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Describing functions to analyze feedback control systems containing nonlinearities of dead zone and backlash
A study was undertaken to model the cryogenic wind tunnel process, to validate the model by the use of experimental data from the Langley 0.3 Meter Transonic Cryogenic Tunnel, and to construct an interactive simulator of the cryogenic tunnel using the validated model. Additionally, this model was used for designing closed loop feedback control laws for regulation of temperature and pressure in the 0.3 meter cryogenic tunnel. The global mathematical model of the cryogenic tunnel that were developed consists of coupled, nonlinear differential governing equations based on an energy state concept of the physical cryogenic phenomena. Process equations and comparisons between actual tunnel responses and computer simulation predictions were examined. Also included are the control laws and simulator responses obtained using the feedback schemes for closed loop control of temperature and pressure were also included.
The design of a control system using the linear-quadratic regulator (LQR) control law theory for time invariant systems in conjunction with an incremental gradient procedure is presented. The incremental gradient technique reduces the full-state feedback controller design, generated by the LQR algorithm, to a realizable design. With a realizable controller, the feedback gains are based only on the available system outputs instead of being based on the full-state outputs. The design is for a remotely piloted research vehicle (RPRV) stability augmentation system. The design includes methods for accounting for noisy measurements, discrete controls with zero-order-hold outputs, and computational delay errors. Results from simulation studies of the response of the RPRV to a step in the elevator and frequency analysis techniques are included to illustrate these abnormalities and their influence on the controller design.
Feedback control system to position satellite in vicinity of unstable collinear libration point with application to lunar communication problem
Alternative computational procedures for obtaining a feedback control law which yields a control signal based on measurable quantitites are evaluated. The three methods evaluated are: (1) the standard linear quadratic regulator design model; (2) minimization of the norm of the feedback matrix, k via nonlinear programming subject to the constraint that the closed loop eigenvalues be in a specified domain in the complex plane; and (3) maximize the angles between the closed loop eigenvectors in combination with minimizing the norm of K also via the constrained nonlinear programming. The third or robust design method was chosen to yield a closed loop system whose eigenvalues are insensitive to small changes in the A and B matrices. The relationship between orthogonality of closed loop eigenvectors and the sensitivity of closed loop eigenvalues is described. Computer programs are described.
Wide-area time-synchronized measurements have recently revealed troublesome forced oscillations (FOs) within modern synchronized power grids. In some cases, these FOs represent a dangerous hazard to the system. Recent research has focused on locating the source of FOs to provide operators with knowledge for mitigating their impact locally. This paper presents a complementary mitigation strategy, which is to purposely induce a second oscillation into the grid which cancels the impact of the FO. Such a strategy is complementary in that it may provide valuable time to operators attempting to locate the FOs source and to determine how to rectify it. This paper presents a suppression control strategy which modulates controllable devices to automatically cancel the impact of the FO without the need for locating the source of the original FO. The strategy is based upon tuned feedback control. In this study, the approach is demonstrated on a simulation system via modulation of inverter-based generation.
The method of feedback linearization for control of the nonlinear nozzle and compressor components of an air breathing engine is presented. This method overcomes the need for a large number of scheduling variables and operating points to accurately model highly nonlinear plants. Feedback linearization also results in linear closed loop system performance simplifying subsequent control design. Feedback linearization is used for the nonlinear partial engine model and performance is verified through simulation.
Motivated by an energy efficient building application, we want to optimize a quadratic cost functional subject to the Boussinesq approximation of the Navier-Stokes equations and to bilateral state and control constraints. Since the computation of such an optimal solution is numerically costly, we design an efficient strategy to compute a sub-optimal (but applicationally acceptable) solution with significantly reduced computational effort. We employ an economic Model Predictive Control (MPC) strategy to obtain a feedback control. The MPC sub-problems are based on a linear-quadratic optimal control problem subjected to mixed control and state constraints and a convection-diffusion equation, reduced with proper orthogonal decomposition. Finally, to solve each sub-problem, we apply a primal-dual active set strategy. The method can be fully parallelized, which enables the solution of large problems with real-world parameters.
In the measurement of the gravitational constant G with angular acceleration method, the equilibrium position of torsion pendulum with tungsten fiber undergoes a linear slow drift, which results in a quadratic slow drift on the angular velocity of the torsion balance turntable under feedback control unit. The accurate amplitude determination of the useful angular acceleration signal with known frequency is biased by the linear slow drift and the coupling effect of the drifting equilibrium position and the room fixed gravitational background signal. We calculate the influences of the linear slow drift and the complex coupling effect on the value of G, respectively. The result shows that the bias of the linear slow drift on G is 7 ppm, and the influence of the coupling effect is less than 1 ppm.
The Laser Interferometer Gravitational-wave Observatory (LIGO) consists of two identical yet independent, widely separated, long-baseline gravitational-wave detectors. Each Advanced LIGO detector consists of complex optical-mechanical systems isolated from the ground by multiple layers of active seismic isolation, all controlled by hundreds of fast, digital, feedback control systems. This article describes a novel state machine-based automation platform developed to handle the automation and supervisory control challenges of these detectors. The platform, called Guardian, consists of distributed, independent, state machine automaton nodes organized hierarchically for full detector control. User code is written in standard Python and the platform is designed to facilitate the fast-paced development process associated with commissioning the complicated Advanced LIGO instruments. While developed specifically for the Advanced LIGO detectors, Guardian is a generic state machine automation platform that is useful for experimental control at all levels, from simple table-top setups to large-scale multi-million dollar facilities.
Artificial intelligence technologies have emerged as a game changer not only in specific applications such as image recognition and machine translation but also in many scientific domains. In particular, as deep reinforcement learning (DRL) has shown great success in complex control problems, DRL-based control has been considered as a potential solution to efficiently control and manage building systems. However, broad assessment of DRL-based building control is still required to characterize their pros and cons in comparison with conventional building control methods (e.g., rule-based feedback controls). In this paper, we assessed DRL-based controls with on-policy learning-based algorithms and continuous control actions for cooling control of large office buildings in the summer season to minimize whole-building energy use and occupant discomfort. We compared DRL-based control methods with two baseline control methods: (1) a pre-determined schedule with supply temperature and static pressure setpoints, and (2) advanced reset method that adjusts setpoints based on heuristic rules, i.e., ASHRAE Guideline 36. We also tested the DRL algorithms to evaluate their performances in multiple climate locations. We found that DRL-based control methods outperformed the baseline control methods in terms of energy savings while maintaining a thermal comfort. DRL reduced energy use between ~4%–22% on average compared to the baseline methods, depending on climate location. We also evaluated DRL-based control in terms of control stability and showed that DRL-based methods should address the span of hardware lifetimes in practical operations.
Discrete minimum principle to derive feedback control law for linear discrete-time systems
The requirements for automatic longitudinal control of a string of closely packed personal vehicles are outlined. Optimal control theory is used to design feedback controllers for strings of vehicles. An important modification of the usual optimal control scheme is the inclusion of jerk in the cost functional. While the inclusion of the jerk term was considered, the effect of its inclusion was not sufficiently studied. Adding the jerk term will increase passenger comfort.
The second law of thermodynamics is studied from the point of view of stochastic control theory. We find that the feedback control laws which are of interest are those which depend only on average values, and not on sample path behavior. We are lead to a criterion which, when satisfied, permits one to assign a temperature to a stochastic system in such a way as to have Carnot cycles be the optimal trajectories of optimal control problems. Entropy is also defined and we are able to prove an equipartition of energy theorem using this definition of temperature. Our formulation allows one to treat irreversibility in a quite natural and completely precise way.
An unconventional method for control of flexible space structures using feedback control of certain elements of the stiffness matrix is discussed. The advantage of using this method of configuration control is that it can be accomplished in practical structures by changing the initial stress state in the structure. The initial stress state can be controlled hydraulically or by cables. The method leads, however, to nonlinear control equations. In particular, a long slender truss structure under cable induced initial compression is examined. both analytical and numerical analyses are presented. Nonlinear analysis using center manifold theory and normal form theory is used to determine criteria on the nonlinear control gains for stable or unstable operation. The analysis is made possible by the use of the exact computer algebra system MACSYMA.
The Wide Field/Planetary Camera is an imaging system developed by the Jet Propulsion Laboratory for the NASA Hubble Space Telescope currently scheduled to be launched in December 1989 aboard the space shuttle. The temperature control design of the instrument utilizes multilayered insulation, electric resistance heaters, aluminum/ammonia heat pipes, thermoelectric coolers, temperature control coatings, and space radiators. A feedback control system maintains stable sensor temperatures. Thermal capacitance maintains stable optics and electronics temperatures during transient conditions. Schedule slips and launch delays have allowed extensive thermal testing of the instrument. Six instrument thermal vacuum tests and a spacecraft thermal vacuum test were performed. Several modifications have been made to the instrument to correct icing and contamination problems that have been discovered during thermal vacuum testing. This paper describes the thermal design, last instrument thermal vacuum test, results, and thermal model correlation.
This paper describes recent advances in structural quieting technology as applied to active truss structures intended for high precision space based optics applications. The active structure incorporates piezoelectric active members which exert control forces internal to the structure and thereby improve the structure's dimensional stability. The control architecture involves two layers of feedback control. The first utilizes collocated measurements of force and velocity at the active member to achieve active damping, the second utilizes noncollocated measurements of acceleration at the location of a simulated optical component to achieve structural stabilization. The local control loops are based on the concept of impedance matching, the global control loops are designed using robust control methods. These two levels of control are intended to operate simultaneously; however, in this paper each approach is applied individually. The combined implementation is left for future work.
Optimal and robust control theories are used to determine feedback control rules that effectively stabilize a linearly unstable flow in a plane channel. Wall transpiration (unsteady blowing/suction) with zero net mass flux is used as the control. Control algorithms are considered that depend both on full flowfield information and on estimates of that flowfield based on wall skin-friction measurements only. The development of these control algorithms accounts for modeling errors and measurement noise in a rigorous fashion; these disturbances are considered in both a structured (Gaussian) and unstructured ('worst case') sense. The performance of these algorithms is analyzed in terms of the eigenmodes of the resulting controlled systems, and the sensitivity of individual eigenmodes to both control and observation is quantified.