Methods to Improve Piezo Dynamics, Accuracy and Linearity: Preshaping / DDL / APC

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Piezoelectric materials, like most electro-ceramics, do not show perfectly linear displacement behavior compared to the input voltage. Closed-loop operation with position feedback usually takes care of the nonlinearities.  Although perfect settling to the desired position is achieved to nanometric scale in positioning operation, the deviation in dynamic continuous motion operation can in some cases be considerable. For high-dynamics applications, bandwidth limitations of the controller and the piezo mechanism can be limiting factors. Several control methods are now available in commercially available controllers to significantly increase dynamic accuracy, linearity while reducing phase errors.  Simple methods, such as feedforward, can only reduce the phase difference control input signal and motion output.

Signal Preshaping, Phase 1
Signal Preshaping, Phase 1

Signal Preshaping

Signal Preshaping, a patented technique, can reduce rolloff, phase error, and hysteresis in applications with repetitive (periodic) inputs. Signal Preshaping is implemented in object code, based on an analytical approach in which the complex transfer function of the system is calculated, then mathematically transformed and applied in a feedforward manner to reduce the tracking error.  Signal Preshaping is not to be confused with phase-shifting approaches and can improve the effective bandwidth up to 10 times and more, especially in tracking applications such as precision, particularly in precision contouring (out-of-round finishes) of mechanical and optical parts. With this technique, it is possible to increase the command rate for a piezomechanism with a natural frequency of 400Hz from 20Hz to 200Hz without compromising stability. At the same time, the tracking error is reduced by 50 fold.

Signal Preshaping, Phase 2
Signal Preshaping, Phase 2

The technique is based on Fast Fourier Transformation (FFT) and external metrology. Frequency response and harmonics (caused by material nonlinearities) are determined in two steps. The data gathered by FFT are then applied to the original control signal to calculate the new, modified control signal. This new, pre-distorted control signal and the nonlinearty from the piezo material cancel each other out, resulting in a very linear response.

Piezo_Mechanism_wo_preshaping
Piezo Mechanism Without Input Preshaping
A: Control input signal (target position)
B: Actual motion output at positioning system
C: Tracking error

 

Signal After Preshaping Phase 2 A: Target motion (old control signal) B: Actual motion output C: New control input (calculated by preshaping) D: Tracking error
Signal After Preshaping Phase 2
A: Target motion (old control signal)
B: Actual motion output
C: New control input (calculated by preshaping)
D: Tracking error

The Simple Integrated Solution: Dynamic Digital Linearization (DDL)

DDL is similar in performance to Input Preshaping, but requires no external metrology; instead it is embedded inside the firmware of the digital piezo motion controller (such as PI’s E-712). In addition, it can optimize multi-axis motion such as XY raster scans or tracing of shapes such as circles or ellipses. Learn more on digital vs. analog piezo controllers.

DDL significantly improves the performance for applications with periodic signals, where conventional piezo controllers cannot completely avoid phase-shift and tracking errors for higher frequency motion. This is caused by the limited control bandwidth of the servo system, the non-linear nature of the piezoelectric material, and the inherent limitations of PID (pro-Portional Integral Derivative) servo- control, which is reactive by nature, feeding off errors.

DDL works for periodic signals and uses the position information available from the highly linear capacitive position feedback sensors integrated in the piezo mechanism to calculate the optimum control signal. As with Signal Preshaping, the result is an improvement in linearity and tracking accuracy of up to three orders of magnitude (see graphs).

Piezo nanopositioning systems with conventional PID controller: Single axis movement with a 312 Hz triangular signal. The difference between target and actual position can be up to 2.6 µm.
Piezo nanopositioning systems with conventional PID controller: Single axis movement with a 312 Hz triangular signal. The difference between target and actual position can be up to 2.6 µm.

Elliptical scan with a XY piezo scanner and conventional P-I-servo controller. The outer curve shows the desired position, the inner curve shows the actual motion.
Elliptical scan with a XY piezo scanner and conventional P-I-servo controller. The outer curve shows the desired position, the inner curve shows the actual motion.

Piezo nanopositioning system with DDL control: Same single axis movement as above, with 312 Hz triangular signal. The deviation from the ideal curve (difference between target position and actual position) is only 7 nanometers, too close to see in this graph.
Piezo nanopositioning system with DDL control: Same single axis movement as above, with 312 Hz triangular signal. The deviation from the ideal curve (difference between target position and actual position) is only 7 nanometers, too close to see in this graph.

The elliptical same scan as before but with DDL control. The tracking error is reduced to a few nanometers, target position and actual position cannot be distinguished in the graph
The elliptical same scan as before but with DDL control. The tracking error is reduced to a few nanometers, target position and actual position cannot be distinguished in the graph.

APC: Advanced Piezo Control: Advanced Algorithm for Faster Settling

Performance comparison of Advanced Piezo Control (pink) and PID algorithm (blue) in digital piezo controller for a 60 µm transient response of a piezo positioning system. The APC algorithm shows significantly faster settling time.
Performance comparison of Advanced Piezo Control (pink) and PID algorithm (blue) in digital piezo controller for a 60 µm transient response of a piezo positioning system. The APC algorithm shows significantly faster settling time.

Advanced Piezo Control is an alternative closed loop algorithm based on a state controller which is, in turn, modelled on the positioning system.  While conventional PID / notch filter concepts “cut” the mechanical resonance out of the excitation spectrum, APC actively damps these unwanted resonant frequencies.

The result is higher stability, faster settling, and lower sensitivity to external disturbances. In addition, there is significantly less phase shift compared to the damping based on one or multiple notch filters with positive effects on the trajectory trueness and the settling response.

APC provides most benefits over PID algorithms for mechanical systems with resonant frequencies below 1 kHz.  It also has limitations when in the case of multiple, closely spaced resonances.

bode_plot
(Left) Bode plot of an open loop piezo positioning system with two resonance frequencies. (Center) Bode plot of a closed loop piezo positioning system with one notch filter set to the first resonance. (Right) Bode plot of a piezo system controlled with APC. The resonances are suppressed better, and the phase deviation is lower compared to the system based on PID + notch filter.

Higher Dynamics with Energy Recovery Driver Design

Most drive electronics for piezo actuators are based on linear amplifiers or charge amplifiers. For industrial 24/7 high dynamics applications, driving large capacitance actuators, the energy consumption can be a factor to be considered. With typical periodic dynamic applications and linear amplifiers, the energy to charge and discharge a piezo actuator is lost after each cycle – actually it is turned into heat that needs to be dissipated.

A new patented amplifier design with an energy recovery circuit is available with standard drivers covering up to 6KVA. The system is based on a combination of PWM (pulse width modulation) where the pulse width of the drive voltage is modulated and the relatively large piezo capacitance smoothes out the signal. In addition, a patented circuit for energy recovery is also integrated. It stores a portion of the returned energy when the piezo discharges in a capacitor, making it available for next charging cycle. The result is significantly higher efficiency with energy savings up to 80%.

Weight savings in the amplifier and significant reduction in the amplifiers heat dissipation are additional benefits. In contrast to conventional switched amplifiers (Class D), the new patented energy recovery piezo amplifier is run in both current and voltage control mode.

This is critical for applications in the field of active vibration control.

Additional Temperature Monitor to Protect the Piezo Mechanisms

The energy loss in static piezo operation is negligible. In continuous dynamic operation, especially with powerful drivers, it is recommended to monitor the temperature of the piezo mechanism.  Integrated sensors are available to hook up to the driver and shut it down when a preset threshold is exceeded.

Comparison of linear piezo driver and switched energy recovery amplifier. For the same output power, PI’s patented consume only around 20% of the power consumed by a corresponding conventional amplifier.
Comparison of linear piezo driver and switched energy recovery amplifier. For the same output power, PI’s patented consume only around 20% of the power consumed by a corresponding conventional amplifier.

 

Measured power consumption of a linear piezo driver and switched energy recovery amplifier, driving a capacitive load of 1μF. Even with higher power consumption, the dynamic range of the linear amplifier is significantly lower than the switched amplifier
Measured power consumption of a linear piezo driver and switched energy recovery amplifier, driving a capacitive load of 1μF. Even with higher power consumption, the dynamic range of the linear amplifier is significantly lower than the switched amplifier

 

Block diagram of a PWM piezo amplifier with energy recovery circuit.
Block diagram of a PWM piezo amplifier with energy recovery circuit.

 

A high-power piezo amplifier with energy recovery, Model E-482
A high-power piezo amplifier with energy recovery, Model E-482
PDF Datasheet >

 

 

Applicable Patents: US Patent No. 6617754B1, German Patent No. 19825210C2, International Patent No. 1080502B1

> Piezo Controller Model Overview

> Digital Piezo Controller with Fast Track-Following Servo

> LEARN more about Low Cost Digital Piezo Controllers

> E-712 High-End Digital Controller Datasheet

> Nanopositioning Basics

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About PI

PI (Physik Instrumente) is a leading manufacturer of precision motion control equipment, piezo motors, air bearing stages and hexapod parallel-kinematics for semiconductor applications, photonics, bio-nano-technology and medical engineering. PI has been developing and manufacturing standard & custom precision products with piezoceramic and electromagnetic drives for 4 decades. The company has been ISO 9001 certified since 1994 and provides innovative, high-quality solutions for OEM and research. PI is present worldwide with fifteen subsidiaries, R&D / engineering on 3 continents and total staff of more than 1,000.

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