Quadratic Optimal Control Algorithm Research Articles

AN INPUT LIMITED REPETITIVE LEARNING CONTROL OF FLEXIBLE-BASE TWO-FLEXIBLE-LINK AND TWO-FLEXIBLE-JOINT SPACE ROBOT WITH INTEGRATION OF MOTION AND VIBRATION

In order to analyze the dynamic simulation and movement control of space robot under the influence of full flexible of base, links and joints, as well as the active vibration suppression of base, links and joints, an input limited repetitive learning controller with integration of motion and vibration is proposed. The design of the algorithm is not based on the system model information. The flexible base and the flexible joints are regarded as linear spring and torsion springs. The flexible links are analyzed by the Eulerian Bernoulli model, and the dynamic equation is established by the Lagrange equation and the assumed mode method. Based on the singular perturbation theory, the model is decomposed into a slow subsystem including the system rigid variables and the link flexible vibration, and a fast subsystem including the base and joint flexible vibration. The corresponding sub controllers are designed for the slow and fast subsystems to form the general controller with joint flexible compensation. For the slow subsystem, an input limited repetitive learning controller is proposed, which is composed of hyperbolic tangent function, saturation function and repetitive learning term. The hyperbolic tangent function and saturation function realize the requirement of limited input torque. The repetitive learning term compensates the periodic system error to complete the gradual stable tracking of the expected trajectory of base attitude and joint. However, in order to suppress the flexible vibration of the links of the slow subsystem, a hybrid trajectory reflecting the flexible vibration of the links and the rigid motion of the system is constructed by using virtual force conception, and an input limited repetitive learning controller on virtual force conception is proposed to ensure the accurate tracking of the trajectory of the base and joint, while actively suppressing the flexible vibration of the links. For the fast subsystem, the linear quadratic optimal control algorithm is used to suppress the flexible vibration of the base and joints. The simulation results show that the controller is suitable for general flexible nonlinear system, meets the requirements of limited input torque, realizes high-precision tracking of periodic signal, effectively suppresses the flexible vibration of base, links and joints, and verifies the feasibility of the algorithm.

Optimal Control of the Vehicle Path Following by Using Image Processing Approach

Nowadays, the importance of the vehicles and its dramatic effects on human life is no secret. The use of trailers with multiple axels for transporting bulky and heavy equipment is essential. Increase in trailers axles which results increment of wheels, needs considerations in order to increase in transporting speed, maneuverability, safety, better control and path following accurately. Therefore, in this paper dynamic modeling and control of a 5 axial trailer was studied. As well as to increase maneuverability and speed up, steering 3 axles was considered. Also, by using image processing trailer path following in desired path with the highest accuracy was achieved. In this study, first a 14 DoF model for a 5 axial trailer with 3 steering axles was considered and its characteristics were described. Then, dynamic equations including kinematic and kinetic of trailer was obtained. Then, with checking trailers behavior a linear quadratic optimal control algorithm was designed. To evaluate the performance of the control algorithm, control problem simulation for 3 maneuver; single lane change, double lane change and overtaking; was done. The results confirmed the performance of designed control algorithm and image processing accuracy in trailer path following.

Effect of Time Delay on Control of Seismic‐Excited Buildings

The sensitivity of a system time delay with respect to the performance of control systems for seismic‐excited buildings is examined. The effect of a system time delay depends on the particular control algorithm and the particular control system used. Four control algorithms feasible for applications to conttrol of seismic‐excited buildings have been studied. These include the linear quadratic optimal control algorithm and three instantaneous optimal algorithms proposed recently. The sensitivity analysis for each control algorithm is performed using a simulation approach. Both the active tendon control system and the active mass damper have been considered, and the tall building is idealized by a shear‐beam lumped‐mass discrete system. Numerical examples are worked out to demonstrate the criticality and tolerance of a system time delay for each control system. It is shown that a time delay always results in a degradation for the efficiency of a control system and that the tolerance for a system time delay is quite stringent for cases investigated.

Effect of System Uncertainty on Control of Seismic‐Excited Buildings

A sensitivity study is conducted to investigate the effect of uncertainties in system identification on the performance of the active control system for seismic‐excited buildings. Four control algorithms feasible for applications to seismic‐excited buildings have been examined, including the linear quadratic optimal control algorithm and three instantaneous optimal control algorithms. A simple simulation approach is used for the sensitivity analysis. Both the active tendon control system and the active mass damper system have been considered. Numerical examples are worked out to illustrate the effect of uncertainties in identifying stiffnesses and dampings on the active control system. The effect of parametric uncertainties on the performance of active control systems for seismic‐excited buildings depends on the particular control algorithm used. It is demonstrated that, while dampings of structures are difficult to identify, the accuracy of damping estimation has a negligible effect on the performance of the control system. For some control algorithms, however, care should be taken to estimate the structural stiffness.

Systolic linear quadratic optimal controller

A square-root, linear quadratic optimal control algorithm is presented and realised on a new systolic array.