Hydraulic Modeling and Simulation

Software tools for simulation and modeling can help verify the design of hydraulic motion control systems. Model-based control provides an accurate tool for indicating when a hydraulic system will not work and offers advanced techniques for using simulation technology in the development, testing and application of software.

“Hydraulic models are here to stay,” says Peter Nachtwey, president of Delta Computer Systems, “because they help engineers develop better systems understanding and better hydraulic solutions.”

Hydraulic modeling offers a series of calculations and generates values for spool acceleration, spool velocity, spool position and pump flow. Calculated parameters include cap side pressure, rod side pressure, plus piston acceleration, velocity and position. Nachtwey says modeling helps engineers evaluate “what if” design scenarios, identify design errors and create an environment where machine and controls design can proceed in parallel.

While simulation could be done using a spreadsheet, software tools such as MATLAB, Simulink or 20-sim, simplify the process. The idea is to create a system of differential equations to effectively model the system. Nachtwey says with 90 percent of applications, creating a state space for linear simulation is effective. For detailed simulation, a system of non-linear differential equations must be solved using methods such as Runge-Kutta (RK4).

Non-linear modeling is the most detailed form and is used to check designs. Utilizing a small time period, typically 100 µsec as a starting point, one can estimate the state in the future. The new state is then used to project and estimate the next state at the next 100 µsec increment. None of the variables is assumed to be constant for any period of time and engineers can compare estimated performance to performance of design specifications.

Getting data for models is difficult because of limited specifications or lack of transfer functions provided by manufacturers. While some data like cylinder size can be easily obtained, motor and valve response must often be obtained empirically.

Motion controllers often use a simple state space method of simulation when dealing with a linear model which deals in gains, time constants, damping factors and natural frequencies instead of the more complex component interactions of non-linear modeling. Motor systems look like first order systems, while hydraulic systems look like second order systems that can be modeled as a mass between two springs. Second order controllers have a PID with a second derivative and velocity, acceleration and jerk feed forwards to compensate for the extra pole (or complexity).

While it can be costly to design hydraulic systems with natural frequencies high enough for higher production rates, one solution is using the motion controller to compensate for systems with low natural frequency because electronics are relatively inexpensive compared to extra machine hardware costs. The challenge is smooth motion profiles where the jerk changes smoothly using jerk feed forward, even though there are physical limitations as to how fast the system can accelerate or decelerate.

Model-based control and auto tuning provide a way to determine the jerk feed forward and second derivative gain. With model-based control, the PID and feed forwards use the positions, velocities and accelerations generated by the model, not the feedback, so the PID loop sees a nearly perfect system virtually free of quantizing errors, sample jitter and noise. The result is smoother output which allows use of higher gains. However, the feedback is continuously updating the model so the model's estimated values stay close to the actual feedback.

The model can be created using data in plots and graphs from the motion controller including time, control output and actual position or velocity. The result is gains and time constants for a first-order model, or gain, damping factor and natural frequency for the second order controller. The engineer can chose the model which provides the best fit. All the closed loop gains are calculated from the model and desired bandwidth.

Information on how to get started and actual formulas are available online.