The Luenberg Observer lets motion-control systems mathematically predict and cancel position errors before they happen.

Steven Reese
Parker Hannifin Corp.
Automation Group
Cleveland, Ohio

For many years the standard means of controlling servoloops on motion controllers (or other devices) has been the PID loop. Back in the days of analog control the motion controller was typically a CNC device responsible for closing the proportional-gain (P) loop and, if used, the steady-state or integral gain ( I ) loop. A tachometer (tach) or speed loop was used in lieu of a derivative-gain (D) function. The closed position and speed loops configured by this type of cascaded control were common.

As processor technology advanced, it became routine for the motion controller to close all servoloops. This was based on the assumption that the fastest and most capable processor was on the controller. Technicians tuning these systems now had loops that were quicker or hotter than anything available previously. However, without a tach loop, the tuning technician had to compensate for stiction and friction. Experienced techs could tune out these impediments to accurate motion using the feed-forward for acceleration (FFACC) and feed-forward for velocity (FFV) settings.

Given the same mechanical system, the usual parameters limiting position loop accuracy were the bandwidth of the servoloop and the PWM frequency of the amplifier. Standard motion controllers can make changes on a multiaxis trajectory approximately every 500 µsec and on each servoloop in a fraction of that time depending on the number of axes. On the other hand, amplifiers can change their output no faster than one cycle of the PWM. With a 20-kHz amplifier, the fastest change in output current still takes 50 µsec creating a hard limit for any updates.

This means the amount of acceptable position error determines the maximum available speed. Motions that are too fast cannot be corrected quickly enough to avoid exceeding the error limits. The need for ultra accuracy requires slowing the motion so that a 50– µsec delay does not produce a gain break or nonlinear situation. Though tricks like an FFACC cutoff started to work their way into modern controllers, in practical terms the controllers have hit a wall for quicker and more accurate control. This is due in large part to the PWM bandwidth limits using a PID with FF control scheme.

Yet the market still needs controllers with quicker response times. In fact, controllers today must often deal with reflected inertia mismatches and lower mechanical and electrical time constants. This is primarily due to the relationship between low inertia and low impedance in today's linear and direct-drive rotary motors.

OBSERVER-BASED MOTION CONTROL
Because standard servosystems are error driven and therefore reactive, they suffer lag between the commanded and actual positions. What's needed is a way to anticipate and correct the error before it occurs. For example, by charting the errors that different acceleration commands produce, the controller could use an internal lookup table to anticipate the dynamic error for any given command. Error compensation could then be added directly to the current command of the controller canceling the error before it happens. The PID system would end up having little or no error to compensate.

Today's modern controllers have the processing power needed to map servo errors at the first (acceleration) and second (jerk) derivatives of speed. So they can solve not just acceleration errors but jerk errors like those created by friction and stiction. By adding offsets to the normal command, servoamplifiers like Parker's Compax3 can correct for many sources of resonance and other repeatable disturbances before the system actually triggers the disturbance.

The base assumption used by this new breed of amplifier is the Luenberg Observer. This type of control gets results that are six times more accurate than those of standard PID controls. Proactively chasing expected errors not only reduces errors in position but also stops resonances before they happen.

For example, a motor coupling winds up as it is accelerating and then, for a short time, overhauls the load as it unwinds. These changes are noted and mapped in the autotune sequence. Once mapped by the controller the low-frequency resonance never happens, nor does the error it would introduce.

Another application concerns an inertia mismatch between a linear motor and its load. That mismatch would be unacceptable with older controllers. At best it would produce large position errors at start and stop. Now that mismatch is acceptable. Its errors are controlled by mapping what happens and by dynamically introducing corrections.

Though quite technical, this type of control is easily implemented. There would be no further tuning necessary if the motion controller and amplifier were a single unit. With separate motion controllers and amplifiers, the cascaded PID control should only have to chase minor errors. Technicians should find its tuning to be easier than that of regular PID systems.

MAKE CONTACT
Parker Hannifin Corp. Automation Group,
(800) 272-7537,
parker.com/automation

Cascade Control For Current, Speed, and Position in a Torque Motor
Symbol
Definition
xw(t)
Setpoint position value
xD(t)
Control difference — position controller (tracking error)
nw(t)
Setpoint speed value
e(t)
Control difference — speed controller
iqw(t)
Setpoint torque-forming motor current
uq(t)
Voltage input signal
iq(t)
Torque-forming motor current
n(t)
Motor speed
x(t)
Motor position

The standard PID loop, shown here in block diagram, has been the principle servoloop-control method in motion and other systems for many years.