Magnetic Levitation

Feedback Loop Control Systems

What is a feedback loop control system anyway? And why do we care? What makes them unstable?

It is appropriate to review some general concepts of feedback loop control systems. This page explains what they are and why they are so great, and introduces terminology for subsequent pages on feedback loop stability.

Feedback Loop Control System

There are four elements in any feedback loop control system.

  1. Sensor of the position to be controlled
  2. Reference input that specifies the value the controlled variable should have
  3. Comparator that compares the actual sensed position, or feedback signal, with the desired position or reference signal. The output of the comparator is usually called an error signal, whose polarity determines which way a correction needs to be made.
  4. Control mechanism which is activated by the error signal and results in a correction of the position. This is often called an actuator.

In our levitator, the sensor is the optical device that measures the position (or lack) of the suspended object. The reference input is establish by another optical device to measure the ambient light. The comparator is an electrical device that subtracts and amplifies the two inputs. The control mechanism is the electromagnetic lifting coil.

Since the four elements just mentioned are all essential to closed loop systems, it follows that any scheme to control something that lacks one or more of these items is not a feedback control system. Thus, it is easy to examine many legislative programs and obvious why so many of them fail. It also follows, from looking at things in a general way, that nothing can be controlled by feedback unless it can be measured.

Benefits of Feedback

The desired position of the suspended object is the only intentional input to the system. But several other factors such as weight and gravity, power supplies, and air currents can affect the position. Such inputs, being unwanted, are often called disturbances. Since they are subject to nonlinear effects and unknown change with time, they are responsible for the impossibility of merely balancing the coil strength with the weight of the object. The main reason for feedback control is to measure and compensate for the effect of disturbances.

In other types of systems, feedback allows the apparent response speed of a component such as a motor can be increased by overdriving it when rapid response is needed. Still another reason to use feedback is to provide a stiff output, which means an output that is not susceptible to being changed by disturbances. And in other instances, it is desirable to have the output exactly proportional to the input, but the amplifiers and other components may not be perfectly linear. The use of feedback can greatly reduce nonlinearities in all other system components except the sensor used to provide the feedback signal. Finally, when systems are being mass-produced with inexpensive components that may have a considerable variation in values, feedback can greatly reduce the effect of differences between one unit and another.

Problems of Feedback

If all these benefits sound almost too good to be true, it is time for a reality check. Actually, they are true enough, but there is always the Dark side of the Force. There are two main costs:

  1. There is an increase in system complexity, which may increase component count. Sometimes this may be offset by the possibility of using cheaper components.
  2. Feedback introduces a stability problem, and this is much more serious. This problem is sufficiently troublesome that 90% of the pages on books about feedback are devoted to it.

By stability problem we mean a tendency to overcontrol, or overshoot, when the input or a disturbance is felt. Alternatively, when looking at the frequency response, the gain may rise near the upper end of the passband, which is usually undesireable. In an extreme case the gain can become high enough to cause oscillation, that is, a sustained cyclic response without any input. This effect generally renders the system useless or even destructive.

Causes of Instability

The stability problem is inevitable. It results from the fact that the feedback, which is connected so as to be negative at low frequencies, usually becomes positive at high frequencies. Good stability is usually possible provided the loop gain is low enough.

The main reason the feedback ultimately becomes positive as the frequency increases is that both the control system and the load it is driving contain components that can store energy. Capacitance and inductance are electrical energy storage elements, and mass and springs and raising an object against gravity are mechanical energy storage elements.

Since the drive to physical devices is not infinite, the response must dwindle toward zero as the frequency approaches infinity, with an associated phase shift approaching 90o. Several phase shifts can add up so that the total around the loop equals 360o, which is positive feedback. Only 180o of additional shift from the energy storage elements is needed to cause positive feedback, since the connection at the comparator introduces 180o to make the feedback negative at low frequencies.

Historical Perspective

Historically, the stability problem was first clearly recognized when centrifugal fly-ball governors were applied to early steam engines shortly after their invention around the middle of the eighteenth century. It was approximately another century before the first mathematical analysis of this problem was carried out by the eminent scientist James Clerk Maxwell. (He is far more widely known for his electromagnetic theory of light, which became known as "Maxwell's Equations".)

It was not until well into the twentieth century that Nyquist, Bode, and many others laid the foundations of modern control theory.

Additional Reading

Much of this information is better explained in "Feedback Loop Stability Analysis" by Walter Friauf, McGraw Hill, ©1998, ISBN 0-07-022844.

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