How to analyze positioning systems

The physics of positioning systems relate the parameters of motion control components to the overall system performance. While the relationships obey, in general, known kinematics, dynamics, and structural equations, they become rather complex as many parameters affect many variables. Consequently, designers can lose that intuitive feel for the right optimization direction, and frequently turn to computer aided engineering tools, with a model representation of their system to simplify the design and analysis process.

There are several tools known in the market to handle such problems and help engineers to better understand the behavior of their system of interest. For example, Matlab/Simulink from MathWorks (Natick, MA) and Easy5 (a Boeing design tool that is now commercialized for general industrial applications), assist design and application engineers in developing a good intuitive feel to the otherwise complex relationship between motion control component parameters and overall system performance.

This article discusses how Bayside developed its own pre-modeled analysis tool for positioning systems using Excel spreadsheet software. The company uses the new analysis tool Bimo (Bayside's Integrated Motion Optimization) internally as a customer support tool and service package to help its customers design better machines. However, plans exist for future commercialization.

Bimo uses simplified positioning system models to integrate structural kinematics, dynamics, frequency response simulation, time domain analysis, 3D precision calculations, and a component selection database in a package that doesn't require any sophisticated analytical background or special programming skills to use.

The first model is used for frequency response analysis. It assists in understanding the effects of each positioning system component on the overall system stability and responsiveness. The second model is used for time domain analysis. It assists in analyzing kinematics, dynamics, settling time, smoothness of motion, and precision of positioning systems, as well as sizing linear motors, amplifiers, and structures.

The requirements. There are many different configurations that can be used to provide a required motion profile. For each configuration, such as gantry, split axes or compounded axes, various component types can be selected for the controllers, amplifiers, motors, actuators, stages, structures, and feedback devices. Typical performance specifications for a positioning system, as shown above, are:

The objective of Bimo is to analyze high performance positioning systems with motion requirements such as listed above. It uses a simplified servo control model for the linear motor positioning system. The controller provides a low power output signal to the servo amplifier. The servo amplifier in turn amplifies the signal and drives a linear motor, which applies a direct force on the stage. The stage, in turn, accelerates and moves the flexible structure to the desired position. The encoder feedback device mounts to the flexible structure.

Frequency response analysis. The analysis starts by considering the frequency response of the system. It provides the means to study the effects of component parameters on the overall system stability and bandwidth. System bandwidth is defined as the maximum frequency that the system can follow with a minimal error of -3dB.

The purpose of frequency response analysis, is to help understand the motion characteristic of each component in the positioning system, as well as the characteristics of the system as a whole. The frequency in the plots is displayed in logarithmic scale; for example, 1 represents 10¹ rad/sec, 2 represents 10² = 100 rad/sec, etc. The analysis is important in determining the closed loop bandwidth of the system, and its stability.

The closed loop bandwidth of the positioning system is about 2 Hz (12 rad/sec, between 10¹ and 10² in the chart). The phase margin is about 30 degrees (between -150 and -180 degrees) and the gain margin is a few dB, indicating a low performance, marginally stable system. The characteristics of the PID (proportional-integral differential), motor/actuator and the structure are noticeable in the overall plot.

In order to study the effect of component parameters on system bandwidth, to yield higher system performance, parameters such as gain, and natural frequency, can quickly be modified. The results indicate an improved performance and stability with 100 Hz bandwidth and a phase angle of about 80 degrees.

Time response analysis. While frequency response analysis considers the effects of component parameters on the closed loop bandwidth and stability of the system in frequency domains, simulations are often used in analyzing complex system performance in time domains. The following example demonstrates Bimo in simulating dynamic settling time and smoothness of motion.

The dynamics analysis assists in finding the required motor forces, needed to drive the positioning system in a motion profile, which was selected in the kinematics phase. It also determines the settling time and settling distance, at the end of the acceleration phase, needed to reach constant velocity, as well as the settling time at the end of the deceleration phase, needed to reach the desired accuracy. Finally, the model provides the structural natural frequency and its stiffness, which are required to meet the desired closed-loop bandwidth. These values can be used as a guideline for a finite element analysis design of the machine structure. The results of the dynamic analysis are then carried over to motor/amplifier sizing.

After sizing each positioning stage individually, a precision analysis of the assembled machine is conducted.