Feedback loops are key elements to the control of a system's behavior, and are used in a variety of areas including optics and photonics, nanotechnology and materials science, quantum technologies, scanning probe microscopy, and sensing. Taking advantage of closed-loop operation makes it possible to accelerate transient processes, reduce the impact of disturbances on the system and tune its steady-state behavior.
The PID controller first compares the system's output with a user-defined setpoint and generates an error signal. It then tries to minimize this error signal by adjusting its output, which in turn drives the system. This driving signal is obtained by adding three terms calculated separately from the error signal: the terms are referred to as proportional (P), integral (I) and derivative (D), and each has its own gain.
PID Controllers for Lock-in Amplifiers
Zurich Instruments offers PID controllers exclusively as upgrade options for lock-in amplifiers, impedance analyzers and boxcar averagers. Consequently, a number of different inputs can be chosen for the PIDs: the set of choices includes amplitude, phase, quadrature and in-phase components of demodulated signals, boxcar outputs, as well as auxiliary inputs and outputs. Integrated digital signal processing guarantees maximum signal-to-noise ratio, minimal feedback loop latency and closed-loop operation with high stability. Even tiny signals can be located in a noisy and spurious-rich background and used as reliable inputs. The feedback signal is then available as an analog output and can also be directly applied to an internal frequency generator output to control its amplitude, frequency, offset and phase.
Characterizing and setting up new control loops is straightforward with the LabOne® software. The available parametric sweeper, oscilloscope and other data acquisition tools make it easy for users to understand the specifics of a system in the time and frequency domains. Further, the PID Advisor offers a number of predefined model functions that can be used to derive an initial set of PID parameters that can be refined manually at a later time, e.g. based on recorded step responses to be compared to the model provided by the PID Advisor. Alternatively, the Auto Tune routine varies P, I and D automatically to minimize the residual error.
In many cases, introducing a D-gain offers the potential to speed up the loop's response. However, this often leads to instability because it introduces increasing gains towards high frequencies. Introducing an adjustable low-pass filter in the D-branch helps take advantage of the D-gain without running into instabilities.
Phase detection facilitated by a lock-in amplifier is usually limited by the arct2(y/x) function to the value range ±π. In turn, this limits the 'capture range' of the PID as well as the stability of operation in the presence of external noise. In the digital domain, this limitation can be overcome thanks to a 'phase unwrap' functionality that detects instances where phase detection exceeds its limits and keeps track of this behaviour accordingly. Zurich Instruments' PIDs support a 'capture range' that extends up to ±1024π.
- The broad choice of PID input and output signals and the fully configurable PID controllers afford the flexibility to design and maintain closed-loop control under a wide range of conditions without the need for additional instruments. Switching from one to another controller as the need arises is not a problem.
- Multiple PID controllers can run simultaneously within the same instrument, thus enabling advanced feedback loops while keeping setup complexity at bay.
- The PID Advisor allows users to model their setup and calculate sensible starting parameters. It is then possible to optimize further those PID parameters thanks to the Auto Tune routine and minimize the residual PID error.
- The LabOne toolset including Scope, Spectrum Analyzer, Sweeper and Plotter facilitates an integrated analysis and monitoring of the locking quality. For instance, it is possible to visualize the PID error as a histogram to spot deviations from a Gaussian distribution, which may indicate that something in the setup does not work as expected.