Control Engineering

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What’s so great about mechatronics?
July 23, 2007

Mechatronics is generally defined as the convergence of mechanical, control and computer disciplines. This convergence creates a number of synergies. Tim Dehne, vice president for R&D at National Instruments, for example, points out that mechatronics shortens the system design process by allowing mechanical, electrical, control, and software engineering tasks to run concurrently instead of serially. Razvan Panaitescu, consulting engineer for mechatronic support and R&D at Siemens Energy and Automation, [www.sea.siemens.com] says mechatronics also makes it possible to diagnose problems in existing systems that defy analysis by any of the disciplines separately.
A simple, and not at all unusual, problem suggested by Panaitescu illustrates both advantages. The system’s job is to automatically slew a mechanical load (such as a radar antenna) to a target direction in the least amount of time.

A system containing a rotating load, shaft, and motor, with the motor armature’s moment of inertia matched to the load forms a symmetrical balanced double torsion pendulum.

In the non-mechatronic world, a mechanical engineer would design the load, bearings and shaft, then “toss it over the wall” to a control system designer. The controls engineer would then select a servomotor with an armature moment of inertia more or less equal to the load moment of inertia, and lots of torque to move the load as quickly as possible; then design a loop with at least two bit (forward/reverse and on/off) control based on feedback from the servomotor’s internal encoder. Then, technicians in the company’s model shop would build a prototype.
When completed, the prototype dutifully drives the load to the target orientation, but instead of stopping, it oscillates back and forth around the target angle.
What happened is, by (correctly) matching the motor armature moment of inertia to that of the load, the control engineer set up a classic symmetrical double torsion pendulum with the motor armature on one end, the load at the other, and the shaft in the middle. To understand the situation, it is necessary to set up and solve the pendulum’s equation of motion and to recognize that, although the controls engineer wants to control angles, all the system can do is provide torques.
Setting up and solving the equation of motion is beyond the scope of this blog entry, but I can show the result:

[1]

, where the subscripts 0 and 1 refer to measurements at the armature and load respectively, and 
θ is the orientation angle;
I is the moment of inertia;
s is the shaft stiffness; and
M is the motor torque.
Look for a more complete analysis in the Mechatronics Supplement to the September 2007 issue of Control Engineering.
We start with the homogeneous equation, where M = 0, which has two solutions:

[2]

The first solution is actually the one we want, because it has the two ends of the shaft moving in unison. Unfortunately, the control system excites the second as well. This is a mode where the armature and the load rotate back and forth by equal amounts 180° out of phase. That is, while one rotates in a positive sense, the other rotates in a negative sense. Together, they twist the shaft until its restoring force slows and stops the two masses and forces them to rotate back the other way, unwinding the shaft twist, then twisting it up again.
Now, let’s see what happens when we turn on the control system so it can apply torque according to the two-bit control algorithm. This is the inhomogeneous equation, where M is not zero.
At first, the control system applies maximum torque to move the armature toward the target angle. The armature accelerates in that sense, storing energy in shaft twist. When the armature reaches the target angle, however, the motor torque switches off and the armature coasts on past. Meanwhile, the shaft twist has begun applying torque to the load, accelerating it toward the target angle. When the armature gets past the target angle, the control system begins applying motor torque in the reverse sense to move it back toward the target. When the armature again passes the target angle, the load is moving rapidly past the target angle in the forward direction. The shaft starts to twist up in the opposite sense, and the process starts again. At each oscillation, the motor adds energy into the mode until something happens to disrupt the motion. Often that something is a broken shaft.
In a mechatronic environment, setting up and solving the equations of motion and testing control solutions can be done in computer simulation, transparent to all engineering-team members. For a new design, this allows fine-tuning the design before any prototypes are built, and even before the specifications are finalized. For a problematical existing design, mechatronics allows analyzing the as-built system to uncover wayward interactions between the mechanics and controls. In either case, problems easily are solved that leave engineers in traditional environments scratching their heads.

Posted by Charlie Masi on July 23, 2007 | Comments (0)