The Remote Control of the Artillery Rocket Set as a Strongly Nonlinear System Subject to Random Loads

A linear quadratic Gaussian (LQG) strategy controls a two-link flexible robot manipulator tracking a two-dimensional square trajectory 12.6 m/spl times/12.6 m. Slew angles together with a Gaussian white process and white or non-white measurement noise are fed into a LQG regulator (Kalman filter). A FLC strategy incorporates two fuzzy controllers substituted for the LQR state-space dynamics equations. Trajectories were obtained for the LQG strategy with Gaussian white and non-white measurement noise. The trajectory obtained for white measurement noise closely approaches a perfect square while those obtained for non-white measurement noise deviate. The trajectory obtained with the FLC strategy is similar to that for LQG with white measurement noise. Fuzzy control is found to provide robustness in operation and can be constructed with less mathematical complexity than LQG. The deviation in trajectories for LQG with non-white measurement noise suggests sub-optimal control and possible instability. This study has demonstrated the extent of deviation in tracking with an LQG strategy for non-white measurement noise and the FLC strategy as a viable option for precise and robust tracking control of a two-link flexible robot manipulator.

In the practical application, the SINS/GPS tightly integrated navigation system is faced with the situation that state error model is inaccurate or noise statistical characteristics are inconsistent with the reality. However, traditional Extended Kalman Filter (EKF) method can not effectively solve it, causing large filter errors in this system. This paper presents a method of GDOP estimation and adaptive Extended Kalman Filter, which combines satellite positions of ephemeris with the output of corrected SINS position instead of GPS positioning results to calculate GDOP; On this basis, using the GDOP value and innovation realizes the online real-time estimation of measurement noise variance matrix Rk while taking advantage of innovation realizes the online estimation of state noise variance matrix Qk to achieve the adaptive effect and improve navigation accuracy in tightly integrated navigation system. Introduction Strap-down Inertial Navigation System (SINS) does not depend on any external information, autonomy is strong and data update speed is fast, but the error of SINS will diverge over time, so SINS is not suitable for long time navigation; Global Positioning System (GPS) can work with high precision and long term, its error does not diverge over time, but there are also some shortcomings such as multipath effects and easily-affected radio interference, resulting in low stability of navigation. Therefore, GPS can’t perform well as a standalone system. In the high accuracy navigation field, GPS and SINS are mostly integrated together to overcome their own shortcomings, which makes the navigation performance better than the performance of two separate systems. SINS/GPS tightly integrated navigation system uses more raw data from GPS receiver pseudo-ranges and pseudo-range rates and has obvious advantages. Therefore, this paper focuses on the study of SINS/GPS tightly coupled system in order to achieve better navigation performance. In practical applications, due to the error of inertial device itself and inaccurate external environment information, there is a system error model inaccuracy and noise uncertainty in the SINS/GPS nonlinear systems. As for the uncertainty of system noise and statistical properties of measurement noise, people proposed various adaptive filtering algorithms. Literature [2-4] proposed a method of real-time estimating the system noise and measurement noise based on the innovation. The method does not increase the system dimensionality, only needs limited innovation to memory, and the calculation is simple and reliable, but cannot effectively solve the question that the system noise and measurement noise are inaccurate at the same time. This paper presents an adaptive filtering method for online estimation of the measurement noise covariance matrix Rk and the system noise covariance matrix Qk based on estimated GDOP value and innovation in EKF, and then applying this method to the SINS/GPS tightly coupled navigation system and verifying the validity of the adaptive algorithm. SINS/GPS tightly integrated system model State equation of integrated system is as follows :

This paper presents the design of a Linear Quadratic Gaussian (LQG) regulator for the frequency control of a multi-area power system in a restructured competitive electricity market environment. A general model of the LQG regulator has been developed for multi-area system (with hydro and thermal generators) having Poolco and bilateral transactions. To account for the modeling uncertainties and non-measurable states, a Kalman filter has been designed to estimate the state variables. The controller uses these estimates, optimizes a given performance index, and reschedules the generators’ outputs according to their bids for the frequency regulation. The functioning of the proposed LQG regulator has been demonstrated on a four area test system and the results have been compared with those obtained by using an optimal PID controller.

Matrix pseudoinverses producing necessary and sufficient conditions for positive and nonnegative definiteness

The paper addresses control of variable mass and configuration mechanical systems subjected to holonomic or nonholonomic constraints, which are imposed due to systems desired performance, tracking specified motions or other control needs. The control design is model-based and an analytical dynamics modeling framework underlying controller design is presented. The framework novelty is that constraints, including nonholonomic ones and these on variable mass, can be merged into variable mass system dynamics and final motion equations are free of the constraint reaction forces so they can be used directly to control design. Many mechanical systems change their mass or configuration when they move, e.g. inertia-based propelled underwater vehicles, mobile robots and manipulators transporting loads or space vehicles flying their space missions. The dynamics modeling framework presented in the paper can be applied to all variable mass system examples mentioned above. An underwater inertia-based propelled vehicle model dynamics and control performance illustrate the theoretical development presented in the paper. The paper contribution is two folded. It presents a unified approach to constrained variable mass or configuration systems modeling and introduces analytical dynamics methods to the nonlinear control domain.

A Linear quadratic Gaussian (LQG) control scheme with either a regular extended Kalman filter (EKF) or a fuzzy logic adaptive EKF (FLAEKF) state estimator implemented in the control loop was used to control a two-link flexible robot manipulator tracking a square trajectory 12.6m x 12.6m. Simulations were performed to ascertain the extent of divergence that may develop in a regular EKF and how effectively a FLAEKF could reduce or eliminate this divergence. Trajectories were obtained using LQG with a regular EKF resulting in divergence according to the intensity of non-white process and measurement noise disturbances. They were compared to more precise trajectories obtained using LQG with a FLAEKF. The results confirm the ability of a FLAEKF state estimator to effectively correct divergence that would otherwise occur with a regular EKF state estimator and to maintain robot-tracking precision albeit at a greater computational time burden.

This paper deals with the implementation of the Linear Quadratic Gaussian (LQG) with an Extended Kalman Filter (EKF) for the position control of a PMDC motor. LQG is a popularly used linear optimal control technique in literature. However, the direct implementation of LQG with the use of the Kalman Filter as the optimal estimator is incapable of adapting to changes in the system parameters which results in a deviation from the expected optimal performance. EKF allows for the estimation of the system parameter values along with the unknown states of the system. The estimated values are used to constantly update the plant model and calculate the gains for optimal performance. The effectiveness of this technique on the DC motor position control system for various changes in system parameter values is studied in this paper and compared with the performance of a simple Kalman Filter to show the improvement in performance. The results show improvements in both step responses and tracking performances with the use of the EKF estimator along with the LQG controller.

Magnetic bearings provide an energy-saving and resource-sparing possibility for supporting rotors running at high speed. This paper studies the potential of reducing the energy demand of magnetic levitation systems. Practical investigations show that this is obtainable by combining an optimal state estimator with an optimal state space controller. This configuration is known as Linear Quadratic Gaussian (LQG) regulator. In a sequential way, all the steps required for implementing this control strategy are depicted, starting with describing and modelling of the system which is a fully magnetically levitated blower in this case. Subsequently, the realization of the system state estimator is delineated. Both hints for carrying out the discretization of the continuous time model and a simple approach for choosing the variance matrices of the estimator are given. Special attention is paid to the design of the state feedback controller. The influence of the weighting matrix elements on the controller performance is investigated as well as an integrative extension of the regulator which ensures good reference response behaviour. Finally, measurements concerning the energy consumption of the levitation system are presented. The results show that both in static and dynamic case the implementation of the LQG regulator yields reduced control energy effort, compared to a system controlled by a conventional PID controller. It is noteworthy that, simultaneously to the enhancement of energy efficiency, implementing the LQG controller improves the dynamic properties of the levitation system, e.g. transient time and overshoot.

This paper proposes a new GNSS signal tracking loop based on linear quadratic Gaussian regulator (LQG) algorithm and evaluates its signal tracking performance. The proposed LQG based tracking loop consists of the extended Kalman filter (EKF) and linear quadratic regulator (LQR). The EKF uses I, Q correlation sum as measurements, and estimates code, carrier phase, the Doppler frequency and the Doppler rate as states. While conventional loop filter uses simple integrator for numerically controlled oscillator (NCO) input, the proposed loop filter adopts optimal control gain using LQR controller. To assess the performance of the proposed tracking loop, this paper performs Monte-Carlo software simulation and IF data processing from hardware GPS signal simulator using GNSS software receiver. The simulation results show that the performance of the proposed LQG based tracking loop ranges in error from 0.1 to 1 Hz DLL and from 20 to 40 Hz PLL for static user and shows equal or better performance than the those of the conventional PLL for high dynamic user.

The purpose of this work is designing a Linear Quadratic Gaussian (LQG) regulator and a Linear Quadratic Integral (LQI) controller for a fixed-wing aircraft. The LQG regulator design is created in two steps. First, an Unscented Kalman Filter (UKF) is selected as an observer for system dynamics to procreate an overall best estimate of system states. Second, an optimal feedback gain is calculated via the Linear Quadratic Regulator (LQR) approach. An LQI controller is designed for robust tracking of referenced outputs which are airspeed, sideslip, pitch angle and roll angle. The proposed LQG/LQI scheme is implemented in the MATLAB, Simulink environment. The simulation results show that the implemented system regulates and controls the system successfully in a noisy environment.

Emerging approaches for nonlinear parameter varying systems

ABSTRACTIn this paper, we study a cooperative linear quadratic Gaussian (LQG) control system realized by a cloud‐based structure, consisting of a user and a server. In this system, the user runs a plant to control and employ the server, sharing necessary information with it to obtain the optimal LQG control inputs. However, the user considers its state trajectories as private. Therefore, we propose a privacy scheme utilizing a public privacy processor, whose certain parameters are also open to the server. This scheme manages to make the server unable to directly access the states of the user, so that the user's privacy is preserved; meanwhile, the server's public knowledge of the privacy processor allows the user to have satisfactory performance of LQG control. We then analyze the performances of privacy preservation and LQG control. Lastly, we propose an optimization problem to analyze the trade‐off between privacy and LQG control, which we solve using an efficient numerical method.

In the paper a linear quadratic Gaussian (LQG) dynamic regulator is applied with an extended Kalman filter (EKF), a LQG with fuzzy logic adaptive EKF (FLAEKF), LQG with an EKF and a FLAEKF combined with time delays in the feedback loop for modeling non-minimum phase (NMP) response for control of the end effector with non-collocated sensor and in the feed-forward loop for corrective control of a two-link flexible robot in the tracking of square trajectory task. The system is compared in simulations with a fuzzy logic system (FLS) vibration suppression control system. Results show that FLS adaptive vibration suppression yields higher tracking precision than FLAEKF, EKF or corrective time delays. It is also more effective while maintaining tracking accuracy and reasonable time efficiency than the classical PID controller or advanced adaptive controllers. Recursive nonparametric identification procedure for nonlinear friction in the joints of flexible robot is introduced. Its asymptotic properties are investigated.

End effector tracking of a two-link flexible robot is simulated using a linear quadratic Gaussian (LQG) dynamic regulator with an extended Kalman filter (EKF), a LQG with fuzzy logic adaptive EKF (FLAEKF), LQG with an EKF and a FLAEKF combined with time delays in the feedback loop to model nonminimum phase (NMP) response for a sensor noncollocated at the end effector and in the feed forward loop for corrective control action. A fuzzy logic system (FLS) vibration suppression control strategy is simulated for comparison. Results demonstrate FLS adaptive vibration suppression produces greater tracking accuracy than an EKF, FLAEKF or corrective time delays. In comparison with classical FID control or even with more advanced adaptive control strategies FLS vibration suppression gives better tracking control while execution time remains acceptable.

Sensor devices suffer severe interference due to multi path effect, non line of sight (NLOS) and variations of the wireless propagation environment in indoor positioning systems. These interferences lead to measurement error during sensor measurement. Kalman filter (KF) and extended Kalman filter (EKF) have been widely used in tracking systems to reduce measurement noise. However, KF and EKF assume the measurement noise follows normal distribution, and the real noise distribution should be based on experimental statistical results. Besides fluctuating wireless condition makes the system unstable in indoor environments. We analyze the time of flight (TOF) measurement statistic model in experiments and design KF and EKF models for indoor positioning system according to the statistic model. We introduce our system architecture for wireless sensor networks (WSN) to overcome KF's drawbacks, which divides the positioning system into three components: measurement, pre-processing and data-processing. Measurement component measures the range based on TOF method. We developed a voting filter (VF) and an averaging filter (AF) in preprocessing to reduce measurement noise for later processing. During data-processing, Kalman filter and extended Kalman filter are used to track the positions. We also implement another scheme, low pass filter (LPF) with KF or EKF, to estimate the positions with the knowledge of geographic information. Three realistic experiments are set up using the sensor equipment nanoPAN 5375 to evaluate these methods. Comparing the experimental results, low pass filter with EKF is most suitable for indoor positioning.