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NASA NTRS1987

Application of gain scheduling to the control of batch bioreactors

The implementation of control algorithms to batch bioreactors is often complicated by the inherent variations in process dynamics during the course of fermentation. Such a wide operating range may render the performance of fixed gain PID controllers unsatisfactory. In this work, a detailed study on the control of batch fermentation is performed. Furthermore, a simple batch controller design is proposed which incorporates the concept of gain-scheduling, a subclass of adaptive control, with oxygen uptake rate as an auxiliary variable. The control of oxygen tension in the biorector is used as a vehicle to convey the proposed idea, analysis and results. Simulation experiments indicate significant improvement in controller performance can be achieved by the proposed approach even in the presence of measurement noise.

Cardello, Ralph↗

DOE OSTI2021

Theoretical Control-Centric Modeling for Precision Model-Based Sliding Mode Control of a Hydraulic Artificial Muscle Actuator

Artificial muscles (AMs) typically rely on pneumatic sources of fluid power. The use of hydraulics can increase the power and force to weight and volume ratios of AM actuators. This paper develops a control-centric third-order single-input single-output (SISO) lumped-parameter dynamic model and sliding mode position controller based on Filippov's principle of equivalent dynamics for a braided hydraulic artificial muscle (HAM) actuator. The model predicts the nonlinear behavior of the HAM free contraction and captures the fluid and actuator nonlinear dynamic interactions in addition to the braid deformation. Model simulations are compared to experimental results for quasi-static pressurization, isometric pressurization, and open-loop square wave commands at 0.25, 0.5, and 1 Hz. Experiments of sine wave tracking at 0.25, 0.5, and 1 Hz and continuous square wave tracking at 0.067 Hz are conducted using a sliding mode controller (SMC) derived from the model. The SMC achieves a steady-state error of 6 μm at multiple setpoints within the actuator's 17 mm stroke. Compared to a proportional-integral-derivative (PID) controller, the SMC root-mean-square (RMS) error, mean error, and absolute maximum error are reduced on average by 53%, 61%, and 44%, respectively, demonstrating the benefit of model-based approaches for controlling HAMs.

42 ENGINEERING↗

DOE OSTI2023

Demonstrate FARM supervisory capabilities for a thermal energy storage problem for the DETAIL facility: IES Simulation Ecosystem Control System Development

The goal of the power dispatch problem for an Integrated Energy System (IES) is to adjust the power output and the heat flow of each component to maximize the profitability of the whole unit. Facilities that can integrate real-time digital signals, mock nuclear power, thermal energy storage and industrial heat use via high-temperature electrolysis were constructed at INL to support the research activities. The Dynamic Energy Technology and Integration Laboratory (DETAIL) houses the Microreactor Agile Non-nuclear Experimental Test Bed (MAGNET) and the Thermal Energy Distribution System (TEDS). In this report, the hierarchical control system architecture proposed in June 2023 milestone for the flexible operation of DETAIL facility is finalized and demonstrated. A brief description of the components and the corresponding Dymola models from the HYRBID repository is first provided. Then, the current control strategy is presented. In particular, the approach for generating the set-point trajectories to be fed to the PI controllers is analyzed, and its limits were identified. To preserve safe operation over both long-time and real-time horizons, the integration of a Supervisory Control layer embedding a modified version of FARM (Feasible Actuator Range Modifier) module is proposed. FARM is a component of the RAVEN-based FORCE framework designed to support HERON module at optimizing the operation of IES units. The proposed control system for DETAIL foresees FARM to be applied twice, i.e., the original version (“FARM-Validator”) aiding the solution of the power dispatch problem, and a modified version (“FARM-Supervisory”) coordinating the PID controllers. Despite the kernel of the two modules is the same, their tasks are quite different. The former intervenes at the beginning of each hour to prevent constraint violations over long time periods, the latter addresses real-time control tasks and monitors the response of constrained variables at a much finer time resolution. A tentative procedure for training the embedded Digital Twins with the experimental data is also proposed. Finally, the capabilities of the designed architecture and the impact of the added Supervisory Control layer are demonstrated by simulating a representative power dispatch scenario.

25 ENERGY STORAGE↗

NASA NTRS2002

A Comparison Study of Magnetic Bearing Controllers for a Fully Suspended Dynamic Spin Rig

NASA Glenn Research Center (GRC) has developed a fully suspended magnetic bearing system for the Dynamic Spin Rig (DSR) that is used to perform vibration tests of turbomachinery blades and components under spinning conditions in a vacuum. Two heteropolar radial magnetic bearings and a thrust bearing and the associated control system were integrated into the DSR to provide noncontact magnetic suspension and mechanical excitation of the 35 lb vertical rotor with blades to induce turbomachinery blade vibration. A simple proportional-integral-derivative (PID) controller with a special feature for multidirectional radial excitation worked very well to both support and shake the shaft with blades. However, more advanced controllers were developed and successfully tested to determine the optimal controller in terms of sensor and processing noise reduction, smaller rotor orbits, and energy savings for the system. The test results of a variety of controllers we demonstrated up to the rig's maximum allowable speed of 10,000 rpm are shown.

Choi, Benjamin↗

NASA NTRS2002

Implementation of Adaptive Digital Controllers on Programmable Logic Devices

Much has been made of the capabilities of FPGA's (Field Programmable Gate Arrays) in the hardware implementation of fast digital signal processing (DSP) functions. Such capability also makes and FPGA a suitable platform for the digital implementation of closed loop controllers. There are myriad advantages to utilizing an FPGA for discrete-time control functions which include the capability for reconfiguration when SRAM- based FPGA's are employed, fast parallel implementation of multiple control loops and implementations that can meet space level radiation tolerance in a compact form-factor. Other researchers have presented the notion that a second order digital filter with proportional-integral-derivative (PID) control functionality can be implemented in an FPGA. At Marshall Space Flight Center, the Control Electronics Group has been studying adaptive discrete-time control of motor driven actuator systems using digital signal processor (DSF) devices. Our goal is to create a fully digital, flight ready controller design that utilizes an FPGA for implementation of signal conditioning for control feedback signals, generation of commands to the controlled system, and hardware insertion of adaptive control algorithm approaches. While small form factor, commercial DSP devices are now available with event capture, data conversion, pulse width modulated outputs and communication peripherals, these devices are not currently available in designs and packages which meet space level radiation requirements. Meeting our goals requires alternative compact implementation of such functionality to withstand the harsh environment encountered on spacecraft. Radiation tolerant FPGA's are a feasible option for reaching these goals.

Gwaltney, David A.↗

NASA NTRS2015

Control System Design Implementation and Preliminary Demonstration for a Tendon-Actuated Lightweight In-Space MANipulator (TALISMAN)

Satellite servicing is a high priority task for NASA and the space industry, addressing the needs of a variety of missions, and potentially lowering the overall cost of missions through refurbishment and reuse. However, the ability to service satellites is severely limited by the lack of long reach manipulation capability and inability to launch new devices due the end of the Space Transport System, or Space Shuttle Program. This paper describes the design and implementation of a control system for a Tendon-Actuated Lightweight In-Space MANipulator (TALISMAN), including; defining the forward and inverse kinematics, endpoint velocity to motor velocity, required cable tensions, and a proportional-integral-derivative (PID) controller. The tensions and velocities necessary to maneuver and capture small and large payloads are also discussed. To demonstrate the utility of the TALISMAN for satellite servicing, this paper also describes a satellite servicing demonstration using two TALISMAN prototypes to grasp and inspect a satellite mockup. Potential avenues for improving the control system are discussed.

Komendera, Erik E.↗

DOE OSTI2022

Experimental testing of a control barrier function on an automated vehicle in live multi-lane traffic

This paper experimentally tests an implementation of a control barrier function (CBF) designed to guarantee a minimum time-gap in car following on an automated vehicle (AV) in live traffic, with a majority occurring on freeways. The CBF supervises a nominal unsafe PID controller on the AV’s velocity. The experimental testing spans two months of driving, of which 1.9 hours of data is collected in which the CBF and nominal controller are active. We find that violations of the guaranteed minimum time-gap are observed, as measured by the vehicle’s on-board radar unit. There are two distinct causes of the violations. First, in multi-lane traffic, Cut-ins from other vehicles represent external disturbances that can immediately violate the minimum guaranteed time gap provided by the CBF. When cut-ins occur, the CBF does eventually return the vehicle to a safe time gap. Second, even when cut-ins do not occur, system model inaccuracies (e.g., sensor error and delay, actuator error and delay) can lead to violations of the minimum time-gap. These violations are small relative to the violations that would have occurred using only the unsafe nominal control law.

99 GENERAL AND MISCELLANEOUS↗

NASA NTRSDate not supplied

Correlated Electromagnetic Levitation Actuator: A Reaction Sphere Based Attitude Control System

To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at NASA’s Marshall Space Flight Center have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. The probe also includes the ability to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL Finite Element Analysis and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller thatmitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.

controls↗

NASA NTRSDate not supplied

Correlated Electromagnetic Levitation Actuator: A Reaction Sphere-Based Attitude Control System

To address problems experienced by current reaction wheels and control moment gyroscopebased attitude control systems (ACS), researchers at National Aeronautics and Space Administration’s (NASA’s) Marshall Space Flight Center (MSFC) have begun developing a reaction sphere actuator based on correlated electromagnetic levitation that will be immune to destructive bearing friction, momentum saturation, and gimbal lock. The Correlated Electromagnetic Levitation Actuator (CELA) advances the state of the art of reaction sphere ACSs by employing the concept of correlated magnetics. It is a frictionless, direct-drive reaction sphere that harnesses a unique technology with an array of applications across multiple disciplines. Correlated electromagnets function in a manner that is analogous to a matched filter; the convolution of two signals is peaked at the index representing the greatest match. For CELA, the signals are the patterns of magnetic flux density as a function of position. The magnitude of the convolution equates to an attractive or repulsive force, and these forces can be azimuthal or radial. The development of CELA is based in four distinct disciplines: Advanced Manufacturing, Prototype Development, Electromagnetic Modeling, and Controls. We are developing novel manufacturing techniques required to build arrays of permanent and electromagnet dipoles on curved surfaces. To print the permanent magnetic array, we have developed a probe with pyramidal magnets that will reside on a robotic arm to induce localized magnetic fields on a surface. We have also used high temperature ovens to erase dipole patterns from a permanent magnet by heating the surface to its Curie temperature. A number of test articles and prototypes have been developed using additive manufacturing methods. These prototypes have included hemispherical motors to test the drive algorithm, and a levitation test bed that demonstrates a magnetic bearing method based on attractive magnetic forces and ratiometric Hall effect sensors. We developed an array of electromagnetic dipoles on a printed circuit board (PCB) with individual H-bridges controlling each coil. This device created various flux density patterns and we measured their magnetic fields using a custom Hall effect 3-D probe and a LabVIEW virtual instrument. These data will serve as a benchmark for characterizing the accuracy of future models. Current work is focused on modeling the magnetic fields of our prototype arrays using COMSOL finite element analysis (FEA) and verifying the model against our test data. Accurate modeling will allow us to quickly test new patterns of electromagnets and their macro behavior. Eventually, the magnetic field models will be implemented in our controls simulations to facilitate precise control of the reaction sphere. Initial model results agree with field measurements to within 1 G (5% of measured flux density). Currently, we are testing different material properties of the electromagnets and their magnetic fields and thermal effects. These results will be used to refine the design of the electromagnetic dipoles. Our control efforts have centered on developing commutation, levitation, and field pattern shaping hardware in the form of breadboards and PCBs with software running on a local microcontroller. In addition, our partners developed MATLAB Simulink models to demonstrate a PID controller that mitigates disturbance forces resulting from the interaction of drive and levitation magnetics. Finally, we have designed a three-axis test stand that will be used in future work to demonstrate CELA’s orientation control capability.

reaction sphere↗

DOE OSTI2025

Microreactor Automated Control System Test Bed Digital Architecture for Real-Time, Hardware-in-the-Loop Simulation

This work describes progress made towards the development of a real-time hardware-in-the-loop (HIL) test bed for non-nuclear testing of microreactor control schemes and failure modes. Non-nuclear testing is a crucial step in developing robust control algorithms for managing microreactor dynamics. The creation of an HIL simulation harnesses the realistic dynamics of physical analogue systems while additionally considering the challenges of variable communication delay. This collaborative effort between Oak Ridge National Laboratory and Idaho National Laboratory has resulted in a LabVIEW-based gRPC communication protocol which couples a TRANSFORM Modelica simulation of nuclear components to the ViBRANT physical hardware for realistic feedback and visual representation of control action in real time. A modular python client structure is developed to manage FMU-based Modelica simulation and real-time gRPC communication. HIL testing suggests that the modeled reactor with natural convection molten salt loop coolant configuration responds well to PID control of drum positioning for modulation of reactor core power, however, future efforts will be made to explore the added thermal inertial delay of system level control and downstream demand changes. Development of this platform with a generalized methodology provides a foundation for exploring a variety of reactor configurations and failure modes in rapid order to provide insight into the most effective avenues of study for further research and development.

McConnell, Jono [ORNL] (ORCID:0000000238984741)↗

DOE OSTI2025

Real-Time Sea State Estimation for Wave Energy Converter Control via Machine Learning

Wave energy converters (WECs) harness the untapped power of ocean waves to generate renewable energy, offering a promising solution to sustainable energy. An optimal WEC control strategy is essential to maximize power capture that dynamically adjusts system parameters in response to rapidly changing sea states. This study presents a novel control approach that leverages neural networks to estimate sea states from onboard WEC measurements such as position, velocity, and force. Using a point absorber WEC device as a test platform, our proposed approach estimates sea states in real-time and subsequently adjusts PID controller gains to maximize energy extraction. Simulation results across diverse sea conditions demonstrate that our strategy eliminates the need for external wave monitoring equipment while maintaining power capture efficiency. The results show that our neural network-based control technique can improve power capture by 25.6% while significantly reducing system complexity. This approach offers a practical alternative for WEC deployments where direct wave measurements are either infeasible or cost prohibitive.

PIDcontrol↗

NASA NTRS2003

Control Study for Five-axis Dynamic Spin Rig Using Magnetic Bearings

The NASA Glenn Research Center (GRC) has developed a magnetic bearing system for the Dynamic Spin Rig (DSR) with a fully suspended shaft that is used to perform vibration tests of turbomachinery blades and components under spinning conditions in a vacuum. Two heteropolar radial magnetic bearings and a thrust magnetic bearing and the associated control system were integrated into the DSR to provide magnetic excitation as well as non-contact mag- netic suspension of a 15.88 kg (35 lb) vertical rotor with blades to induce turbomachinery blade vibration. For rotor levitation, a proportional-integral-derivative (PID) controller with a special feature for multidirectional radial excitation worked well to both support and shake the shaft with blades. However, more advanced controllers were developed and successfully tested to determine the optimal controller in terms of sensor and processing noise reduction, smaller rotor orbits, more blade vibration amplitude, and energy savings for the system. The test results of a variety of controllers that were demonstrated up to 10.000 rpm are shown. Furthermore, rotor excitation operation and conceptual study of active blade vibration control are addressed.

Choi, Benjamin↗

DOE OSTI2026

Preliminary proof-of-concept of real-time divertor heat flux control from infrared cameras with nitrogen injection in the DIII-D tokamak

In future tokamak reactors like ITER and the Fusion Pilot Plant (FPP), real-time feedback control of heat flux to the plasma-facing components (PFC) will be critical for steady-state operation. This work presents the first experimental demonstration of real-time divertor heat flux estimation with infrared thermography and feedback control with impurity seeding on the DIII-D tokamak. The flexible infrastructure of the Plasma Control System (PCS) on DIII-D makes this new capability possible. The PCS software runs on a gateway computer system, and five real-time compute nodes. An array of low latency streaming digitizers from D-TACQ Solutions connects to these real-time computers to collect and process data, and send commands to actuators during plasma discharges. This system handles the signal IO from the tokamak and allows the PCS to utilize the diagnostic data necessary to perform control in real-time. Feedback control on heat flux was accomplished by feeding infrared camera data from the “Infrared TV” (IRTV) camera to a custom-developed User Datagram Protocol (UDP) server. This server transmits infrared data to a newly developed PCS algorithm that estimates the heat flux to PFC. Here, a proportional integral derivative (PID) controller minimizes the error between a heat flux reference and the real-time estimate by injecting nitrogen gas into the divertor.

Algorithm development↗

NASA NTRS1990

Development of a control system for a pair of robotic platforms

This thesis is a discussion of the development of a control system for a pair of three-degree-of-freedom robotic platforms. The platform system and its computer support are described at both the hardware and the software levels, including a section detailing diagnostics which can be run in the event of specific system errors. The design and implementation of a PID controller for the platforms based on experimentally-determined system dynamics is described. Finally, the tracking performance of each joint controller is examined. A path planner is used to map a smooth trajectory between starting and destination positions, and the controller's tracking ability is observed along this path.

Cosentino, James L.↗

DOE OSTI2025

Flexible Resource Scheduler for FAST-DERMS (FRS-FASTDERMS) v0.9

The Flexible Resource Scheduler is a hierarchical controller that manages the distributed energy resources in a distribution substation or distribution feeder to provide a firm commitment of power flow at the substation or feeder head to be scheduled in transmission-level markets as an aggregated demand resource. It is the reference controller for the FAST-DERMS Architecture, developed in tandem with the architecture under the DOE FAST-DERMS project. It is comprised of a day-ahead stochastic optimization, which schedules substation power flow and reserves, a intra-hour MPC, which generates dispatch base points for DER, and a real-time PID controller maintaining that dispatches DER to maintain the substation power around the base points. The repository also includes a representative aggregator controller, and all of the necessary components to run a simulation using PNNL's GridAPPS-D software with the controller.

MacDonald, Jason [Lawrence Berkeley National Labor↗

DOE OSTI2023

Creating a Simulation Platform for Research and Development of Advanced Control Methods

Advanced nuclear reactors are essential to meet the changing energy requirements throughout both the United States and the rest of world. In addition to other features, they are designed to enable deployment in remote locations and operate in a fully (or near-fully) autonomous manner, which will require a new control paradigm. To realize autonomously operating reactors, the U.S. Department of Energy’s Nuclear Energy Enabling Technologies Advanced Sensors and Instrumentation (NEET ASI) program conducts research and development into the enabling technologies and methods needed, including digital twins, machine learning, and risk modeling, in addition to various types of control methods. These technologies and methods are the key foundations needed to achieve fully autonomous systems. To develop and evaluate the technologies and methods necessary for achieving autonomous operations, it is critical to identify a software tool capable of integrating all the required elements. In surveying the available solutions, no software platforms were identified that could accomplish what was needed without introducing drawbacks. This challenge was the motivation for the current effort: to develop a software platform that can seamlessly integrate autonomouscontrol-enabling technologies and methods, allowing for accelerated research and development and transfer of ideas. The resulting platform, known as the Control and Optimization Modular Modeling Application for Nuclear Deployment (COMMAND), is Python-based, and leverages open-source tools to provide flexibility and facilitate building upon prior research. It is designed to enable advanced reactor developers to deploy and test advanced control technologies and methods coupled with their own models, solutions, and hardware. Given the substantial undertaking of developing such a platform, the current effort focused on laying down scalable, flexible software foundations and infrastructure, then demonstrating the platform via a use case. These foundations included developing generic modules, which contain the base variable and system blocks (the information and functional building blocks, respectively, that can be used to design a simulation) and the data handling and storage blocks needed to exchange information between the various blocks; as well as enablingtechnology-specific modules. This platform was evaluated via a use case, which was to simulate and control a process for the Microreactor Automated Control System (MACS) test bed. While MACS is not currently directly coupled to any specific microreactor physics, it was initially developed in concert with the Microreactor Applications Research Validation and Evaluation (MARVEL) microreactor, and so the MARVEL physics are used here. As part of this use case, several enabling-technology-specific blocks within COMMAND were integrated, including a proportional integral derivative (PID) control block, a Reactor Excursion and Leak Analysis Program (RELAP5-3D) block, and an anomaly detection block. The COMMAND software platform was successfully demonstrated to achieve the scalability and flexibility objectives of this effort and will be leveraged by the program’s research efforts to advance state of the art control methodologies towards autonomous operations of advanced reactors. As new use cases are created and implemented, it is anticipated that COMMAND will continue to grow and evolve to meet new requirements.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS2012

Quaternion-Based Control Architecture for Determining Controllability/Maneuverability Limits

Dynamic inversion has often been used in the simulation environment to rapidly prototype controls for the full flight envelope, because of its capacity for assessing a vehicle s maneuver performance and proper sizing of control surfaces. Generally, the architectures involve either a direct inversion of the entire set of equations of motion or a sequential set of inversions exploiting time scale separation in the vehicle dynamics where faster parameters are considered as controls for slower varying parameters. The proposed architecture builds on the latter using a quaternion formulation that provides singularity free tracking. Of interest, the proposed architecture simplifies the sequential approach by exploiting a simpler kinematic inversion in place of a more difficult inversion typically used. This kinematic relationship accurately describes the angular rate required to drive some reference frame of interest to a desired attitude at some desired quaternion error rate. A simple PID control is used to define the desired quaternion error rate. The paper develops the theoretical framework for the approach, and shows results in tracking a desired trajectory.

Bacon, Barton J↗

NASA NTRS1991

Robust and real-time control of magnetic bearings for space engines

Currently, NASA Lewis Research Center is developing magnetic bearings for Space Shuttle Main Engine (SSME) turbopumps. The control algorithms which have been used are based on either the proportional-intergral-derivative control (PID) approach or the linear quadratic (LQ) state space approach. These approaches lead to an acceptable performance only when the system model is accurately known, which is seldom true in practice. For example, the rotor eccentricity, which is a major source of vibration at high speeds, cannot be predicted accurately. Furthermore, the dynamics of a rotor shaft, which must be treated as a flexible system to model the elastic rotor shaft, is infinite dimensional in theory and the controller can only be developed on the basis of a finite number of modes. Therefore, the development of the control system is further complicated by the possibility of closed loop system instability because of residual or uncontrolled modes, the so called spillover problem. Consequently, novel control algorithms for magnetic bearings are being developed to be robust to inevitable parametric uncertainties, external disturbances, spillover phenomenon and noise. Also, as pointed out earlier, magnetic bearings must exhibit good performance at a speed over 30,000 rpm. This implies that the sampling period available for the design of a digital control system has to be of the order of 0.5 milli-seconds. Therefore, feedback coefficients and other required controller parameters have to be computed off-line so that the on-line computational burden is extremely small. The development of the robust and real-time control algorithms is based on the sliding mode control theory. In this method, a dynamic system is made to move along a manifold of sliding hyperplanes to the origin of the state space. The number of sliding hyperplanes equals that of actuators. The sliding mode controller has two parts; linear state feedback and nonlinear terms. The nonlinear terms guarantee that the systems would reach the intersection of all sliding hyperplanes and remain on it when bounds on the errors in the system parameters and external disturbances are known. The linear part of the control drives the system to the origin of state space. Another important feature is that the controller parameter can be computed off-line. Consequently, on-line computational burden is small.

Sinha, Alok↗