * theta_dot ** 2 * sin_theta * cos_theta
    denominator = l * (M + m - m * cos_theta ** 2)
    denominator = np.sign(denominator) * max(1e-6, abs(denominator))  # 避免除以零
    theta_ddot = numerator / denominator

    # 计算x''
    if abs(cos_theta) < 1e-6:
        cos_theta = np.sign(cos_theta) * 1e-6
    x_ddot = (g * sin_theta - l * theta_ddot) / cos_theta

    return np.array([x_dot, x_ddot, theta_dot, theta_ddot])


class ADRC:
    def __init__(self, dt, r, h, beta1, beta2, beta3, k1, k2, b0):
        self.dt = dt
        self.r = r
        self.h = h
        self.beta1 = beta1
        self.beta2 = beta2
        self.beta3 = beta3
        self.k1 = k1
        self.k2 = k2
        self.b0 = b0

        # 状态初始化
        self.v1 = 0.0
        self.v2 = 0.0
        self.z1 = 0.0
        self.z2 = 0.0
        self.z3 = 0.0
        self.u_prev = 0.0

    def fhan(self, x1, x2, r, h):
        d = r * h
        d0 = h * d
        y = x1 + h * x2
        a0 = np.sqrt(d ** 2 + 8 * r * np.abs(y))

        if np.abs(y) > d0:
            a = x2 + (a0 - d) / 2 * np.sign(y)
        else:
            a = x2 + y / h

        if np.abs(a) > d:
            return -r * np.sign(a)
        else:
            return -r * a / d

    def TD(self, target):
        e = self.v1 - target
        fh = self.fhan(e, self.v2, self.r, self.h)
        self.v1 += self.dt * self.v2
        self.v2 += self.dt * fh
        return self.v1, self.v2

    def ESO(self, y, u):
        e = self.z1 - y
        self.z1 += self.dt * (self.z2 - self.beta1 * e)
        self.z2 += self.dt * (self.z3 + self.b0 * u - self.beta2 * e)
        self.z3 += self.dt * (-self.beta3 * e)
        return self.z1, self.z2, self.z3

    def NLSEF(self, v1, v2, z1, z2):
        e1 = v1 - z1
        e2 = v2 - z2
        return self.k1 * e1 + self.k2 * e2

    def control(self, y, target):
        v1, v2 = self.TD(target)
        z1, z2, z3 = self.ESO(y, self.u_prev)
        u0 = self.NLSEF(v1, v2, z1, z2)
        u = (u0 - z3) / self.b0
        self.u_prev = u
        return u


# 仿真参数
dt = 0.001
sim_time = 5.0
t = np.arange(0, sim_time, dt)
n = len(t)

# 初始状态 (x, x_dot, theta, theta_dot)
state = np.array([0.0, 0.0, np.pi / 6, 0.0])  # 初始角度30度

# ADRC参数
b0 = -1 / (l * M)  # 控制增益
adrc = ADRC(
    dt=dt,
    r=30,  # TD速度因子
    h=dt,  # TD滤波因子
    beta1=300,  # ESO参数 (3w)
    beta2=30000,  # (3w^2)
    beta3=1e6,  # (w^3)
    k1=150,  # NLSEF增益
    k2=50,
    b0=b0
)

# 初始化记录数组
states = np.zeros((n, 4))
F_history = np.zeros(n)
theta_history = np.zeros(n)

# 主循环
for i in range(n):
    # 获取当前角度作为系统输出
    current_theta = state[2]

    # ADRC控制
    F = adrc.control(current_theta, 0.0)
    F = np.clip(F, -50, 50)  # 限制控制力

    # 记录状态
    states[i] = state
    F_history[i] = F
    theta_history[i] = current_theta

    # 更新状态
    state_deriv = pendulum_model(state, F)
    state += state_deriv * dt

    # 角度归一化到[-pi, pi]
    if state[2] > np.pi:
        state[2] -= 2 * np.pi
    elif state[2] < -np.pi:
        state[2] += 2 * np.pi

# 绘图
plt.figure(figsize=(12, 8))
plt.subplot(2, 1, 1)
plt.plot(t, np.degrees(theta_history), label='Theta')  # 将弧度转换为度数
plt.plot([0, sim_time], [0, 0], 'r--', label='Target')
plt.ylabel('Angle (degrees)')  # 修改ylabel为度数
plt.legend()
plt.grid(True)

plt.subplot(2, 1, 2)
plt.plot(t, F_history, label='Control Force')
plt.ylabel('Force (N)')
plt.xlabel('Time (s)')
plt.legend()
plt.grid(True)

plt.tight_layout()
plt.show()
```

ADRC算法平衡倒立摆的代码

## API调用

登录这里：
https://console.volcengine.com/ark/region:ark+cn-beijing/endpoint?config=%7B%7D

注册后，创建DeepSeek R1 API接入点：

![image.png](/static/img/f7bd0508dac987671565f7b081c4efe6.image.webp)



接着Python就可以直接调用了：

```python
import os
from openai import OpenAI

client = OpenAI(
    api_key = "填写自己的key",
    base_url = "https://ark.cn-beijing.volces.com/api/v3",
)

# Non-streaming:
print("----- standard request -----")
completion = client.chat.completions.create(
    model = "ep-20250211175825-填写自己的模型名字",  # your model endpoint ID
    messages = [
        {"role": "system", "content": "你是豆包，是由字节跳动开发的 AI 人工智能助手"},
        {"role": "user", "content": "常见的十字花科植物有哪些？"},
    ],
)
print(completion.choices[0].message.content)

```

## OpenWebUI使用

安装：

```
docker run -d -p 8888:8080 \
  -v /root/ollama:/root/.ollama \
  -v /root/openwebui-test:/app/backend/data \
  --restart always -e HF_HUB_OFFLINE=1 \
  ghcr.io/open-webui/open-webui:ollama
```

增加这个函数到OpenWebUI：

```bash
"""
title: DeepSeek R1
author: zgccrui
description: 在OpwenWebUI中显示DeepSeek R1模型的思维链 - 仅支持0.5.6及以上版本
version: 1.2.6
licence: MIT
"""

import json
import httpx
import re
from typing import AsyncGenerator, Callable, Awaitable
from pydantic import BaseModel, Field
import asyncio


class Pipe:
    class Valves(BaseModel):
        DEEPSEEK_API_BASE_URL: str = Field(
            default="自己的baseurl",
            description="Base Url",
        )
        DEEPSEEK_API_KEY: str = Field(
            default="", description="用于身份验证的DeepSeek API密钥，可从控制台获取"
        )
        DEEPSEEK_API_MODEL: str = Field(
            default="deepseek-reasoner",
            description="API请求的模型名称，默认为 deepseek-reasoner ",
        )

    def __init__(self):
        self.valves = self.Valves()
        self.data_prefix = "data: "
        self.thinking = -1  # -1:未开始 0:思考中 1:已回答
        self.emitter = None

    def pipes(self):
        return [
            {
                "id": self.valves.DEEPSEEK_API_MODEL,
                "name": self.valves.DEEPSEEK_API_MODEL,
            }
        ]

    async def pipe(
        self, body: dict, __event_emitter__: Callable[[dict], Awaitable[None]] = None
    ) -> AsyncGenerator[str, None]:
        """主处理管道（已移除缓冲）"""
        self.thinking = -1
        self.emitter = __event_emitter__

        # 验证配置
        if not self.valves.DEEPSEEK_API_KEY:
            yield json.dumps({"error": "未配置API密钥"}, ensure_ascii=False)
            return

        # 准备请求参数
        headers = {
            "Authorization": f"Bearer {self.valves.DEEPSEEK_API_KEY}",
            "Content-Type": "application/json",
        }

        try:
            # 模型ID提取
            model_id = body["model"].split(".", 1)[-1]
            payload = {**body, "model": model_id}

            # 处理消息以防止连续的相同角色
            messages = payload["messages"]
            i = 0
            while i < len(messages) - 1:
                if messages[i]["role"] == messages[i + 1]["role"]:
                    # 插入具有替代角色的占位符消息
                    alternate_role = (
                        "assistant" if messages[i]["role"] == "user" else "user"
                    )
                    messages.insert(
                        i + 1,
                        {"role": alternate_role, "content": "[Unfinished thinking]"},
                    )
                i += 1

            # yield json.dumps(payload, ensure_ascii=False)

            # 发起API请求
            async with httpx.AsyncClient(http2=True) as client:
                async with client.stream(
                    "POST",
                    f"{self.valves.DEEPSEEK_API_BASE_URL}/chat/completions",
                    json=payload,
                    headers=headers,
                    timeout=300,
                ) as response:
                    # 错误处理
                    if response.status_code != 200:
                        error = await response.aread()
                        yield self._format_error(response.status_code, error)
                        return

                    # 流式处理响应
                    async for line in response.aiter_lines():
                        if not line.startswith(self.data_prefix):
                            continue

                        # 截取 JSON 字符串
                        json_str = line[len(self.data_prefix) :]

                        try:
                            data = json.loads(json_str)
                        except json.JSONDecodeError as e:
                            # 格式化错误信息，这里传入错误类型和详细原因（包括出错内容和异常信息）
                            error_detail = f"解析失败 - 内容：{json_str}，原因：{e}"
                            yield self._format_error("JSONDecodeError", error_detail)
                            return

                        choice = data.get("choices", [{}])[0]

                        # 结束条件判断
                        if choice.get("finish_reason"):
                            return

                        # 状态机处理
                        state_output = await self._update_thinking_state(
                            choice.get("delta", {})
                        )
                        if state_output:
                            yield state_output  # 直接发送状态标记
                            if state_output == "<think>":
                                yield "\n"

                        # 内容处理并立即发送
                        content = self._process_content(choice["delta"])
                        if content:
                            if content.startswith("<think>"):
                                match = re.match(r"^<think>", content)
                                if match:
                                    content = re.sub(r"^<think>", "", content)
                                    yield "<think>"
                                    await asyncio.sleep(0.1)
                                    yield "\n"

                            elif content.startswith("</think>"):
                                match = re.match(r"^</think>", content)
                                if match:
                                    content = re.sub(r"^</think>", "", content)
                                    yield "</think>"
                                    await asyncio.sleep(0.1)
                                    yield "\n"
                            yield content

        except Exception as e:
            yield self._format_exception(e)

    async def _update_thinking_state(self, delta: dict) -> str:
        """更新思考状态机（简化版）"""
        state_output = ""

        # 状态转换：未开始 -> 思考中
        if self.thinking == -1 and delta.get("reasoning_content"):
            self.thinking = 0
            state_output = "<think>"

        # 状态转换：思考中 -> 已回答
        elif (
            self.thinking == 0
            and not delta.get("reasoning_content")
            and delta.get("content")
        ):
            self.thinking = 1
            state_output = "\n</think>\n\n"

        return state_output

    def _process_content(self, delta: dict) -> str:
        """直接返回处理后的内容"""
        return delta.get("reasoning_content", "") or delta.get("content", "")

    def _format_error(self, status_code: int, error: bytes) -> str:
        """错误格式化保持不变"""
        try:
            err_msg = json.loads(error).get("message", error.decode(errors="ignore"))[
                :200
            ]
        except:
            err_msg = error.decode(errors="ignore")[:200]
        return json.dumps(
            {"error": f"HTTP {status_code}: {err_msg}"}, ensure_ascii=False
        )

    def _format_exception(self, e: Exception) -> str:
        """异常格式化保持不变"""
        err_type = type(e).__name__
        return json.dumps({"error": f"{err_type}: {str(e)}"}, ensure_ascii=False)

```

保存函数，配置函数参数：


![image.png](/static/img/da12b1b2235d9d6cfa4fe7ce8f5462a3.image.webp)

## 使用

可以自己修改一个模型名称便于认识，然后这个函数就可以显示出思考过程了。

![image.png](/static/img/b3fe3411c4f6fa3aaf6de917ef428f81.image.webp)

OpenWebUI使用DeepSeek R1满血版，DeepSeek R1 API调用

安装 Docker Compose 可以通过几种方式进行，最常见的是通过下载官方提供的二进制文件或者使用包管理器安装。以下是两种主要的方法：



### 方法一：通过下载二进制文件安装 Docker Compose

1. **下载最新版本的 Docker Compose**：
   
   首先，确定最新版本的 Docker Compose。你可以在 [GitHub Releases](https://github.com/docker/compose/releases) 页面找到最新版本。目前最新的稳定版本是 1.29.2（截至2021年）。

   使用以下命令下载：

   ```bash
   sudo curl -L "https://github.com/docker/compose/releases/download/1.29.2/docker-compose-$(uname -s)-$(uname -m)" -o /usr/local/bin/docker-compose
   ```

2. **设置执行权限**：

   下载完成后，你需要为二进制文件设置执行权限：

   ```bash
   sudo chmod +x /usr/local/bin/docker-compose
   ```

3. **创建符号链接（可选）**：

   为了避免打字错误或者简化路径，可以创建一个符号链接到 `/usr/bin`：

   ```bash
   sudo ln -s /usr/local/bin/docker-compose /usr/bin/docker-compose
   ```

4. **验证安装**：

   最后，使用以下命令验证安装是否成功：

   ```bash
   docker-compose --version
   ```

### 方法二：通过包管理器安装 Docker Compose

如果你更喜欢通过包管理器来管理软件，可以使用 Python 的包管理工具 `pip` 来安装 Docker Compose。

1. **安装 pip**：

   首先，确保你已经安装了 `pip`。如果没有，可以使用以下命令来安装：

   ```bash
   sudo apt update
   sudo apt install -y python3-pip
   ```

2. **使用 pip 安装 Docker Compose**：

   使用 `pip` 安装 Docker Compose：

   ```bash
   sudo pip3 install docker-compose
   ```

3. **验证安装**：

   使用以下命令验证安装是否成功：

   ```bash
   docker-compose --version
   ```

### 方法三：通过官方 APT 源安装 Docker Compose Plugin

Docker 现在提供了 Docker Compose 的插件版本，可以直接与 Docker CLI 集成。

1. **更新包索引并安装 Docker Compose 插件**：

   ```bash
   sudo apt update
   sudo apt install -y docker-compose-plugin
   ```

2. **验证安装**：

   你可以使用以下命令来确保安装成功：

   ```bash
   docker compose version
   ```

无论你选择哪种方法，都应该能够成功安装 Docker Compose 并开始使用它来定义和管理多容器 Docker 应用。

Ubuntu22 安装Docker Compose

在 Ubuntu 22.04 上安装 Docker 是一个相对简单的过程。以下是步骤：

### 1. 更新系统包

首先，确保系统包信息是最新的：

```bash
sudo apt update
sudo apt upgrade -y
```



### 2. 安装依赖包

在安装 Docker 之前，需要一些依赖包：

```bash
sudo apt install -y apt-transport-https ca-certificates curl software-properties-common
```

### 3. 添加 Docker 的官方 GPG 密钥

为了确保下载软件包的安全性，我们需要添加 Docker 的官方 GPG 密钥：

```bash
curl -fsSL https://download.docker.com/linux/ubuntu/gpg | sudo gpg --dearmor -o /usr/share/keyrings/docker-archive-keyring.gpg
```

### 4. 添加 Docker 的 APT 源

将 Docker 的 APT 源添加到你的系统中：

```bash
echo "deb [arch=amd64 signed-by=/usr/share/keyrings/docker-archive-keyring.gpg] https://download.docker.com/linux/ubuntu $(lsb_release -cs) stable" | sudo tee /etc/apt/sources.list.d/docker.list > /dev/null
```

### 5. 更新包索引

添加 Docker 的软件源之后，需要更新 APT 包索引：

```bash
sudo apt update
```

### 6. 安装 Docker 引擎

现在可以安装 Docker 引擎了：

```bash
sudo apt install -y docker-ce docker-ce-cli containerd.io
```

### 7. 启动并启用 Docker

安装完成后，启动 Docker 并设置开机自启：

```bash
sudo systemctl start docker
sudo systemctl enable docker
```

### 8. 验证安装

运行以下命令查看 Docker 的版本，并确保 Docker 报告了其版本信息：

```bash
docker --version
```

还可以运行一个简单的测试容器，确保 Docker 工作正常：

```bash
sudo docker run hello-world
```

### 9. （可选）将当前用户加入 `docker` 组

为了不在每次运行 Docker 命令时都使用 `sudo`，可以将当前用户加入 `docker` 组：

```bash
sudo usermod -aG docker $USER
```

然后，重新登录或重新启动系统以使更改生效。

现在，你已经在 Ubuntu 22.04 上成功安装了 Docker！

Ubuntu22 安装Docker

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