主要内容

两个具有负载限制的气缸模型

开放型号

This example shows how to model a rigid rod supporting a large mass interconnecting two hydraulic actuators. The model eliminates the springs as it applies the piston forces directly to the load. These forces balance the gravitational force and result in both linear and rotational displacement.

See two related examples that use the same basic components:four cylinder model和单缸模型。

  • 注意：这是一个基本的液压示例。您可以更轻松地使用SimScape™Driveline™和Simscape Flys™构建液压和汽车型号。

  • Simscape Fluidsprovides component libraries for modeling and simulating fluid systems. It includes models of pumps, valves, actuators, pipelines, and heat exchangers. You can use these components to develop fluid power systems such as front-loader, power steering, and landing gear actuation systems. Engine cooling and fuel supply systems can also be developed with Simscape Fluids. You can integrate mechanical, electrical, thermal, and other systems using components available within the Simscape product family.

  • SIMSCAPE DRIVELINEprovides component libraries for modeling and simulating one-dimensional mechanical systems. It includes models of rotational and translational components, such as worm gears, planetary gears, lead screws, and clutches. You can use these components to model the transmission of mechanical power in helicopter drivetrains, industrial machinery, vehicle powertrains, and other applications. Automotive components, such as engines, tires, transmissions, and torque converters, are also included.

模型的分析和物理

我们假设杆的旋转角度很小。杆的运动方程在下面的方程块1中给出。描述气缸和泵行为的方程与单缸示例相同。

Equation Block 1:

$$M \frac{d^2 z}{d t^2} = F_b + F_a + F_{ext} $$

$$ i \ frac {d^2 \ theta} {d t^2} = \ frac {l} {2} f_b - \ frac {l} {2} f_a $$

$$ z- \ mbox {中心位移} $$

$$ m- \ mbox {总质量} $$

$$ F_a - \mbox{ piston A force } $$

$$ F_b - \mbox{ piston B force } $$

$$ F_{ext} - \mbox{ external force at center } $$

$$ \ theta- \ mbox {顺时针方向} $$

$$ i - \ mbox {杆的惯性矩} $$

$$ L - \mbox{ rod length } $$

单个活塞的位置和速度直接来自几何形状。请参阅方程式2中的以下相应方程。

等式块2：

$$ z_a = z - \theta \frac{L}{2} $$

$$ z_b = z + \ theta \ frac {l} {2} $$

$ \ frac {d z_a} {dt} = \ frac {d z} {dt} - \ frac {d \ theta} {dt} {dt} \ frac {l} {2} $$

$ \ frac {d z_b} {dt} = \ frac {d z} {dt} + \ frac {d \ theta} {dt} {dt} \ frac {l} {2} $$

$$ z_a- \ mbox {活塞a置换} $$

$$ z_b - \mbox{ piston B displacement } $$

打开模型并运行模拟

Toopen this model， 类型sldemo_hydrod进入MATLAB®命令窗口（如果使用MATLAB帮助，请单击超链接）。要运行模拟，在“仿真”选项卡上，按Run。该模型：

  • 将信号数据记录到MATLAB工作空间Simulink.SimulationOutputobject出去。The signal logging data is stored in出去, in a金宝appsimulink.simulationdata.dataset对象调用SLDEMO_HYDROD_OUTPUT。

  • 日志连续将数据列为MATLAB工作区。状态数据也包含在出去工作区变量，作为称为的结构xout。每个状态都在模型中分配一个名称，以方便使用已记录数据。各州的名称可在Statenamefield ofxout.signals。For more information, see记录模拟数据的数据格式。

  • 使用可自定义的Circular Gauge和Vertical Gaugeblocks to visualize the fluid flow, pressure, and linear displacement in the cylinders.

Figure 1:Two cylinder model and simulation results

'Mechanical Load' Subsystem

该子系统如图2所示。它求解运动方程，我们使用标准的Simulink块直接计算。金宝app假定旋转角度很小。在“机械负载”子系统的面罩下查看其结构（右键单击子系统，然后选择面具>Look Under Mask）。

Figure 2:“机械负载”子系统

仿真参数

此模拟中使用的参数与单缸模型，除了以下内容：

L = 1.5 m m = 2500公斤我= 100公斤/ m ^ 2 Qmax = 0.005m^3/sec (constant) C2 = 3e-9 m^3/sec/Pa Fext = -9.81*M Newtons

尽管泵流量是恒定的，但模型独立控制阀门。最初，在t = 0, the cross-section of valve B is zero. It grows linearly to1.2e-5 m^2att = 0.01秒, and then linearly decreases to zero att = 0.02秒。The cross-section of valve A is1.2e-5平方米att = 0和it linearly decreases to zero att = 0.01秒，然后线性增加到1.2e-5平方米att = 0.02秒。Then the behavior of the valves A and B repeats periodically with the same pattern. In other words the valves A and B are 180 degrees out of phase.

结果

图3和4显示了杆的线性和角位移。线性位移响应是一个类型的集成系统的典型特征。杆的相对位置和角移动说明了两个活塞对隔离控制信号（阀A和B的横截面）的响应。

图3：Linear displacement of the pistons and the load (load is in the middle of the rod)

图4：Angular displacement of the rod

Close Model

Close the model and clear all generated data.

Conclusions

Simulink provides a productive environment for simulating hydraulic systems, offering enhancements that provide enormous productivity in modeling and flexibility in numerical methods. The use of masked subsystems and model libraries facilitates structured modeling with automatic component updates. As users modify library elements, the models that use the elements automatically incorporate the new versions. Simulink can use differential-algebraic equations (DAEs) to model some fluid elements as incompressible and others as compliant, allowing efficient solutions for complex systems of interdependent circuits.

诸如此类的模型最终可以用作整体植物或车辆系统的一部分。Simulink的分层性质允许在较大的系统模型中放置独金宝app立开发的液压执行器（例如，以传感器或阀形式添加控件）。在这样的情况下，Control System Toolbox™的工具可以分析和调整整体闭环系统。因此，MATLAB/S金宝appIMULINK环境可以支持整个设计，分析和建模周期。金宝app

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Model-Based Design for Embedded Control Systems

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