理解模型预测控制,第7部分:自适应MPC设计与Simulink和模型预测控制工具箱
从这个系列中:理解模型预测控制
Melda Ulusoy, MathWorks
在本视频中,您将学习如何为自动转向车辆系统设计自适应MPC控制器,该系统的动态变化与纵向速度有关。
在为控制系统最可能的操作条件设计MPC控制器之后,您可以基于该设计实现自适应MPC控制器。在每个时间步,自适应MPC更新工厂模型和当前运行条件的标称条件。在本视频中,您将学习如何计算和更新自适应MPC块所需的离散工厂模型。您还将学习如何从自适应MPC控制器生成代码,您将看到一个示例,显示一个真正的自动驾驶汽车,它使用MPC控制和图像处理算法来保持自己在车道内。
在本视频中,我们将使用自适应MPC来自动驾驶一辆由于纵向速度变化而随时间变化的横向车辆动力学的汽车。在之前的视频中,我们讨论了车辆的线性横向动力学,并假设汽车具有恒定的纵向速度。所以,植物的动态没有改变状态矩阵A是恒定的。为了控制该系统,我们使用了传统的MPC控制器。但是现在我们让纵向速度随着车的移动而变化。所以状态矩阵A也会改变。传统的MPC控制器不能有效地处理动态变化,因为它使用恒定的内部植物模型。那么,我们该如何应对不断变化的植物动态呢?在第4部分视频中,我们讨论了自适应MPC允许您在操作条件发生变化时在每个时间步提供新的线性工厂模型,因此它在新的操作条件下做出更准确的预测。因此,为了应对不断变化的植物动态,我们将使用自适应MPC。
我们打开一个新的Simulink模型,并开始从这个自定义库中添加植物。在之前的视频中,该对象被开发为一个状态空间系统,其输入为转向角,输出为横向位置和偏航角。这一次,它的动力学随着纵向速度的变化而变化。因此,这现在成为植物块的输入。我们要用一个恒定的块来表示纵向速度,我们一开始设为15米/秒,然后改变为另一个值。另一个输出是我们稍后将使用的状态。如果你想看看这些积木是如何建造的,你可以从视频描述中给出的链接下载这个Simulink模型。接下来,我们将连接模型预测控制工具箱下的自适应MPC块。该块具有与常规MPC块相同的输入和输出,除了它还采用针对当前操作条件在每个时间步更新的工厂模型。之前,我们为横向位置和偏航角设计了一个自定义参考。 We’ll first connect this reference to the controller. Then we connect the plant output to the measured outputs and the steering angle to the controller output. To implement the adaptive MPC, we can simply start with the MPC controller that we designed in the previous video for a longitudinal velocity of 15 m/s. We already have the MPC controller object in our workspace. By typing it in the command window, we can see the design parameters such as the prediction and control horizons, constraints and weights. One thing to note is that the adaptive MPC block requires a discrete plant model. So, we need to convert the continuous time state space model used by mpc1 to discrete time. There are different ways to do it. Here, we use the c2d command and update the plant model of the MPC object with the discretized plant. Now, we go back to the adaptive MPC block and type in the MPC object. Next, we need to provide the controller with a plant model that is updated at each time step for the current operating condition. The pre-built update plant model block takes care of this calculation. When we double click on it, we see that it has been implemented as a MATLAB function. As inputs, this function takes Vx, u and x and first calculates the state space matrices. It then computes the discrete model and also updates the nominal conditions with the current operating conditions. Now it’s time to connect the inputs and outputs for this block. We already have all the inputs here, longitudinal velocity, the steering angle and the states. The “model” input of the adaptive MPC control block requires the discrete-time model and nominal conditions in this order that we’ve created in the MATLAB function. To connect the outputs to the controller, we select the block, and create a bus signal. Now, we’re ready to try different longitudinal velocities and see how the controller handles the varying plant dynamics. In the previous video, the traditional MPC controller designed for an operating condition of 15 m/s had worked well while it failed to control the system at a different longitudinal velocity of 35 m/s. With adaptive MPC, we get a good controller performance when longitudinal velocity is 15 m/s. If we now change it to 35 m/s, we still get a good tracking of the lateral position and the yaw angle. We can even replace this constant block with a continuously changing signal such a sine wave and see that adaptive MPC still can deal with the changing plant dynamics and successfully control the system. We designed an adaptive MPC controller, ran several simulations to evaluate the controller performance. Now if you want to run your controller on your autonomous car, you can simply generate code using Embedded Coder and deploy it to your car. Here’s the generated C code. You can call the MPC controller code from your real-time scheduler using the entry points shown in the code interface report. Embedded Coder also lets you customize the call interfaces as required by your software framework and architecture.
这段视频展示了如何在自动驾驶汽车上运行MPC控制器和图像处理算法的生成代码,以使其保持在车道内。在Simulink之外开发的图像处理和车道检测算法为MPC控制器提供了这些输入。这些算法是这样工作的。汽车的前视图是由安装在汽车顶部的摄像头拍摄的。图像处理算法识别实线和虚线标记,并检测汽车行驶的车道。车道的中间是中心线,它用来计算汽车的位置与这条线的偏移量以及偏航角。MPC控制器使用这些信息来保持汽车在中心线上。左边的图用红色表示汽车与中心线的偏差,用绿色表示偏航角,而右边的图则显示了方向盘的角度。
在这个视频中,我们讨论了如何使用自适应MPC来控制动态变化的工厂,还讨论了如何生成C代码并部署它进行实时控制。有关模型预测控制的更多信息,请查看我们之前的Tech Talk视频。
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