Optimal feedback gains of a delayed proportional-derivative(PD) control for balancing an inverted pendulum

In the dynamics analysis and synthesis of a controlled system, it is important to know for what feedback gains can the controlled system decay to the demanded steady state as fast as possible. This article presents a systematic method for finding the optimal feedback gains by taking the stability of an inverted pendulum system with a delayed proportional-derivative controller as an example. First, the condition for the existence and uniqueness of the stable region in the gain plane is obtained by using the D-subdivision method and the method of stability switch. Then the same procedure is used repeatedly to shrink the stable region by decreasing the real part of the rightmost characteristic root. Finally, the optimal feedback gains within the stable region that minimizes the real part of the rightmost root are expressed by an explicit formula. With the optimal feedback gains, the controlled inverted pendulum decays to its trivial equilibrium at the fastest speed when the initial values around the origin are fixed. The main results are checked by numerical simulation.

Switching Control Method for Optimal State Feedback Controller of Nuclear Reactor Power System

Due to the nonlinearity of the reactor power system, the load tracking situation is closely related to the initial steady-state power and the final steady-state power after the introduction of the state feedback controller. Therefore, when the initial power and the final stable power are determined, the particle swarm optimization algorithm is used to find the optimal controller parameters to minimize the load tracking error. Since there are many combinations of initial stable power and final stable power, it is not possible to find the optimal controller parameters for all combinations, so the neural network is used to take the final stable power and the initial stable power as input, and the optimal controller parameters as the output. This method obtains the optimal state feedback controller switching control method can achieve a very excellent load tracking effect in the case of continuous power change, in the power change time point, the response is fast, in the controller parameter switching time point, the actual power does not fluctuate due to the change of controller parameters. .

Numerical Solution to Optimal Feedback Control by Dynamic Programming Approach:A Local Approximation Algorithm

This paper considers optimal feedback control for a general continuous time finite-dimensional deterministic system with finite horizon cost functional. A practically feasible algorithm to calculate the numerical solution of the optimal feedback control by dynamic programming approach is developed. The highlights of this algorithm are: a) It is based on a convergent constructive algorithm for optimal feedback control law which was proposed by the authors before through an approximation for the viscosity solution of the time-space discretization scheme developed by dynamic programming method; b) The computation complexity is significantly reduced since only values of viscosity solution on some local cones around the optimal trajectory are calculated. Two numerical experiments are presented to illustrate the effectiveness and fastness of the algorithm.

Optimal state feedback control of brushless direct-current motor drive systems based on Lyapunov stability criterion

This paper develops a unified methodology for a real-time speed control of brushless direct-current motor drive systems in the presence of measurement noise and load torque disturbance. First, the mathematical model and hardware structure of system is established. Next, an optimal state feed back controller using the Kalman filter state estimation technique is derived. This is followed by an adaptive control algorithm to compensate for the effects of noise and disturbance. Those two algorithms working together can provide a very-high-speed regulation and dynamic response over a wide range of operating conditions. Simulated responses are presented to highlight the effectiveness of the proposed control strategy.

RandWPSO-LSSVM optimization feedback method for large underground cavern and its engineering applications

According to the characteristics of large underground caverns, by using the safety factor of surrounding rock mass point as the control standard of cavern stability, RandWPSO-LSSVM optimization feedback method and flow process of large underground cavern anchor parameters were established. By applying the optimization feedback method to actual project, the best anchor parameters of large surge shaft five-tunnel area underground cavern of the Nuozhadu hydropower station were obtained through optimization. The results show that the predicted effect of LSSVM prediction model obtained through RandWPSO optimization is good, reasonable and reliable. Combination of the best anchor parameters obtained is 114131312, that is, the locked anchor bar spacing is 1 m x 1 m, pre-stress is 100 kN, elevation 580.45-586.50 m section anchor bar diameter is 36.00 mm, length is 4.50 m, spacing is 1.5 m × 2.5 m; anchor bar diameter at the five-tunnel area side wall is 25.00 mm, length is 7.50 m, spacing is 1 m× 1.5 m, and the shotcrete thickness is 0.15 m. The feedback analyses show that the optimization feedback method of large underground cavern anchor parameters is reasonable and reliable, which has important guiding significance for ensuring the stability of large underground caverns and for saving project investment.

PRF: a process-RAM-feedback performance model to reveal bottlenecks and propose optimizations

Performance models provide insightful perspectives to predict performance and to propose optimization guidance.Although there has been much researches,pinpointing bottlenecks of various memory access patterns and reaching high accurate prediction of both regular and irregular programs on various hardware configurations are still not trivial.This work proposes a novel model called process-RAM-feedback(PRF)to quantify the overhead of computation and data transmission time on general-purpose multi-core processors.The PRF model predicts the cost of instruction for singlecore by a directed acyclic graph(DAG)and the transmission time of memory access between each memory hierarchy through a newly designed cache simulator.By using performance modeling and feedback optimization method,this paper uses PRF model to analyze and optimize convolution,sparse matrix-vector multiplication and sn-sweep as case study for covering with typical regular kernel to irregular and data dependence.Through the PRF model,it obtains optimization guidance with various sparsity structures,algorithm designs,and instruction sets support on different data sizes.

FEEDBACK CONTROL OPTIMIZATION FOR SEISMICALLY EXCITED BUILDINGS

A feedback control optimization method of partially observable linear structures via stationary response is proposed and analyzed with linear building structures equipped with control devices and sensors. First, the partially observable control problem of the structure under horizontal ground acceleration excitation is converted into a completely observable control problem. Then the It6 stochastic differential equations of the system are derived based on the stochastic averaging method for quasi-integrable Hamiltonian systems and the stationary solution to the Fokker-Plank-Kolmogorov （FPK） equation associated with the It6 equations is obtained. The performance index in terms of the mean system energy and mean square control force is established and the optimal control force is obtained by minimizing the performance index. Finally, the numerical results for a three-story building structure model under E1 Centro, Hachinohe, Northridge and Kobe earthquake excitations are given to illustrate the application and the effectiveness of the proposed method.

Optimal terminal-time determination for the ZEM/ZEV feedback guidance law with generalized performance index

This paper investigates a problem of determining the optimal terminal-time or time-to-go of the ZEM/ZEV(Zero-E ort-Miss/Zero-E ort-Velocity)feedback guidance law for a variety of orbital intercept or rendezvous maneuvers.A generalized ZEM/ZEV guidance problem,whose objective is to minimize a combination of the control energy and terminal time,is examined.Algebraic equations whose solution provides the optimal terminal-time of the orbital intercept/rendezvous problems are derived based on the optimal control theory.The e ectiveness of the proposed approach is demonstrated for various orbital maneuver problems.

OPTIMAL TRACKING FOR BILINEAR STOCHASTIC SYSTEM DRIVEN BY FRACTIONAL BROWNIAN MOTIONS

This paper discusses a problem of optimal tracking for a linear control system driven by fractional Brownian motion.An equation is obtained for the linear Markov feedback control.The existence and uniqueness of the solution to the equation are also studied.