Digital Feedback Control System Research Articles

Compact and efficient radio frequency digital feedback control system for accelerator applications

The digital feedback (DFB) setup employed in a low-level radio frequency (LLRF) control system is crucial to ensure RF field stability in accelerating cavities, thus guaranteeing successful operation. To this end, a novel in-house and multi-purpose prototype DFB setup was developed for multiple applications at the Japan Proton Accelerator Research Complex (J-PARC). Being efficient, low-cost, and compact is key to achieving a cost-effective system that fulfills the performance specifications. It also reduces the production and maintenance costs of future DFB setups. A field-programmable gate array (FPGA)-based design with a digital signal processing (DSP) function uses an analog in-phase/quadrature-phase (I/Q) demodulator for RF-to-baseband signal conversion and an I/Q modulator to generate RF power. This arrangement compensates for RF phase fluctuations and amplitude modulations by employing a proportional and integral (PI) feedback controller. In addition, systematic errors are minimized by applying a hardware-error-compensation process. The system was utilized to conduct high-power tests on the interdigital H-mode drift-tube linac (IH-DTL) cavity of a muon linac for short RF pulses. The setup was also tested on a buncher cavity (Buncher-2) in the J-PARC linac, achieving efficient performance for longer RF pulses. The stability of the RF accelerating field in the IH-DTL was achieved at ±0.25% peak-to-peak (pp) in amplitude and ±0.36 degree pp in phase. For the Buncher-2, the amplitude stability of ±0.18% pp and phase stability of ±0.13 degree pp were obtained. Therefore, this DFB setup can be used to conduct high-power tests of RF cavities and klystrons. This study discusses the design aspects of a cost-effective DFB system and reports high-power measurements.

Development of an L-band rapid scan EPR digital console.

The development of a digital console for in-vivo rapid scan electron paramagnetic resonance (RS-EPR) spectroscopy and imaging is described in detail. The console was build using field programmable gate array (FGPA) technology that permits real-time control of the resonator and scanning magnetic fields during the measurements. Automatic resonator tuning and matching are achieved by implementing a digital feedback control system and using voltage-tunable capacitors. A band-pass subsampling method is used to directly digitize EPR signals at the carrier frequencies of about 1.2 GHz. The magnetic field scan waveforms, excitation EPR frequency, and sampling clock are all internally synchronized. Full-cycle RS-EPR signals are accumulated in the FPGA in real time without any time gaps. The result is the elimination of the re-arm time, during which data are not acquired. The proposed design in this manuscript has a small footprint and is relatively low cost. The FPGA-based RS-EPR system was tested using standard LiNc-BuO and tempone-d16 samples. The RS-EPR linewidth of the LiNc-BuO sample was consistent with an independent pulsed EPR measurement.

A digital feedback control and real-time monitoring system of PF coil power supplies for HL-2A

An upgrade to the magnet power digital feedback system (DFS) for the real time control of the PF coil power supplies is currently being developed and commissioned in HL-2A. The system aims to perform higher control resolution, more stable control cycle, real time monitoring and protection. The DFS has been shown to have better performance than the existing system in the control of the PF coil power supplies. It can control effectively all the PF coil power supplies, including the ohmic heating power supply (OHPS), vertical field power supply (VFPS), radial field power supply (RFPS) and the divertor coil power supply (DCPS). Meanwhile, the high-speed data transmission with reflective memory is used to transfer the control parameters of the PF coil power supplies. Moreover, the DFS also provides the real time monitor and protection based on the experimental physics and industrial control system (EPICS).

Stability of digital feedback control systems

Specific problems arising, when Von Neumann type computer is used as feedback element, are considered. It is shown, that due to specifics of operation this element introduce pure lag into control loop, and lag time depends on complexity of algorithm of control. Method of evaluation of runtime between reading data from sensors of object under control and write out data to actuator based on the theory of semi- Markov process is proposed. Formulae for time characteristics estimation are obtained. Lag time characteristics are used for investigation of stability of linear systems. Digital PID controller is divided onto linear part, which is realized with a soft and pure lag unit, which is realized with both hardware and software. With use notions amplitude and phase margins, condition for stability of system functioning are obtained. Theoretical results are confirm with computer experiment carried out on the third-order system.

Real-time digital signal recovery for a multi-pole low-pass transfer function system.

In order to solve the problems of waveform distortion and signal delay by many physical and electrical systems with multi-pole linear low-pass transfer characteristics, a simple digital-signal-processing (DSP)-based method of real-time recovery of the original source waveform from the distorted output waveform is proposed. A mathematical analysis on the convolution kernel representation of the single-pole low-pass transfer function shows that the original source waveform can be accurately recovered in real time using a particular moving average algorithm applied on the input stream of the distorted waveform, which can also significantly reduce the overall delay time constant. This method is generalized for multi-pole low-pass systems and has noise characteristics of the inverse of the low-pass filter characteristics. This method can be applied to most sensors and amplifiers operating close to their frequency response limits to improve the overall performance of data acquisition systems and digital feedback control systems.

RF phase stability in the 100-MeV proton linac operation

The 100-MeV proton linac of the Korea multi-purpose accelerator complex (KOMAC) has been operated to provide a proton beam to users. The 100-MeV linac consists of a 3-MeV radio-frequency quadrupole accelerator (RFQ), four 20-MeV drift-tube linac (DTL) tanks, two medium-energy beam-transmitter (MEBT) tanks, and seven 100-MeV DTL tanks. The requirements of the field stability are within ±1% in RF amplitude and ±1 degree in RF phase. The RF phase stability is influenced by a RF reference line, RF transmission lines, and a RF control system. The RF reference signal is chosen to be a 300-MHz local oscillator (LO) signal, and a rigid copper coaxial line with temperature control was installed for an RF reference distribution. A phase stability of ±0.1 degrees was measured under a temperature change of ±0.1 °C. A digital feedback control system with a field-programmable gate-array (FPGA) module was adopted for a high RF stability. The RF phase was maintained within ±0.1 degrees with a dummy cavity and was within ±0.3 degrees at RFQ operation. In the case of the 20-MeV DTL tanks, one klystron drives 4 tanks, and the input phases of 4 tanks were designed to be in phase. The input phases of 4 tanks were fixed within ±1 degree by adjusting a phase shifter in each waveguide.

Distributed digital real-time control system for TCV tokamak

A new digital feedback control system (named the SCD “Système de Contrôle Distribué”) has been developed, integrated and used successfully to control TCV (Tokamak à Configuration Variable) plasmas. The system is designed to be modular, distributed, and scalable, accommodating hundreds of diagnostic inputs and actuator outputs. With many more inputs and outputs available than previously possible, it offers the possibility to design advanced control algorithms with better knowledge of the plasma state and to coherently control all TCV actuators, including poloidal field (PF) coils, gas valves, the gyrotron powers and launcher angles of the electron cyclotron heating and current drive system (ECRH/ECCD) together with diagnostic triggering signals. The system consists of multiple nodes; each is a customised Linux desktop or embedded PC which may have local ADC and DAC cards. Each node is also connected to a memory network (reflective memory) providing a reliable, deterministic method of sharing memory between all nodes. Control algorithms are programmed as block diagrams in Matlab-Simulink providing a powerful environment for modelling and control design. The C code is generated automatically from the Simulink block diagram and compiled, with the Simulink Embedded Coder (SEC, formerly Real-Time Workshop Embedded Coder), into a Linux shared library (“.so” file) and distributed to target nodes in the discharge preparation phase. During the TCV discharge, an application on each node is executed that dynamically loads the shared library at runtime. In order to obtain reliable and reproducible real time execution of the algorithm, all interrupts to the CPU on each node are suspended just before firing the shot and re-enabled afterwards. Since installation, the new digital control system has been used for a multitude of plasma control applications, ranging from basic experiments of coil current and density control to advanced experiments of MHD (magnetohydrodynamics) and plasma profile control, as well as real-time plasma transport simulations. Recently, a real-time version of a plasma equilibrium reconstruction code was developed and implemented, providing the future possibility to control the plasma shape and profiles directly during the discharge evolution. This paper presents the architecture of the new control system, its integration into the TCV plant and a sample of control applications used for TCV plasma discharges.

IMPLEMENTATION OF FPGA BASED DA-PID CONTROLLER FOR TEMPERATURE SYSTEM

In this paper, modular design of embedded feedback controllers using the Field Programmable Gate Array (FPGA) technology is presented. To this end, a novel Distributed Arithmetic (DA)-based Proportional Integral Derivative (PID) controller algorithm is implemented and integrated into a digital feedback control system. The DA-based PID controller savings 80% hardware utilization to the multiplier-based scheme. It also offers good closed-loop performance while using less resource, resulting in cost reduction, high speed, and low power consumption, which is desirable in embedded control applications. The complete digital control system is built using commercial FPGAs to control a simple temperature loop.

A Spool Displacement Control System of Proportional Valve Based on Digital Observer

To solve the problems that general proportional valve can’t meet the requirements of high precision control, the paper describes the generation mechanism of kinetic energy in the accurate spool displacement control system of the small flow rate proportional valve. The mechanism of kinetic energy and displacement control of spool under disturbance are discussed quantitatively. Based on DSP and the mathematical model established, the digital state observer feedback control system is designed. The experiment shows that the system can restrain disturbance effectively, and the control accuracy of spool displacement is high, which is up to the level of 5μm.

Smith predictor in digital feedback control systems

This paper continues the issue of improving automatic feedback control systems as one of the most important complexes in automated industrial process control systems (AIPCS). It is experimentally verified that Smith predictor represents an efficient tool to improve performance of delayed objects and high-order objects. Principles of operation and adjustment are described for the controller operating on the basis of the predictor. Digital controllers are demonstrated well-adapted for embedding the option of Smith predictor. Experimentally tested versions of the predictor's program realization are suggested for the programmable controllers and PID controllers of industrial application.

Digital real-time control for an ICRF fast ferrite tuning system on Alcator C-Mod

A double-stub fast ferrite tuning (FFT) system has been developed and installed on the Alcator C-Mod tokamak for real-time ion cyclotron range of frequencies (ICRF) antenna matching. The FFT uses a digital feedback control system consisting of a Linux server, a compact PCI digitizer and MDSplus interface. The software is written in IDL, and runs with interrupts disabled. During a plasma discharge, the computer records the forward RF power, reflected power, and phase data on both the antenna side and the transmitter side of the tuning system, calculates the required magnetic coil currents in the ferrite tuners to minimize the reflected power to the antenna, and sends out the current demands in each computation cycle. The FFT system has been demonstrated to achieve good matching to antenna loading in low confinement modes (L-mode), high confinement modes (H-mode), and plasmas with edge-localized modes (ELMs) in Alcator C-Mod.

Design and Implementation of Modular FPGA-Based PID Controllers

In this paper, modular design of embedded feedback controllers using field-programmable gate array (FPGA) technology is studied. To this end, a novel distributed-arithmetic (DA)-based proportional-integral-derivative (PID) controller algorithm is proposed and integrated into a digital feedback control system. The DA-based PID controller demonstrates 80% savings in hardware utilization and 40% savings in power consumption compared to the multiplier-based scheme. It also offers good closed-loop performance while using less resources, resulting in cost reduction, high speed, and low power consumption, which is desirable in embedded control applications. The complete digital control system is built using commercial FPGAs to demonstrate the efficiency. The design uses a modular approach, so that some modules can be reused in other applications. These reusable modules can be ported into Matlab/Simulink as Simulink blocks for hardware/software cosimulation or integrated into a larger design in the Matlab/Simulink environment to allow for rapid prototyping applications.

Floating quantization effects on multirate sampled-data% nonlinear control systems

In this article, floating quantization effects on multirate sampled-data control systems are studied. It shows that the solutions of multirate digital feedback control systems with nonlinear plant and with floating quantization in the controller are uniformly ultimately bounded if the associated linear systems consisting of linearization of the plant and controller with no quantization are Schur stable. Moreover, it also shows that the difference between the response of multirate digital controllers without quantizers and the same plant with floating quantization in the controllers can be made as small as desired by selecting proper quantization level.

Digital closed-loop nanopositioning using rectilinear flexure stage and laser interferometry

To enhance the accuracy of nanopositioning and the metrological capability of scanning probe microscopy, we construct a two-dimensional interferometric nanopositioning system consisting of rectilinear flexure stage, calibrated laser interferometer, and digital feedback control system. We implement a correlation matrix, determined by the piezoelectric constant and the crosstalk between two axes, into the closed-loop control algorithm to compensate the nonlinearity and the crosstalk of the PZT-driven stage. In the tests on nanopositioning, the 1-nm-step motion and the tracking along a 1-nm-radius circular target path are accomplished to verify the short-term repeatability and the subnanometer-level precision. Additionally, a scanning tunneling microscope equipped with the interferometric nanopositioning system is built up to demonstrate the metrological functions of scanning probe microscopy.

Sparse controller realisation with small roundoff noise

The effect of roundoff noise in a digital controller is analysed for a digital feedback control system. An analytical expression for the roundoff noise gain, defined as the ratio between the variances of the output error and the rounding error, is obtained. The problem of identifying the minimum roundoff noise realisations can be solved using an existing procedure. Noting that the optimal realisations are fully parametrised, based on a polynomial operator approach a new sparse controller realisation is derived. This realisation is a generalisation of the direct forms in the classical shift operator and the prevailing delta-operator. It provides more degrees of freedom with which to reduce the roundoff noise. The problem of finding optimal polynomial operators can be solved by an exhaustive search, and a design example is given. It is shown that with the proposed sparse realisation the optimal polynomial operators can outperform the shift- and delta-operators.

Moment stability of discontinuous stochastic dynamical systems

In this note, we establish new Lyapunov and Lagrange stability results in the pth mean for a class of discontinuous stochastic dynamical systems. We apply these results in the qualitative analysis of a class of digital feedback control systems that are subjected to multiplicative and additive disturbances in the plants. The present results constitute natural extensions of our earlier results for discontinuous deterministic dynamical systems.

Stability analysis of digital feedback control systems with time-varying sampling periods

We consider digital feedback control systems with time-varying sampling periods consisting of an interconnection of a continuous-time nonlinear plant (described by systems of first-order ordinary differential equations), a nonlinear digital controller (described by systems of first-order ordinary difference equations), and appropriate interface elements between the plant and controller (A/D and D/A converters). For such systems we study the stability properties of an equilibrium (in the Lyapunov sense) and derive some results for local stability and instability via a linearization approach. These results are then used in the analysis of certain classes of switched systems and in the stabilization problem of nonlinear cascade control systems via hybrid feedback controllers.

Robustness analysis of digital feedback control systems with time-varying sampling periods

In the present paper, we study robustness properties of a class of digital feedback control systems with time-varying sampling periods consisting of an interconnection of a continuous-time nonlinear plant (described by systems of first-order ordinary differential equations), a nonlinear digital controller (described by systems of first-order ordinary difference equations), and appropriate interface elements between the plant and controller (A/D and D/A converters). For such systems, we establish results for exponential stability of an equilibrium (in the Lyapunov sense) in the presence of vanishing perturbations and for the boundedness of solutions (i.e., Lagrange stability) under the influence of nonvanishing perturbations. We apply these results in the study of quantization effects.

Some qualitative properties of multirate digital control systems

The authors consider multirate digital control systems which consist of an interconnection of a continuous-time nonlinear plant (described by ordinary differential equations), a digital controller (described by ordinary difference equations) which has quantizers (but is otherwise linear), along with the required interface elements (A/D and D/A converters). The input to the digital controller consists of the multirate sampled output of the plant. In the present paper, the authors show that when quantizer nonlinearities are neglected, then under reasonable conditions (which exclude the critical cases), the stability properties (in the Lyapunov sense) of the trivial solution of a nonlinear multirate digital control system can be deduced from the stability properties of the trivial solution of its linearization. For such systems we also present a result concerning the existence and construction of stabilizing multirate-output digital controllers. In the present paper, the authors also show that the solutions of a multirate digital feedback control system with nonlinear plant and quantizers are uniformly ultimately bounded if the trivial solution of the corresponding linear system consisting of the linearization of the plant and with the quantization removed from the digital controller is asymptotically stable. We also provide a result which compares the response of multirate digital control systems with nonlinear plant and quantizers in the controller with the response of the corresponding nonlinear multirate digital control systems without quantizers in the digital controller.

Analysis of sensitivity measures of finite-precision digital controller structures with closed-loop stability bounds

The problem of digital controller structures and the effect of finite-word-length (FWL) implementation on the closed-loop stability of digital feedback control systems is addressed. A framework is presented to derive two lower stability bounds for a closed-loop system, which are controller structure dependent, and then to solve the optimal FWL controller structure problem by maximising one of these lower bounds. This yields an improved method to design optimal finite-precision controller structures with better numerical accuracy and closed-loop stability characteristics. Comparisons using numerical examples from two digital controller structures demonstrate that the procedure proposed for the more efficient measure yields an improved finite controller realisation with combined lower bits and higher lower stability bounds.