Conventional Optimal Control Research Articles

PDF‐based tuning of stochastic optimal controller design for cyber‐physical systems with uncertain delay dynamics

Uncertain dynamics in communication network, including random delays and packet losses make it difficult to guarantee stability of cyber-physical systems (CPSs). Many existing works consider the uncertainties of network channel with strong assumptions that network delay bounds and its distribution are known a priori and time-invariant. However, these assumptions could be invalidated in realistic CPSs by malicious attacks, system hardware faults, topology changes etc. A probability density function (PDF)-based tuning of stochastic optimal control (PTSOC) is proposed to manage the unknown dynamics in the embedded network. The update law of the proposed controller is derived and updated based on the PDF estimation of network delays that explicitly consider delays and its time-varying distribution. The results illustrate that the proposed PTSOC has a better performance in terms of the overshoot, convergence time, and cost when compared with the conventional stochastic optimal control.

Maximizing Wind Energy Capture for Speed-Constrained Wind Turbines During Partial Load Operation

With the development of wind turbine technology, more wind turbines operate in the partial load region, where one of the main objectives is to maximize captured wind energy. This paper presents the development of an optimal control framework to maximize wind energy capture for wind turbines with limited rotor speed ranges. Numerical optimal control (NOC) techniques were applied to search for the achievable maximum power coefficient, thus maximum wind energy capture. Augmentations of these optimal techniques significantly reduced the computational cost. Simulation results show that, in comparison with the traditional torque feedback and conventional optimal control algorithms, the proposed augmented optimal control algorithm increases the harvested energy while minimizing the computational expense for speed-constrained wind turbines during partial load operation.

Adaptive hill-climb searching method for MPPT algorithm based DFIG system using fuzzy logic controller

This paper proposes a variable speed control algorithm for a grid connected doubly-fed induction generator system. The main objective is to track the maximum power point by using an adaptive hill climb searching (HCS) technique based on fuzzy logic controller (FLC), and compare it with the conventional optimal torque control method for large inertia wind turbines. The role of the FLC is to adapt the step-size of the HCS method according to the operating point. The control system has two sub-systems for the rotor side and the grid side converters (RSC, GSC). Active and reactive power control of the back-to-back converters has been achieved indirectly by controlling q-axis and d-axis current components. The main function of the RSC controllers is to track the maximum power through controlling the rotational speed of the wind turbine. The GSC controls the DC-link voltage, and guarantees unity power factor between the GSC and the grid regardless of the magnitude and direction of the slip power. The proposed system is developed and tested in MATLAB/SimPowerSystem environment.

On the properness of an impulsive control extension of dynamic optimization problems

This article investigates the properness, or well-posedness, of impulsive extension of a conventional optimal control problem. This includes both well-posedness of the solution to impulsive control systems arising as result of an impulsive extension of ordinary differential systems, and existence theorems. Well-posedness in the classic Cauchy sense is proved. Approximation lemmas that guarantee sensitivity to small perturbations in control variables are obtained. Filippov type existence theorems are established. A model example is provided to show the relevance of the impulsive controls problems which are under study.

Doubly-Fed Induction Generator Drive System Based on Maximum Power Curve Searching using Fuzzy Logic Controller

This paper proposes a novel variable speed control algorithm for a grid connected doubly-fed induction generator (DFIG) system. The main objective is to track the maximum power curve characteristic by using an adaptive fuzzy logic controller, and to compare it with the conventional optimal torque control method for large inertia wind turbines. The role of the FLC is to adapt the transfer function of the harvested mechanical power controller according to the operating point in variable wind speed. The control system has two sub-systems for the rotor side and the grid side converters (RSC, GSC). Active and reactive power control of the back-to-back converters has been achieved indirectly by controlling q-axis and d-axis current components. The main function of the RSC controllers is to track the maximum power through controlling the electromagnetic torque of the wind turbine. The GSC controls the DC-link voltage, and guarantees unity power factor between the GSC and the grid. The proposed system is developed and tested in MATLAB/SimPowerSystem (SPS) environment.

Optimal control problems with stopping constraints

We consider a novel optimal control problem in which the terminal time is governed by a stopping constraint. This stopping constraint is a nonlinear equality constraint depending on the state variables, and the terminal time is defined as the first time at which this constraint is satisfied. Since the stopping constraint causes the terminal time to be an implicit function of the control, the optimal control problem we consider cannot be solved using conventional techniques. We propose a new computational approach that involves approximating the original problem by a standard optimal control problem with fixed terminal time. Our main result shows that this approximation, which depends on two adjustable parameters, can be made to arbitrarily high accuracy. On this basis, the original optimal control problem with stopping constraints can be transformed into a sequence of approximate problems, each of which can be solved readily using conventional optimal control techniques. We conclude the paper by demonstrating this approach with numerical simulations in three application areas: range maximization of a hang glider, range maximization of a hypersonic re-entry vehicle, and time-optimal control of a nuclear reactor.

A design of a robust discrete-time controller

In this paper, we proposed a robust discrete-time controller. This control system, which is derived from the idea of the normalized plant, does not include plant parameters. Thus, we obtain a control system independent of plant parameters and that has the same structure as a conventional optimal servo control system. Simulation and experimental results show that the proposed method is fairly robust to plant parameter variations and external disturbances.

A novel hybrid DEPS optimized fuzzy PI/PID controller for load frequency control of multi-area interconnected power systems

In this paper, a novel hybrid Differential Evolution (DE) and Pattern Search (PS) optimized fuzzy PI/PID controller is proposed for Load Frequency Control (LFC) of multi-area power system. Initially a two-area non-reheat thermal system is considered and the optimum gains of the fuzzy PI/PID controller are optimized employing a hybrid DE and PS (hDEPS) optimization technique. The superiority of the proposed controller is demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as DE, Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA) and conventional Ziegler Nichols (ZN) based PI controllers for the same interconnected power system. Furthermore, robustness analysis is performed by varying the system parameters and operating load conditions from their nominal values. It is observed that the optimum gains of the proposed controller need not be reset even if the system is subjected to wide variation in loading condition and system parameters. Additionally, the proposed approach is further extended to multi-area multi-source power system with/without HVDC link and the gains of fuzzy PID controllers are optimized using hDEPS algorithm. The superiority of the proposed approach is shown by comparing the results with recently published DE optimized PID controller and conventional optimal output feedback controller for the same power systems. Finally, Reheat turbine, Generation Rate Constraint (GRC) and time delay are included in the system model to demonstrate the ability of the proposed approach to handle nonlinearity and physical constraints in the system model.

동일한 인접구조물의 효율적 진동제어방안

Abstract : This study proposes a new control approach for efficient vibration suppression of two identical adjacent structures. The conventional control approach of two adjacent structures is to interconnect the two structures with passive, semi-active or active control devices. However, when the two adjacent structures are identical to each other, their dynamical behaviors such as frequency and damping properties are also the same. In this case, the interconnected control devices cannot exhibit the dissipative control forces on the both structures as expected since the relative displacements and velocities of the devices become close to zero. In other words, the interconnection method does not work for the twin structures as enough as expected. In order to solve this problem, we propose several new control approaches to effectively and efficiently reduce the identically-fluctuating responses of the adjacent structures with minimum control efforts. In order to demonstrate the proposed control systems, the proposed several control systems are optimally designed and their control performances are compared with that of the conventional optimal control system where each TMD(tuned mass damper) is installed in each structure for independent control purpose. The simulated results show that one of the proposed control systems(System 04) is able to guarantee enhanced control performance compared with the conventional system.

Discrete-Time Robust Controller Based on a Switching Function

This paper describes a robust controller design method based on switching functions. The proposed method is independent of plant parameters and has the same configuration as a conventional optimal servo controller. Simulation results show that the cost performance of the proposed method is superior to that of a conventional optimal servo controller. 

JITL-based concentration control for semi-batch pH-shift reactive crystallization of l-glutamic acid

Although concentration control (C-control) strategy has been shown to give effective and robust control performance for batch cooling and semi-batch antisolvent crystallizations in recent years, no research work was reported concerning the potential application of conventional C-control for the more challenging semi-batch pH-shift reactive crystallization that is common in the process industries. To this end, this paper presents detailed analysis to find out that it is not feasible to apply the C-control to semi-batch pH-shift reactive crystallization. To circumvent this problem, a variant of C-control strategy by incorporating the Just-in-Time Learning (JITL) method to cope with strong process nonlinearity inherent in the pH-shift reactive crystallization is developed in this paper. Simulation results are presented to illustrate the proposed design and a comparison with conventional optimal control is made.

Dual hierarchical genetic-optimal control: A new global optimal path planning method for robots

A new two-stage analytical-evolutionary algorithm considering dynamic equations is presented to find global optimal path. The analytical method is based on the indirect open loop optimal control problem and the evolutionary method is based on genetic algorithm (GA). Initial solutions, as start points of optimal control problem, are generated by GA to be used by optimal control. Then, a new sub-optimal path is generated through optimal control. The cost function is calculated for every optimal solution and the best solutions are chosen for the next step. The obtained path is used by GA to produce new generation of start points. This process continues until the minimum cost value is achieved. In addition, a new GA operator is introduced to be compatible with optimal control. It is used to select the pair chromosomes for crossover. The proposed method eliminates the problem of optimal control (being trapped in locally optimal point) and problem of GA (lack of compatibility with analytical dynamic equations). Hence problem is formulated and verification is done by comparing the results with a recent work in this area. Furthermore effectiveness of the method is approved by a simulation study for spatial non-holonomic mobile manipulators through conventional optimal control and the new proposed algorithm.

An optimal control strategy with enhanced robustness for air-conditioning systems considering model and measurement uncertainties

Model-based optimal controls in HVAC systems involve uncertainties due to model uncertainties and measurement uncertainties. These uncertainties affect the accuracy and reliability of the outputs of optimal control strategies, and therefore affect the energy and environmental performance of buildings. This study proposes a method to enhance the robustness of optimal control strategies. A fuzzy approach is adopted to predict the errors in models outputs. Such predicted errors are then used to correct the model outputs. The method is validated in an optimal control strategy for HVAC cooling water systems. The operation data of a real building system is used to validate the error prediction method. A simulation platform is built to validate the enhanced strategy. Measurement uncertainties are deliberately added to the simulated system for validation tests. Test results indicate that the method is effective in predicting the errors in model outputs. Significant energy savings are achieved compared with the conventional optimal control method.

Constrained optimal control of switched systems and its application

In this paper, we consider an optimal co with state and control constraints, where a prespecified sequence of active subsystems is given. Both the switching instants and the control function are to be chosen such that the cost functional is minimized. Firstly, we convert the problem into a conventional optimal control problem based on parameterization of the switching instants. Next, through discretizing the control space, applying a time-scaling transformation and using the smoothing technique, the optimal control problem is approximated by a non-linear optimization problem with linear constraints and bounds on the variables. Furthermore, an algorithm that finds a suboptimal solution to the original problem is proposed. One major advantage with the new algorithm implementation is the only need to solve a non-linear optimization problem with linear constraints and bounds on the variables. The gradients of these linear constraints and the objective function can be easily obtained. Therefore, the original optimization problem can be solved efficiently using any gradient-based method, such as sequential quadratic programming algorithm. Finally, a flight planning example illustrates the efficiency of the proposed approach.

Vertical stabilization of ITER plasma using explicit model predictive control

In this work we explore advanced control algorithms for the vertical stabilization of plasma in the ITER tokamak for the case where a combination of ohmic in-vessel and superconducting poloidal actuators is used for effective response to disturbances subject to thermal constraints. We apply constrained linear-quadratic optimal control, which is a hybrid between conventional linear quadratic optimal control and model predictive control (MPC). We discuss the issues of practical implementation in the form of explicit MPC, which allows application to fast processes by avoiding the use of on-line optimization.

Combined optimal pulse width modulation and pulse frequency modulation strategy for controlling switched mode DC–DC converters over a wide range of loads

This paper develops a combined optimal pulse width modulation (PWM) and pulse frequency modulation (PFM) strategy for controlling switched mode DC-DC converters. The peak ripple magnitudes of both the output-voltages and -currents during all operating modes over a wide range of loads are minimised subject to specifications on the minimum efficiency bounds of the converters. This problem is posed as a multi-objective functional inequality constrained optimal control problem. By expressing the initial state of each operating mode at the steady state as a function of the switched time instants, as well as applying the time scaling transform method and the constraint transcription method, the multi-objective functional inequality constrained optimal control problem is converted to a conventional optimal control problem. Finally, a control parameterisation technique is applied to solve the problem. Computer numerical simulations show that the combined control strategy could achieve low peak ripple magnitudes of both the output-voltages and -currents for all operating modes over a wide range of loads and guarantees the satisfaction of the specifications on the minimum efficiency bounds of the converter over a wide range of loads. © 2012 The Institution of Engineering and Technology.

Nonlinear multi-objective receding horizon design utilizing state-dependent formulation

The art of multi-objective design is to extract the best compromise among conflicting requirements. The analytical multi-objective parameter synthesis adopts closed-form specifications that make the multi-objective design in linear systems computationally efficient. In this paper, the analytical multi-objective parameter synthesis method is extended to nonlinear systems via the state-dependent coefficients parametrization method in combination with the receding horizon control technique. The novel contributions presented in this paper are demonstrated on two fronts. First, the objective functions in infinite-time domain are replaced by equivalent finite-time functions with certain terminal terms, where the analytical formulations for the finite-time functions are made available and offer a computationally cost-effective approach. Second, the stability is addressed by adopting the receding horizon control technique. In addition, the proposed design approach shows benefits over the conventional nonlinear optimal control method. Two numerical examples further demonstrate the promising features of the proposed design framework.

Fast and save container cranes as bilevel optimal control problems

For the use of container cranes in high rack warehouses, reference trajectories can be obtained from optimal control problems in order to control the swinging of the crane system during the fast movement and in order to reach an equilibrium position at the end of the trajectory. Safety requirements extend these problems to bilevel optimal control problems, where the existence of alternative stop trajectories has to be guaranteed. A method as to how these complex problems can be reduced to conventional optimal control problems, even under control and state constraints, is presented together with numerical examples.

Modeling of a mobile manipulator for redundancy resolution

Purpose Recently, various applications of robotic systems to construction sites have been tried. In this research, a mobile platform-based serial manipulator, the so called ‘mobile manipulator’, is employed for construction tasks such as material handling, beam assembly, welding, and so on. Generally, a serial manipulator has 6 DOF (degrees of freedom). The mobile manipulator suggested in this paper adds 2 or 3 DOF, so that there are a total of 8 or 9 DOF. In 3-dimensional space, the minimum DOF for manipulation is 6. A manipulator that has more DOF than 6 is called a manipulator with ‘redundancy’. While a manipulator with redundancy like the proposed mobile manipulator has several advantages such as large flexibility, singularity avoidance, easy obstacle avoidance, and so on, the redundancy resolution for optimal manipulation is not easy. In this research, modeling of the mobile manipulator for redundancy resolution is studied. Method Since the suggested mobile manipulator is a MIMO(multi-input multi-output) robot system with 8 or 9 links, a state-space model is derived for redundancy resolution. Analysis of kinematics and dynamics for a serial manipulator and a mobile platform is performed. An integration of the serial manipulator and the mobile platform is used. Results & Discussion In this research, a state-space model for the proposed mobile manipulator is derived. This model enables redundancy resolution for optimal solution of 8 or 9 DOF-robot system. In order to solve the redundancy resolution problem, a linear quadratic method, which is one of the conventional optimal control methods, or a reinforcement learning method can be used.

Active control of unbalance response of rotor systems supported by tilting-pad gas bearings

This article establishes an optimal control model using piezoelectric actuators, proportional–derivative (PD) compensation, and gap sensors to control the vibration of rotor systems supported by tilting-pad gas bearings with active pads. The optimal control law between the voltage applied on the actuator and dynamic displacement of rotor is obtained by means of conventional optimal control theory. Using this active control model, the unbalance responses of rotor system are numerically controlled. Results show that the unbalance responses of system can be effectively suppressed by this optimal control system. This article provides a theoretical basis for further improving the stability of rotor systems supported by tilting-pad gas bearings.