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At least 343 records · Page 19

Small Body GN&C Research Report: A Robust Model Predictive Control Algorithm with Guaranteed Resolvability

A robustly stabilizing MPC (model predictive control) algorithm for uncertain nonlinear systems is developed that guarantees the resolvability of the associated finite-horizon optimal control problem in a receding-horizon implementation. The control consists of two components; (i) feedforward, and (ii) feedback part. Feed-forward control is obtained by online solution of a finite-horizon optimal control problem for the nominal system dynamics. The feedback control policy is designed off-line based on a bound on the uncertainty in the system model. The entire controller is shown to be robustly stabilizing with a region of attraction composed of initial states for which the finite-horizon optimal control problem is feasible. The controller design for this algorithm is demonstrated on a class of systems with uncertain nonlinear terms that have norm-bounded derivatives, and derivatives in polytopes. An illustrative numerical example is also provided.

model predictive control algorithm (MPC)↗

Reinforcement Learning-based Output Structured Feedback for Distributed Multi-Area Power System Frequency Control

Load frequency control (LFC) is a key factor to maintain the stable frequency in multi-area power systems. As the modern power systems evolve from centralized to decentralized paradigm, LFC needs to consider the decentralized scheme that considers limited information from the information-exchange graph for the generator control of each interconnected area. This paper aims to solve a data-driven constrained LQR problem with mean-variance risk constraints and output structured feedback, and applies this framework to solve the LFC problem in multi-area power systems. By reformulating the constrained optimization problem into a minimax problem, the stochastic gradient descent max-oracle (SGDmax) algorithm with zero-order policy gradient (ZOPG) is adopted to find the optimal feedback gain from the learning, while guaranteeing the convergence. In addition, to improve the adaptation of the proposed learning method to new or varying models, we construct an emulator grid that approximates the dynamics of a physical grid and performs training based on this model. Once the feedback gain is obtained from the emulator grid, it is applied to the physical grid with a robustness test to check whether the controller from the approximated emulator applies to the actual system. Numerical tests show that the obtained feedback controller can successfully control the frequency of each area, while mitigating the uncertainty from the loads, with reliable robustness that ensures the adaptability of the obtained feedback gain to the actual physical grid.

Kwon, Kyung-bin↗

Cross Feedback Control of a Magnetic Bearing System: Controller Design Considering Gyroscopic Effects

For flywheel rotors or other rotors with significant ratios of moments of inertia, the influence of gyroscopic effects has to be considered. While conservative or damped systems remain stable even under gyroscopic effects, magnetically suspended rotors can be destabilized with increasing rotational speed. The influence of gyroscopic effects on the stability and behavior of a magnetic bearing system is analyzed. The analysis is carried out with a rigid body model for the rotor and a nonlinear model for the magnetic bearing and its amplifier. Cross feedback control can compensate gyroscopic effects. This compensation leads to better system performance and can avoid instability. Furthermore, the implementation of this compensation is simple. The main structure of a decentralized controller can still be used. It has only to be expanded by the cross feedback path.

Ahrens, Markus↗

Investigation, development and application of optimal output feedback theory. Volume 2: Development of an optimal, limited state feedback outer-loop digital flight control system for 3-D terminal area operation

This report contains the development of a digital outer-loop three dimensional radio navigation (3-D RNAV) flight control system for a small commercial jet transport. The outer-loop control system is designed using optimal stochastic limited state feedback techniques. Options investigated using the optimal limited state feedback approach include integrated versus hierarchical control loop designs, 20 samples per second versus 5 samples per second outer-loop operation and alternative Type 1 integration command errors. Command generator tracking techniques used in the digital control design enable the jet transport to automatically track arbitrary curved flight paths generated by waypoints. The performance of the design is demonstrated using detailed nonlinear aircraft simulations in the terminal area, frequency domain multi-input sigma plots, frequency domain single-input Bode plots and closed-loop poles. The response of the system to a severe wind shear during a landing approach is also presented.

Broussard, J. R.↗

Dynamic analysis of a class of mixed lumped-distributed parameter systems via numerical techniques

The modeling via transfer matrices of mixed lumped-distributed parameter systems with feedback control is discussed and novel methods of obtaining information on the controlled system's dynamic response via numerical methods is presented. These methods utilize numerical searches in the complex plane for the roots of the transcendental characteristic equation to determine the closed loop system eigenvalues. The fast Fourier transform (FFT) algorithm is utilized but in the inverse fashion (from frequency domain to time domain). The information obtained is identical to that contained in a model in modal coordinates, and can be used to construct such a model. An interactive computer program to do the required calculation is described, as well as its application to a manipulator arm design problem.

Book, W. J.↗

Robot arm force control through system linearization by nonlinear feedback

Based on a differential geometric feedback linearization technique for nonlinear time-varying systems, a dynamic force control method for robot arms is developed. It uses active force-moment measurements at the robot wrist. The controller design fully incorporate the robot-arm dynamics and is so general that it can be reduced to pure position control, hybrid position/force control, pure force control. The controller design is independent of the tasks to be performed. Computer simulations show that the controller improves the position error by a factor of ten in cases in which position errors generate force measurements. A theorem on linearization of time-varying system is also presented.

Tarn, T. J.↗

Multivariable control of the Space Shuttle Remote Manipulator System using linearization by state feedback

This paper demonstrates an approach to nonlinear control system design that uses linearization by state feedback to allow faster maneuvering of payloads by the Shuttle Remote Manipulator System (SRMS). A nonlinear feedback law is defined to cancel the nonlinear plant dynamics so that a linear controller can be designed for the SRMS. First a nonlinear design model was generated via SIMULINK. This design model included nonlinear arm dynamics derived from the Lagrangian approach, linearized servo model, and linearized gearbox model. The current SRMS position hold controller was implemented on this system. Next, a trajectory was defined using a rigid body kinematics SRMS tool, KRMS. The maneuver was simulated. Finally, higher bandwidth controllers were developed. Results of the new controllers were compared with the existing SRMS automatic control modes for the Space Station Freedom Mission Build 4 Payload extended on the SRMS.

Gettman, Chang-Ching L.↗

Real-Time Optical Fuel-to-Air Ratio Sensor for Gas Turbine Combustors

The measurement of the temporal distribution of fuel in gas turbine combustors is important in considering pollution, combustion efficiency and combustor dynamics and acoustics. Much of the previous work in measuring fuel distributions in gas turbine combustors has focused on the spatial aspect of the distribution. The temporal aspect however, has often been overlooked, even though it is just as important. In part, this is due to the challenges of applying real-time diagnostic techniques in a high pressure and high temperature environment. A simple and low-cost instrument that non-intrusively measures the real-time fuel-to-air ratio (FAR) in a gas turbine combustor has been developed. The device uses a dual wavelength laser absorption technique to measure the concentration of most hydrocarbon fuels such as jet fuel, methane, propane, etc. The device can be configured to use fiber optics to measure the local FAR inside a high pressure test rig without the need for windows. Alternatively, the device can readily be used in test rigs that have existing windows without modifications. An initial application of this instrument was to obtain time-resolved measurements of the FAR in the premixer of a lean premixed prevaporized (LPP) combustor at inlet air pressures and temperatures as high as 17 atm at 800 K, with liquid JP-8 as the fuel. Results will be presented that quantitatively show the transient nature of the local FAR inside a LPP gas turbine combustor at actual operating conditions. The high speed (kHz) time resolution of this device, combined with a rugged fiber optic delivery system, should enable the realization of a flight capable active-feedback and control system for the abatement of noise and pollutant emissions in the future. Other applications that require an in-situ and time-resolved measurement of fuel vapor concentrations should also find this device to be of use.

Nguyen, Quang-Viet↗

Controlling Microbial Byproducts using Model-Based Substrate Monitoring and Control Strategies

We have developed a computer-controlled bioreactor system to study various aspects of microbially-mediated nitrogen cycling. The system has been used to investigate methods for controlling microbial denitrification (the dissimilatory reduction of nitrate to N2O and N2) in hydroponic plant growth chambers. Such chambers are key elements of advanced life support systems being designed for use on long duration space missions, but nitrogen use efficiency in them is reduced by denitrification. Control software architecture was designed which permits the heterogeneous control of system hardware using traditional feedback control, and quantitative and qualitative models of various system features. Model-based feed forward control entails prediction of future systems in states and automated regulation of system parameters to achieve desired and avoid undesirable system states. A bacterial growth rate model based on the classic Monod model of saturation kinetics was used to evaluate the response of several individual denitrifying species to varying environmental conditions. The system and models are now being applied to mixed microbial communities harvested from the root zone of a hydroponic growth chamber. The use of a modified Monod organism interaction model was evaluated as a means of achieving more accurate description of the dynamic behavior of the communities. A minimum variance parameter estimation routine was also' used to calibrate the constant parameters in the model by iterative evaluation of substrate (nitrate) uptake and growth kinetics. This representation of processes and interactions aids in the formulation of control laws. The feed forward control strategy being developed will increase system autonomy, reduce crew intervention and limit the accumulation of undesirable waste products (NOx).

Smernoff, David T.↗

Robust stability of second-order systems

Nonlinear control using feedback linearization or inverse dynamics for robotic manipulators yields good results in the absence of modeling uncertainty. However, modeling uncertainties due to unknown joint friction coefficients and payload variations can give rise to undesirable characteristics when these control systems are implemented. It is shown how passivity concepts can be used to supplement the feedback linearization control design technique, in order to make it robust with respect to the uncertain effects mentioned above. Results are obtained for space manipulators with freely floating base; however, they are applicable to fixed base manipulators as well. The controller guarantees asymptotic tracking of the joint variables. Closed-loop simulation results are illustrated for planar space manipulators for cases where uncertainty exists in friction modeling and payload inertial parameters.

Chuang, C.-H.↗

On the stabilization of decentralized control systems.

This paper considers the problem of stabilizing a linear time-variant multivariable system by using several local feedback control laws. Each local feedback control law depends only on partial system outputs. A necessary and sufficient condition for the existence of local control laws with dynamic compensation to stabilize a given system is derived. This condition is stated in terms of a new notion, called fixed modes, which is a natural generalization of the well-known concept of uncontrollable modes and unobservable modes that occur in centralized control system problems. A procedure that constructs a set of stabilizing feedback control laws is given.

Wang, S.-H.↗