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Four Hydraulic Cylinder Simulation

This example shows how to use Simulink® to create a model with four hydraulic cylinders. See two related examples that use the same basic components: single cylinder model and model with two cylinders and load constraints.

  • Note: This is a basic hydraulics example. You can more easily build hydraulic and automotive models using Simscape™ Driveline™ and Simscape Fluids™.

  • Simscape Fluids provides 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 Driveline provides 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.


Figure 1 shows the top level diagram of the model. This model has a single pump and four actuators. The same pump pressure (p1) drives each cylinder assembly and the sum of their flows loads the pump. Although each of the four control valves could be controlled independently, as in an active suspension system, in this case all four receive the same commands, a linear ramp in orifice area from zero to 0.002 sq.m..

Opening the Model and Running the Simulation

To open this model, type sldemo_hydcyl4 at MATLAB® terminal (click on the hyperlink if you are using MATLAB Help). Press the "Play" button on the model toolbar to run the simulation.

The model logs relevant data to MATLAB workspace, into the Simulink.SimulationOutput object out. The signal logging data is stored within out, in a structure called sldemo_hydcyl4_output. Logged signals have a blue indicator (see the model). For more information, see Visualize and Access Signal Logging Data.

Figure 1: Four cylinder model and simulation results

Model Description

The pump flow begins at 0.005 m3/sec (just like in the single cylinder model), then it drops to 0.0025 m3/sec at t=0.05 sec. The parameters C1, C2, Cd, rho, and V30 are identical to those in the single cylinder model. However, by assuming individual values for K, A, and beta, each one of the four cylinders exhibit distinctive transient responses. The table below gives the characteristics of the four actuators.

Parameter       |  Actuator1   Actuator2   Actuator3   Actuator4
Spring Constant |  K           K/4         4K          K
Piston Area     |  Ac          Ac/4        4Ac         Ac
Bulk Modulus    |  Beta        Beta        Beta        Beta/1000
Beta = 7e8  Pa  [fluid bulk modulus]
K    = 5e4  N/m [spring constant]
Ac   = 1e-3 m^2 [cylinder cross-sectional area]

The ratio of area and spring constant is the same for all pistons, so they should have the same steady state output. The dominant time constant for each actuator subsystem is proportional to


(result obtained from dimensional analysis), so we can expect the piston assembly 2 to be somewhat faster than assembly 1. The piston assembly 3 is expected to be slower than 1 or 2. The piston assembly 4 has a significantly lower bulk modulus beta (as would be the case with air), thus we expect piston 4 to respond more sluggishly than piston 1.


Figure 2: Piston positions in four cylinder example

Figure 3: Pump Supply Pressure, p1

The initial jolt of flow at t=0 is seen by the four actuators as a pressure impulse. The pump pressure (p1), which is initially high, drops rapidly because there is a high flow demand from the four loads. During the initial transient (about 4 msec), distinct responses identify the individual dynamic characteristics of each assembly unit.

As predicted by the parameter values, actuator 2 responds much faster than actuator 1. The third and fourth pistons are much slower because they require more working fluid to move the same distance. In case 3, the piston displaces more volume due to its larger cross-sectional area. In case 4, although the displaced volume is the same as in case 1, the device requires more fluid because it is subsequently compressed.

As the pump pressure falls to the level within the cylinders, the distinctions in behavior are blurred. The individual responses blend into an overall system response which maintains the flow balance between the components. At t=0.05 sec, the pump flow drops to a level that is close to the equilibrium and the actuator flows are nearly zero. The individual steady state piston positions are equal, as predicted by the design.

Closing the Model

Close the model. Clear generated data.

See Also


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