Software for Fluid Power Technology

From Editor

1 Introduction

So, Little, Moler and Steve Bangert developed a sec-ond generation, professional version of MATLAB written in C and integrated with graphics. The Math-works, Inc. was founded in 1984 to market and con-tinue development of MATLAB. The purpose of this review is to highlight the abilities of MATLAB and SIMULINK for system simulation and controller de-sign problems in the field of fluid power.

2 MATLAB

• numerical computation routines for calculations with scalars, vectors and matrices
• routings for solving ordinary differential equa-tions numerically,
• 2D and 3D Graphic routines for data visualiza-tion,
• interactive language and programming environ-ment,
• tools for building custom GUIs,
• interface to external languages, like C, Fortran and Java (allows also interaction with e.g. multi-body-simulation environments like ADAMS),
• support for data acquisition and real time control via external toolboxes

Fig. 1: The MATLAB command window

Hundreds of built-in functions come with the basic MATLAB and there are optional (commercial and non-commercial) toolboxes of functions for specific purposes. For automatic control, these are

• Control Systems Toolbox,
• Signal Processing Toolbox,
• Robust Control Toolbox and more.

• Simulink and perhaps the
• Hydraulic Block Set Toolbox

Many of the functions in MATLAB and the toolboxes are written in the MATLAB language where the source code is readable.

3 Simulink

Fig. 2: The SIMULINK environment

Figure 2 shows a block diagram for the first stage of a hydraulic servo valve (torque motor + flap-per/nozzle system). In this case the stage is simply modelled as a second order PT2 system, were, how-ever, limited integrators as nonlinear elements to in-clude the effects of limited velocity and position re-placed the standard integrators. The elements are sim-ply dragged from the Simulink library window to the block diagram editor and connected to each other. For generating input signals and viewing simulation data (e.g. step response) the Simulink libraries provide a number of input signal generators as well as display blocks for graphs and output blocks to the MATLAB workspace or a file for further processing, like filtering etc. Of course, Simulink also provides functionality for generating subsystems, for masking of subsystems and for the generation of custom libraries. All these func-tions help to keep track of things and the diagram "clean".

Fig. 3: Subsystems in SIMULINK

Even though Simulink is very easy to use and simulation models are created rather quickly, in some cases the block diagram may become very large, although the nonlinear algebraic or differential equations do not look very difficult, e.g. the throttle equation or cylinder friction forces in the equation of motion. For these cases Simulink offers to include C-code (or Fortran or Matlab language) into the block diagrams, called S-functions. When using C-code, these blocks have to be written in a Simulink-accessable format, called CMEX. This method is very simple, since the algebraic and differential equations are written into a template file in a state space like format, which is very familiar to all users with experience in state space sys-tem description and controller design. Figure 4 shows for example the complete code (headers and not re-quired functions are not shown) for a servo pump model used for the C-code block of Fig. 3.
The use of CMEX files has the additional benefit of much faster simulation execution times compared to block diagrams based upon the standard elements only, especially in cases of trigonometric functions of if-then-else-clauses, like needed for modelling saturation effects. For compiling the CMEX files, either the MATLAB C-Compiler (additional charge) or an exter-nal compiler like Microsoft Visual C/C++ can be used.

Fig. 4: CMEX file for pump simulation (C-Code)

It has to be mentioned, that ready-made component toolboxes, like the Hydraulic Block Set Toolbox (which is not very sophisticated from my point of view), are available at additional cost. This allows the user not to model every single component from the very beginning by writing down the differential equa-tions. On the other hand, modelling the system to be investigated from the basics, gives the user a much higher insight into the system’s behaviour and its char-acteristics, which is highly beneficial to controller design approaches, but does also require much more time.
After all, Simulink is a very powerful tool to model even large-scaled systems for dynamic simulations. Complex simulation models, like complete aircraft hydraulic systems, including actuators, aerodynamic forces and controllers or other hydraulic systems found in mobile machines, excavator, wheel loaders etc. can be simulated at very reasonable effort and simulation time. Especially for the last mentioned systems the ability of MATLAB/Simulink to to realize a co-simulation with the multi-body simulation tool AD-AMS has to be pointed out. This allows the simultane-ous simulation of reaction and inertia forces of the mechanical system and the hydraulic actuators.

4 Control System Toolbox

Fig. 5: Interactive controller design

Figure 5 illustrates this design process. The upper windows shows the root locus design tool, while the lower windows shows the according system step re-sponse of the system. Alternatively, the design tool would also show Bode plots for compensator or the closed loop as well as the Nyquist plot. After importing the open loop transfer function from the MATLAB workspace the design tool shows the root loci of all poles, assuming a proportional controller. The user can now modify the compensator by adding additional poles and zeros, while the tool adjusts the root loci and the plots immediately. This allows the user to study the influence of different control structures simultaneously. However, it has to be mentioned, that only the forward branch of the controller design can be modified inter-actively. Other elements, like pre-filter and sensor dynamics (in the feedback branch) can only be modified by re-importing a new or adjusted transfer function from the MATLAB workspace.

5 Summary

• easy to use and efficient user interface,
• interactive design and modelling tools,
• almost unlimited extendibility, via C-Code, com-mercial and non commercial toolboxes and other add-on products,
• excellent documentation and help function.

• the costs for a MATLAB license are rather high (especially for commercial users),
• most toolboxes come only at additional charge,
• educational versions (Student Edition and Class-room Kit) are not free of charge,
• the high number of functions makes it difficult for the user to get a complete overview of MAT-LAB’s capabilities.

JG