From the series:State-Space Models
使用MATLAB创建和分析状态空间模型®and Control System Toolbox™. State-space models are commonly used for representing linear time-invariant (LTI) systems.
This video shows how you can:
在此视频中,我们将看到如何在MATLAB和控制系统工具箱中创建,操纵和分析基于状态的系统。让我们构建一个直流电动机的状态空间模型,其中施加的电压V是输入,轴速度欧米茄是输出,而电流,I和轴速度,Omega是两个状态。电机参数已经在基本工作空间中定义。因此,让我们从建立基于州的矩阵开始。
Now we use the SS command on the state space matrices to create the state space model of the motor. Now that we have developed a state space model of the motor, let's add a voltage amplifier represented by the following first order transfer function that amplifies the input voltage. This amplifier provides a steady state voltage gain of five and a bandwidth of 1,000 radians per second.
现在,我们已经设计了电压放大器,让我们通过使用Star操作员组合电动机和放大器来创建整体植物模型。这说明了如何使用控制系统工具箱,我们可以轻松地在具有不同表示状态空间和传输功能(例如状态空间和传输功能)的模型之间结合和转换。例如,这两个模型的组合导致三阶状态空间模型。
Now that we have developed our plant model, let us analyze our plant stability by calculating the poles or eigenvalues of the plant using the pull function, which returns negative real values, indicating a stable plant. Instead of calculating poles with the pole function, we could also have used the is stable function to analyze stability. This function returns a logical one if the system is stable or zero if unstable.
Now that we have determined that our plant is stable, let us analyze the step response for a unit step voltage applied using the step function. From the transient system characteristics, we see that the system takes a little over one second to rise and takes over two seconds to settle. So now we have seen how to create, manipulate, and analyze state space systems in MATLAB and Control System Toolbox. In the next video in this series on state space systems, we will design a full state feedback controller for our plant to show how state space models can be utilized in control design. This concludes the video.
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