Control Parameterization Research Articles

Optimal dynamic operation of pumped storage power plants with variable and fixed speed generators

This paper studies the optimal dynamic operation of pumped storage power plants with variable and fixed speed generators. A control strategy for the dynamic operation is proposed based on a detailed physics-based plant model. It combines a stationary optimizer with a nonlinear model predictive control strategy and a nonlinear state observer for non-measurable system quantities. Contrary to earlier works on this topic, all system constraints are systematically taken into account, e.g., the pressure limits over the whole hydraulic system. The physics-based model allows for an easy model and controller parametrization and application to different plant topologies. This work studies the optimal combined operation of multiple (different) generators in the turbine and pump mode. The results show that a synchronous generator with a full-rated converter is the optimal choice for single-unit operation and that a synchronous generator with a converter-fed synchronous generator is the optimal combination of two units. A clear advantage of variable speed units is identified in the dynamic operation. The performance of the combined operation of variable and fixed speed generators is only slightly lower than for two variable speed units since the proposed control strategy allows to partially mitigate the shortcomings of the fixed speed unit by the variable speed unit.

Robust [formula omitted] parameterization with low tuning complexity of cascaded control for feed drives

This paper presents a robust parameterization method for the well-established cascaded control structure of feed drives and applies it to both proportional (P) and sliding mode (SMC) position controllers. The controller parameterization is based on the structured μ-synthesis technique, which allows direct robust tuning of fixed control structures with respect to the conflicting goals of tracking and disturbance rejection over different frequency ranges. The proposed strategy explicitly takes into account both matched and unmatched uncertainties and considers the dynamics of the Kalman filter and feedforward control, ensuring robust stability and performance based on a simple low-order plant model with only two parameters. To ensure industrial applicability, the parameterization problem is formulated in a signal-based manner and the tuning complexity is limited to the selection of only two hyperparameters by directly extracting the information from measurements. Extensive experimental results are performed on an industrial feed drive to validate the performance and robustness of the proposed approach. For example, compared to P-PI cascade control with feedforward and nominally tuned SMC position control, the robustly parameterized SMC position controller reduces the root-mean-square tracking error by 79% and 61% during high-speed milling experiment. Even under variation of model parameters by 20%, the robustly parameterized SMC still cuts the tracking error by more than 44% in the comparison.

Optimal switching control of 1,3-propanediol fed-batch production with a cost on smooth feeding rate variation

In this paper, we propose a nonlinear switched control system for microbial 1,3-propanediol (1,3-PD) fed-batch production, where the smooth feeding rate of glycerol as well as the switching instants between batch process and feeding process are taken as control variables. To maximize 1,3-PD yield and minimize the fluctuation of feeding rate, we then present an optimal switching control problem with a cost on the smooth feeding rate variation and subject to path constraints reflecting the operational requirements. For solving this problem, we convert it to a series of parameter optimization problems by using a novel control parameterization scheme, a time-scaling transformation and a constraint transcription technique. An analytical expression of the total variation for the smooth feeding rate is also derived. On this basis, we develop a parallel Particle Swarm Optimization (PSO) algorithm together with the gradient-based optimization to solve the resulting problem. Finally, numerical simulations indicate that sacrificing a small amount of 1,3-PD can reduce the feeding rate variation significantly.

Adaptive Two-Degrees-of-Freedom Current Control for Solenoids: Theoretical Investigation and Practical Application

In this article, an adaptive two-degrees-of-freedom current control algorithm for solenoids is presented comprising an adaptive pole placement controller in combination with a regularized least-squares parameter estimation law. An additional adaptive feedforward controller takes advantage of the estimated plant parameters to further enhance the tracking performance. The stability of the overall closed-loop system is rigorously proven. The proposed solution differs from existing approaches by the adaptive feedforward controller and the way the parameter estimation is performed. The control concept is applied with the same controller parametrization to three solenoids from different applications, with substantially differing parameters. The experimental results show high tracking performance and fast parameter convergence even with poor initial estimates and despite the nonlinear dependence of the inductance on the current and position. The experimental results are also compared to two benchmark control design paradigms known from the literature, i.e. a second-order sliding mode controller and a nonlinear model reference adaptive control solution, which are both outperformed by the proposed controller.

On the use of adjoint gradients for time-optimal control problems regarding a discrete control parameterization

AbstractIn this paper, we discuss time-optimal control problems for dynamic systems. Such problems usually arise in robotics when a manipulation should be carried out in minimal operation time. In particular, for time-optimal control problems with a high number of control parameters, the adjoint method is probably the most efficient way to calculate the gradients of an optimization problem concerning computational efficiency. In this paper, we present an adjoint gradient approach for solving time-optimal control problems with a special focus on a discrete control parameterization. On the one hand, we provide an efficient approach for computing the direction of the steepest descent of a cost functional in which the costs and the error in the final constraints reduce within one combined iteration. On the other hand, we investigate this approach to provide an exact gradient for other optimization strategies and to evaluate necessary optimality conditions regarding the Hamiltonian function. Two examples of the time-optimal trajectory planning of a robot demonstrate an easy access to the adjoint gradients and their interpretation in the context of the optimality conditions of optimal control solutions, e.g., as computed by a direct optimization method.

Self-tuning methodology for adaptive controllers based on genetic algorithms applied for grid-tied power converters

The performance and stability of adaptive controllers is highly dependent on its parameter initialization. For non-expert designers, the parametrization of these controllers can be highly time consuming and an exhausting task. In order to improve the response of adaptive controllers without needing more specialized knowledge, this work proposes a procedure for self-tuning (optimal parametrization) of direct type adaptive controllers using a genetic algorithm. The proposal does not harm any property of stability and convergence of the adaptive strategy, only adding an off-line stage of parameter selection, which is carried out in a reasonable computational time. As a case study, this self-tuning procedure is applied for initialization of nine parameters of a Robust Model Reference Adaptive Controller and Adaptive Super-Twisting Sliding Mode, a known adaptive structure from the literature, suitable for current regulation of three-phase voltage source converters operating under grid impedance variations. For comparison with the proposed self-tuning, a similar procedure using fmincon and simulated annealing algorithms are also tested. The experimental results show that the proposed procedure using Genetic Algorithm can provide lower tracking error, faster regulation dynamics and reduced settling time, leading to better performance than the same controller with parameters initialized empirically.

Analysis and design of control systems via parameter‐based approach

Analysis and design of control systems via parameter‐based approach

An enhanced control parameterization technique with variable switching times for constrained optimal control problems with control-dependent time-delayed arguments and discrete time-delayed arguments

In this paper, we consider an optimal control problem whose dynamic system consists of control-dependent time-delayed arguments in the control and discrete time-delayed arguments in the state. Recently, control parameterization methods using hybrid time-scale transformation techniques have been developed to optimize both the control parameters and their switching times when the dynamic system consists of discrete time-delayed arguments only. This transformation maps the variable switching times in the original time horizon to fixed switching times in the new time horizon. Thus, the purpose of this paper is to extend the above technique to solve problems with both control-dependent time-delayed arguments and discrete time-delayed arguments. Using the above technique, we convert both the delayed state vector and the delayed control vector into non-delayed vectors in the new time horizon; hence both the control parameters and their switching times can be optimized. The gradients of the objective functions and the constraint functions with respect to the switching times and the controls are obtained. Two numerical examples, one of which is a practical problem involving the optimal transmission of messages in an internet, are solved to demonstrate the efficiency of our method.

Hybrid dynamic optimal tracking control of hydraulic cylinder speed in injection molding industry process

<p style='text-indent:20px;'>Injection speed control is one of the most essential components in the injection molding process. It is critical to implement fast and reliable injection speed optimization control for the effective manufacturing of injection molding products. In this paper, the speed tracking control problem of the hydraulic cylinder of an injection molding machine driven by a typical servo motor is studied. An efficient two-stage optimization framework that leverages the ideas of both control parameterization (CP) and particle swarm optimization (PSO) is proposed for generating the optimal signal input to achieve the required injection speed tracking over a certain time. To this end, the dynamic model of the hydraulic system in the injection molding equipment is firstly established and the optimal controller design problem is transformed into sequential optimal parameter decision problems, and the explicit expressions of the gradient information of the objective function as well as the constraint on the parameters of the decision variables are derived. Then, the PSO combined with the CP and gradient-based algorithm is utilized to to solve the parameters of the controller efficiently. The two-stage optimization framework proposed in this paper can improve the convergence speed of the CP method and the precision of the PSO and easy-to-implement in engineering and industrial deployment. Finally, the feasibility and effectiveness of the proposed design method are verified by experimental simulations.</p>

Control parameterization approach to time-delay optimal control problems: A survey

<p style='text-indent:20px;'>Control parameterization technique is an effective method to solve optimal control problems. It works by approximating the control function by piece-wise constant (or linear) function. In this way, the optimal control problems are approximated by optimal parameter selection problems, which can be regarded as finite-dimensional optimization problems, where the control heights and switching times of the piece-wise constant function are taken as the decision variables. They can be solved by using gradient-based optimization methods. For this, it requires the gradient formulas of the objective and constraint functions with respect to the decision variables. There are two methods for deriving the required gradient formulas. The aim of this paper is to survey various numerical methods developed based on control parameterization for solving optimal control problems governed by time-delay systems. Particular focus is on those numerical methods for optimizing switching time points. This is because the process of optimizing the switching time points is much more complicated for optimal control problems with time delays. In addition, we shall also review the computational methods developed based on control parameterization technique for solving two optimal control problems involving more complicated time delays.</p>

Adapting the control of the magnetic bearings of a highly flexible and gyroscopic rotor to the excitations by the motor

A test rig was built to perform fatigue tests on thick-walled cylinders made of fibre reinforced plastic (FRP). During the fatigue test, the rotational speed of an FRP cylinder is periodically varied until it fails. The FRP cylinder is connected to a drive spindle that accelerates and decelerates it using a permanent magnet synchronous machine (PMSM). To avoid excessive wear, the rotor is supported by active magnetic bearings (AMB). After the fatigue test was finished with the first cylinder, a new cylinder was attached to the test stand. With this new specimen, previously uncritical radial vibrations became more severe. For high accelerations, these vibrations led to instability of the rotor. However, high accelerations are desirable to perform the fatigue tests in the shortest possible time. Hence, the AMB control should be made insensitive to these vibrations. Since the vibrations depend on the acceleration of the rotor, it is reasonable to assume that they are induced by the PMSM. To reduce the vibrations, these excitations from the PMSM are included in the model-based controller parametrization process for the radial AMB, in which the parameters are adjusted via optimization. With the adjusted control, the amplitude of the vibration was significantly reduced and higher accelerations were possible. The described parameter tuning process can easily be adapted to different AMB systems with disturbances and changes in the system.

The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey

<abstract><p>The study of harvesting mechanisms in predator-prey systems with an Allee effect on prey has always garnered significant attention. In this paper, the dynamics and harvesting strategies of a predator-prey system are investigated, where the prey is subject to the Allee effect. The positivity and boundedness of solutions, the existence and stability of equilibria are further studied. The existence of a Hopf bifurcation at the interior equilibrium point of the system is investigated and verified by numerical simulations. Furthermore, we investigate the maximum sustainable yield (MSY), maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system. We find that MSY can be attained through predator harvesting, while MSTY is observed when harvesting efforts are uniform across species. In these situations, the biological system maintains stability. Using the method of control parametrization, the optimal economic profit and harvesting strategy are obtained. The results show that the harvesting efforts can affect the stability of the system, resulting in several interesting biological phenomena. This research provides a theoretical basis for biological resource management.</p></abstract>

Optimal control of fish-feeding in a three-dimensional calm freshwater pond considering environmental concern

<p style='text-indent:20px;'>This paper describes the optimal fish-feeding in a three-dimensional calm freshwater pond based on the concentrations of seven water quality variables. A certain number of baby fishes are inserted into the pond simultaneously. They are then taken out of the pond simultaneously for harvest after having gone through a feeding program. This feeding program creates additional loads of water quality variables in the pond, which becomes pollutants. Thus, an optimal fish-feeding problem is formulated to maximize the final weight of the fishes, subject to the restrictions that the fishes are not under-fed and over-fed and the concentrations of the pollutants created by the fish-feeding program are not too large. A computational scheme using the finite element Galerkin scheme for the three-dimensional cubic domain and the control parameterization method is developed for solving the problem. Finally, a numerical example is solved.</p>

Time-optimal control strategies for tungiasis diseases with limited resources

Tungiasis, as an epidermal parasitic skin disease, leads to long-term injury and life threats to humans in resource-limited countries. In this paper, we aim to minimize the epidemic duration of tungiasis disease with limited resources. A human-jigger parasite system with four control policies for humans and jiggers is established. We propose a time-optimal control problem, in which the eradication time and limited resources are involved. By applying the Pontryagin’s minimum principle, we prove that, only bang-bang controls are admitted for all the control policies. Furthermore, a numerical scheme combining the control parametrization scheme with the interior point algorithm is constructed. Finally, numerical simulations are carried out using actual data of humans and jiggers in Brazil. From all the results, we conclude that, there is a trade-off between the optimal eradication time and the effective funding; once the effective funding is properly used, the disease can be controlled effectively; strengthening personal protections, improving treatments for humans and making adulticiding efforts contribute to keeping humans away from the disease.

Model Predictive Control as a Secure Service for Cyber–Physical Systems: A Cloud-Edge Framework

This article proposes a model predictive control as a secure service (MPCaaSS) framework for cyber–physical systems (CPSs) in the presence of both cyber threats and external disturbances. First, in order to take advantage of the cloud-edge computing, we design a double-layer controller architecture by using a novel control parameterization based on Gaussian radial basis functions. In this controller architecture, the cloud-side controller optimizes the controller parameters of the edge-side controller, whereas the edge-side controller implements the real-time control law using the generated controller parameters. Second, in order to securely transmit data packets, we integrate an encoding scheme and an elliptic curve cryptography (ECC)-based encryption into the proposed MPCaaSS framework. Then, the controller parameters and the state measurements can be encrypted such that no malicious attackers can corrupt and intercept the transmission. It is shown that the recursive feasibility of MPCaaSS is achieved under some sufficient conditions, and the robust stability of the closed-loop system is guaranteed if the optimization problem is recursively feasible. Simulated examples are conducted to demonstrate the effectiveness of the proposed method.

A switched system approach for the direct solution of singular optimal control problems

Optimal control problems where the control variable appears linearly in the formulation lead to singular control arcs that introduce analytical and numerical complications during the solution process. In this work, the switching behavior (switching between singular and nonsingular control arcs) is exploited to solve singular optimal control problems using a direct method. The problem is reformulated as a switched system optimal control problem where each control arc defines a different subsystem, i.e., lower and upper limits and a singular arc. The switching between control arcs is handled using binary functions that depend on time. The switched system is embedded into a larger family by relaxing the binary functions to avoid integer variables. The variable switching times at which the control switches between arcs are mapped to fixed points in a new time domain using a time-scaling transformation. A direct transcription method along with control parametrization is applied to transform the embedded problem into a nonlinear programming formulation that contains few variables and constraints. A penalty term is introduced to obtain binary solutions for the optimal selection of control arcs. The proposed reformulation avoids the use of mesh refinement techniques and continuation methods, and allows to solve challenging problems in very short CPU times with high accuracy.

Perimeter Control With State-Dependent Delays: Optimal Control Model and Computational Method

Perimeter control is to manipulate traffic flows in different regions through adjusting traffic signals at the border of the regions. Traditionally, the complete trips in a region are assumed to be dependent on the current accumulated vehicles in this region. This assumption is invalid because the vehicle needs time to complete its trip in a region. In order to solve this shortcoming, some recent studies have introduced a time-delay dynamical system to describe the dynamical behaviour of the accumulated vehicles in a region. However, in these studies, the perimeter control problem is formulated as a tracking problem with a given optimal reference point. In reality, such an optimal reference point is unavailable in advance. This paper will fill this gap through formulating perimeter control as an optimal control problem governed by a state-dependent time delay system. The control parametrization technique and an exact penalty method are introduced to solve such a challenging optimal control problem. Model predictive control is applied to obtain close-loop solution through solving a series of online optimal control problems. Some experiments are performed to demonstrate the effectiveness of our method.

Learning-PDE-Based Approximate Optimal Control for an MHD System With Uncertainty Quantification

Handling uncertainty is one of the most important challenges in real physical systems. In this article, we study an approximate optimal magnetic control strategy for a one-dimensional (1-D) magnetohydrodynamic (MHD) system with uncertainty quantification within the learning framework of the underlying MHD model. First, the MHD flow system is modeled by coupled partial differential equations (PDEs) wherein the Reynolds number is not deterministic but random. Then, the optimal magnetic control problem is formulated and reduced to a parameter selection problem with stochastic PDE constraints by means of the control parameterization method. Significantly different from the conventional sensitivity analysis and adjoint methods, a polynomial chaos expansion (PCE) based on a multifidelity model is developed to construct the underlying PDEs model by polynomial functions. Thus, the relationship between the objective function and the control sequence is derived explicitly, which, in turn, transforms the optimal parameter selection problem with stochastic PDE constraints into a typical algebraic optimization problem that can be easily solved by the existing nonlinear programming algorithm. Numerical simulations are illustrated to demonstrate the high performance of our proposed method.

Unified Control Parameterization Approach for Finite-Horizon Feedback Control With Trajectory Shaping

This article presents control parameterization as a unifying framework for designing a linear feedback control law that achieves the finite-time transfer of output as well as trajectory shaping. Representing control input as a linear combination of independent basis functions allows wide variability in the resultant feedback control laws through the selection of the number and types of basis functions. Given an array of basis functions that meets the trajectory shaping necessities, the unified design approach proceeds with the determination of the coefficients so that the predicted trajectory attains the desired output at the final time. The input evaluated with the coefficients found at each instance essentially turns out to be a linear state feedback policy with an additional feedforward term and time-dependent gains, which is appropriate for practical use. The unified control parameterization approach lends itself well to missile guidance applications with the expandability and direct trajectory shaping capability that it provides. To emphasize the expandability of the framework, this study revisits the trajectory shaping guidance laws from the control parameterization viewpoint and shows how the notion of specifying input basis functions not only generalizes various existing methods but also enables further extensions. Furthermore, an application to integrated guidance and control illustrates the strength of the design process in handling the shaping requirements more directly through the construction of appropriate basis.

Sequential adaptive switching time optimization technique for optimal control problems

The control parameterization method used together with time-scaling transformation is an effective approach to transform optimal control problems into optimal parameter selection problems. The approximate problems can then be solved by gradient-based optimization methods. However, the conventional time-scaling transformation requires that all the control component functions switch simultaneously, which can be undesirable in practice. In this paper, we introduce a novel technique where the switching times for each of the control component functions can be adaptively selected. To demonstrate the effectiveness and flexibility of the proposed approach, two example problems with control input and terminal state constraints are solved using the method proposed. Numerical results show that the new method achieves much better objective values with some increase in computation time compared to the conventional time-scaling transformation technique.