Integrated direct optimization of structure/regulator/observer for large flexible spacecraft

A two-degree-of-freedom quarter-car model is used as the basis for linear quadratic (LQ) and linear quadratic Gaussian (LQG) controller design for an active suspension. The LQ controller results in the best rms performance trade-offs (as defined by the performance index) between ride, handling and packaging requirements. In practice, however, all suspension states are not directly measured, and a Kalman filter can be introduced for state estimation to yield an LQG controller. This paper (i) quantifies the rms performance losses for LQG control as compared to LQ control, and (ii) compares the LQ and LQG active suspension designs from the point of view of stability robustness. The robustness of the LQ active suspensions is not necessarily good, and depends strongly on the design of a backup passive suspension in parallel with the active one. The robustness properties of the LQG active suspension controller are also investigated for several distinct measurement sets.

Optimal LQG Controller for Variable Speed Wind Turbine Based on Genetic Algorithms

The brushless dc motor position tracking system to be controlled includes a friction and a backlash as disturbances. In this paper, we propose a robust linear quadratic sliding-mode controller for precision positioning in a brushless dc motor system. The control algorithm includes a linear quadratic control for an optimal feedback gain and an integral nonlinear sliding-surface based on a new reaching law to remove the reaching phase. It has robust performance against parameter variation which causes an oscillation in case of linear quadratic control. Simulation results show that the proposed controller gives an improved accurate driving tracking result and is robust to plant parameter variation and load torque disturbances.

Notice of an instrument to be used in land surveying, for reducing the length of lines over undulating surfaces to the length of the base, or level line

A two-sided (simultaneous) optimization technique is presented for the two-player linear quadratic Gaussian (LQG) multistage game. This direct solution method allows for further interpretation of results as compared to previously used formal solution methods. For example, this direct solution method naturally decomposes the problem into separate deterministic and stochastic terms. This decomposition provides insight into the resulting optimal control strategies. In addition to the optimal control strategies, we derive a Lagrange multiplier (influence) sequence and an expression for the performance index differential, as well as an expression for the optimal performance index value.

Vibration signature of flexible structures can be used as a tool to monitor the structural health and predict failure. This work presents a practical low cost technique for predicting vibration signature of a mechanical structure and relates it to its structural health. The technique utilizes a model constructed from Modal frequencies and Eigen vectors obtained via finite element analysis (FEA) of the structure. Linear Quadratic Gaussian (LQG) servo controller of the acceleration output of the model is utilized to minimize error between actual acceleration measurements and its estimates. The LQG controller requires minimal feedback measurements from the physical system and can provide acceleration estimates at any location on the structure. Thus, it is adaptable to structures that are complex and/or have limited accessible measurements points. Anytime during operation, a shift in estimated Modal frequencies of the structure is shown to have a strong relationship with variation in structural parameters, (i.e. structural damage). Therefore, the presented technique is unique for three reasons, (a) it uses estimates, rather than actual measurements to identify structural damage, (b) requires minimal feedback measurements from the structure and (c) uses an effective low-cost reduced order model to achieve (a) and (b). The proposed technique is utilized on a pipeline structure and is evaluated both numerically and experimentally as a proof of concept. Research outcomes are presented and discussed.

Classical and modern methods are used for computing the maximum allowable time delay a closed-loop system can tolerate before destabilizing. Maximum allowable time delays are computed using both methods for three control systems previously designed for a simple process. The three control systems are proportional plus integral (PI), linear quadratic Gaussian (LQG), and linear quadratic Gaussian with loop transfer recovery (LQG/LTR). The allowable time delays computed using the modern technique yields conservative values in comparison with exact values computed using the classical method. Even though the LQG/LTR control system yields good performance and stability robustness, the closed-loop system is easily destabilized by small process time delay. The PI and LQG control systems can tolerate a significant amount of delay in the process control systems. Thus it appears that the design of a control system robust with regard to parameter variations, disturbance rejection, noise, and model uncertainty will not inherently be closed-loop stable when there is significant process delay. >

Spillover problems can occur when modal cross couplings introduced by the residual modes come into feedback in a closed—loop distributed control system. Observation spillover is due to the infinite summation of feedback control forces in the closed—loop control equations, and this spillover can introduce unstable dynamic responses in undamped structural systems (Meirovitch & Baruh, 1983). Thus, it is highly desirable that sensors only monitor those modes needed to be controlled such that observation spillover is prevented. In reality, however, sensors not only respond to controlled modes, but also those uncontrolled residual modes. There are several techniques of reducing the observation spillover. Conventional practice is to place sensors, spatially discrete sensors, at modal nodes or nodal lines of the residual modes. The difficulty with this arrangement is that it is very difficult, if not impossible, to avoid all uncontrolled residual modes. Another common approach is to pre—filter the sensor data using a comb filter with phase—locked loops (Gustafson & Speyer, 1976). The phase—locked loop filter reduces the observation spillover in the frequency domain. This technique requires that 1) the controlled modal frequencies are precisely known; 2) there is a reasonable separation from the nearby residual modes; 3) the signal—to—noise ratio is sufficiently high. The other method is to use spatially distributed modal sensors which respond only to a structural mode or a group of modes. In addition, feedback control forces for controlled modes could also appear in the governing equations of other uncontrolled modes resulting from modal interactions among all participating modes — control spillover.

Loop transfer recovery (LTR) techniques are known to enhance the input or output robustness properties of linear quadratic gaussian (LQG) designs. Here, novel loop recovery techniques are applied to LQG designs based on H ∞ /H 2 optimization methods. The motivation is to exploit the power of the H ∞ /H 2 approach so as to avoid high estimator or control loop gains, to cope systematically with non-minimum phase plants, and to maintain availability of the optimal state estimates when required. In the new methods, the simplicity of the original loop recovery approach is retained, in that a scalar parameter can be adjusted to achieve a compromise between optimality for the nominal plant model and robustness at the plant input or output. There is also a built in frequency shaping in the sensitivity function-based performance index used for the H ∞ /H 2 optimization. This emphasizes crossover frequencies. However, in our method there is an increase in the controller complexity of at most 2n–1 (n being ...

A unified state-space approach to linear quadratic Gaussian (LQG) and generalised predictive controller (GPC) control problems based on state-space representations of ARMAX models and explicit delay performance indices is presented. Links between the state-space and polynomial approaches to prediction and control problems are highlighted. Both the one-stage and infinite horizon solutions can be found within the unified framework.

Results are presented of on-going closed-loop ground experiments on the MACE test article, the objective of which is to investigate the extent to which closed-loop behavior of flexible spacecraft in zero gravity can be predicted, as well as to examine orbit system identification and control reconfiguration. The MACE hardware consists of three torque wheels, a two-axis gimballing payload, inertial sensors, and a flexible support structure. With the acquisition of a second payload, this is to represent a multiple payload platform with significant structural flexibility. When linear quadratic Gaussian control is used, payload pointing accuracy is improved by an order of magnitude when disturbed by a broadband torque disturbance. The successes and failures of the design and implementation process are discussed.

A comprehensive treatment of the discrete-time, steady-state linear quadratic Gaussian stochastic control problem which is based entirely on the z-transfer-function point of view is presented. The optimal solution is found for the general multi-variable case by exploiting the properties of the newly defined discrete generalized spectral factor. The proposed method of solution is developed independently of the results found by the time-domain approach. This method can easily cope with cases of discrete stationary coloured signals and dynamical operators in the performance index and its computational superiority over existing time-domain techniques is discussed.

A linear low‐order state space dynamic model for a catalytic butane hydrogenolysis reactor which has been fitted to reactor dynamic data is used to develop a multivariable linear quadratic feedback control algorithm for regulatory control of the reactor exit concentrations using temperature measurements only. Kalman filter theory is used to obtain state estimates for the system. The control algorithm developed is implemented on the pilot plant reactor in a series of DDC control studies. The controller is shown to perform very well and considerably better than a single loop PI controller with a feedback on the hot spot temperature. Performance is evaluated both under the normal stochastic disturbances in the system and under a severe deterministic load disturbance. Exit concentrations predicted by the model and used in the performance index are shown to compare very favorably with actual concentrations obtained from a process gas chromatograph.

A comprehensive treatment of the steady-state linear quadratic Gaussian stochastic control problem which is based on the transfer-function point of view is presented. The optimal solution is found, for the general multivariable case, by exploiting the properties of the newly defined generalized spectral factors. The exact equivalence between the results found by the time domain and the transfer-function approaches is established, even for the case of unstable systems. The proposed method of solution can easily cope with cases of stationary coloured signals, dynamical operators in the performance index and singular noise autocorrelation and control weighting matrices ; its computational superiority over existing time-domain techniques is demonstrated.

SummaryIn this paper, we consider a linear quadratic regulator control problem for spacecraft rendezvous in an elliptical orbit. A new spacecraft rendezvous model is established. On the basis of this model, a linear quadratic regulator control problem is formulated. A parametric Lyapunov differential equation approach is used to design a state feedback controller such that the resulting closed‐loop system is asymptotically stable, and the performance index is minimized. By an appropriate choice of the value of a parameter, an approximate state feedback controller is obtained from a solution to the periodic Lyapunov differential equation, where the periodic Lyapunov differential equation is solved on the basis of a new numerical algorithm. The spacecraft rendezvous mission under the controller obtained will be accomplished successfully. Several illustrative examples are provided to show the effectiveness of the proposed control design method. Copyright © 2014 John Wiley & Sons, Ltd.