On some attitude control syntheses for satellites with flexible appendages

The ship steering system is a typical electro-hydraulic servo system, which has the characteristics of non self-balance, large inertia, heavy load and uncertain disturbance. The load of the ship determines the depth of the draught. The depth of the draught determines the load of the steering system. The load of the rudder directly affects the dynamic and static tracking accuracy of the steering angle of the rudder. Therefore, the ship load is an important part of the ship steering system, and the establishment of a complete and accurate mathematical model is the necessary condition for the accurate control of the system. Based on the characteristics of the ship steering system, a general mathematical description with an uncertain disturbance system is presented. In order to obtain good performance of tracking control and resistance to load disturbance, a feedforward linear quadratic optimal tracking control method is proposed. The ship steering system designed based on this method can not only make the steering angle fast and accurately track the given, but also effectively suppress the heavy load uncertain disturbance. The simulation results show that feedforward linear quadratic optimal tracking control system has good tracking control performance and strong resistance to heavy load disturbance.

Motion control and flexible vibration synchronous suppression of base, links and joints for flexible space robot are studied. By combining linear spring, torsion spring, simply supported beam and hypothetical modal method, and using Lagrange equation, the dynamic model of flexible-base, flexible-link and flexible-joint space robot is established. Then, by using singular perturbation method, the model is decomposed into a joint motion slow subsystem and joint flexible vibration fast subsystem. In order to control the rigid motion of the base and joints in the slow subsystem and suppress flexible vibration of links, according to the concept of virtual control force, an output feedback repetitive learning algorithm based on the finite-dimensional Fourier series analytical periodic signal is proposed. The algorithm uses virtual force to suppress the flexible vibration of the robotic links. The output feedback method is designed so that the controller can be implemented based on position measurement only. It is proposed that the repetitive learning algorithm can effectively compensate for repeated errors in periodic tasks and improve the control quality of the system. The Lyapunov direct method confirms the stability of the above controller. In addition, in order to suppress the flexible vibration of the base and joint in the fast subsystem, the linear quadratic optimal control method and the joint flexible compensator are used to indirectly increase the joint equivalent stiffness, so that the control algorithm cannot be limited to solving the weak nonlinear problem. Simulation results show that the proposed controller can effectively suppress the vibration of multiple flexible components of the system, and achieve high-quality tracking of the desired signal.

This paper presents a variable ratio control strategy for a rear wheel active steering in order to improve the vehicle control stability and obtain an ideal steering characteristic. Considering the vehicle's control response performance at low speed and driving stability performance at high speed, using an expected yaw velocity with variable ratio and linear quadratic regulator LQR optimal control method, we design a vehicle rear wheel active steering controller to ensure the tracking at expected yaw velocity. The simulation result showed that the proposed control strategy has not only improved the control response at low speed but also enhanced the driving stability performance at high speed.

For a networked control system with both packet loss and Gaussian white noise disturbances in the sensor-controller and controller-actuator network paths, we propose a linear quadratic Gaussian optimal control method based on event-triggering. Considering the joint design problem of optimal event-triggered and optimal control, we firstly deduce an event-triggered quadratic optimal cost function. Secondly, we use a dynamic programming method to carry out the optimal co-controller design for the established mathematical model. Finally, we verify the effectiveness of the proposed control strategy through intelligent cart trajectory tracking simulation experiments on MATLAB platform.

Trade-Off Between Energy Capture and Dynamic Loads in Variable Speed Wind Turbines

This paper proposes a control theoretic formulation and a controller design method for the feature-based visual servoing with redundant features. The linear time-invariant (LTI) formulation copes with the redundant features and provides a simple framework for controller design. The proposed linear quadratic (LQ) method can deal with the redundant features, which is important because the previous LQ methods are not applicable to redundant systems. Moreover, this LQ method gives flexibility for performance improvement instead of the very limited design parameters provided by the generalized inverse and task function controllers. Validity of the LTI model and effectiveness and flexibility of the LQ optimal controller are evaluated by real-time experiments on a PUMA 560 manipulator.

This paper is an overview of fundamental linear–quadratic optimal control techniques used for linear dynamic systems. The presentation is suitable for undergraduate and graduate students and practicing engineers. The paper can be used by class instructors as supplemental material for undergraduate and graduate control system courses. The paper shows how to find the solution to a dynamic optimization problem: optimize an integral quadratic performance criterion along trajectories of a linear dynamic system over an infinite time period (steady-state linear–quadratic optimal control problem). The solution is obtained by solving a static optimization problem. All derivations done in the paper require only elementary knowledge of linear algebra and state space linear system analysis. The results are presented also for the observer-driven linear–quadratic steady-state optimal controller, output feedback-based linear–quadratic optimal controller, and the Kalman filter-driven linear–quadratic stochastic optimal controller. Having full understanding of derivations of the linear–quadratic optimal controller, observer-driven linear–quadratic optimal controller, optimal linear–quadratic output feedback controller, and optimal linear–quadratic stochastic controller, students and engineers will feel confident to use these controllers in numerous engineering and scientific applications. Several optimal linear–quadratic control case studies involving models of real physical systems, with the corresponding Simulink block diagrams and MATLAB codes, are included in the paper.

This paper discusses about synthesizing a state-feedback controller for a quadcopter based on an optimal linear quadratic control method. The resulting flight control system enables the quadcopter to maintain stability and to track a reference input. The solution to this control problem involves solving an algebraic Riccati equation. The reference-input tracking capability is simulated to show the capability of the quadcopter flight control system.

Optimal controller properties from closed-loop experiments

This paper presents a method to design a static output feedback active suspension controller for ride comfort improvement and motion sickness reduction in a real vehicle system. Full-state feedback controller has shown good performance for active suspension control. However, it requires a lot of states to be measured, which is very difficult in real vehicles. To avoid this problem, a static output feedback (SOF) controller is adopted in this paper. This controller requires only three sensor outputs, vertical velocity, roll and pitch rates, which are relatively easy to measure in real vehicles. Three types of SOF controller are proposed and optimized with linear quadratic optimal control and the simulation optimization method. Two of these controllers have only three gains to be tuned, which are much smaller than those of full-state feedback. To validate the performance of the proposed SOF controllers, a simulation is carried out on a vehicle simulation package. From the results, the proposed SOF controllers are quite good at improving ride comfort and reducing motion sickness.

Inverted decoupling and LMI-based controller design for a turboprop engine with actuator dynamics

In this design, through the analysis of the physical model of the linear double inverted pendulum, the motion equation of the system is obtained by using the classical Newtonian mechanical formula, and the obtained equation is linearized at the stable point, and the state space model of the system is obtained. In order to realize the stable control of the trolley position and the secondary linkage in the linear inverted pendulum system, the linear quadratic optimal controller is used in this design to obtain an excellent output response. In order to design the optimal state feedback control matrix K, the shortcomings of weight matrices Q and R in general LQR control design that depend on experience selection and trial and error are overcome. This design attempts to apply PSO algorithm to LQR controller parameter optimization. PSO algorithm is applied to optimize Q parameters and R parameters of LQR weighting matrix of linear quadratic optimal controller, and K matrix is obtained. The matrix is applied to a fuzzy PID controller designed by the fusion algorithm to overcome the disadvantage that a single PSO cannot adapt itself. Finally, a comparative simulation study is carried out in the Simulink environment of Matlab software toolbox, which verifies the effectiveness of the fuzzy PID controller based on particle swarm optimization algorithm, laying a theoretical foundation for the practical application of the inverted pendulum system, and has certain application value.

Based on the dynamic model of 1/4 vehicle suspension, an active control system is designed using the fractional order exponential reaching law of model following variable structure control strategy. An active suspension with linear quadratic optimal control is used as the reference model. The sliding mode switching surface parameters is designed by pole placement method to ensure the stability of the system. At the same time, combined with the index reaching law proposed by Professor Gao Wei Bing and the definition and properties of fractional index, constructs a similar fractional order exponent reaching law to improve the dynamic quality of sliding mode motion. And in MATLAB, system modeling and controller design are implemented. By setting up experiments, the different suspensions are compared. The results show that compared with the passive suspension, the performance of the vehicle can be improved better, and the performance of the tracking reference model has good tracking performance. Moreover, compared with the integral exponential reaching law, the chattering can be more effectively weakened. Finally, before and after the change of vehicle parameters in the simulation, the results show that the system has good robustness.

Linear quadratic (LQ) controller design is considered for continuous-time systems with harmonic signals of known frequencies and it is shown that the design is reducible to an interpolation problem. All LQ optimal loops are parametrized by a particular solution of this interpolation problem and a (free) stable/proper transfer function. The appropriate choice of this free parameter for optimal stability robustness is formulated as a multiobjective design problem and reduced to a Nevanlinna-Pick interpolation problem with some interpolation points on the boundary of the stability domain. Using a related result from the literature, it is finally shown that, if there is sufficient penalization on the power of the control input, the level of optimum stability robustness achievable with LQ optimal controllers is the same as the level of optimum stability robustness achievable by arbitrary stabilizing controllers.

This paper studies the output feedback stochastic linear quadratic (LQ) optimal control with state and control dependent noise. Firstly, some necessary/sufficient conditions for the static output feedback stabilizability are given. Secondly, infinite horizon static and dynamic output feedback LQ control are studied, respectively.