Control Parameterization Research Articles

On-line and real-time controller tuning architecture based on Youla–Kucera controller parameterization

This paper presents an on-line and real-time controller tuning architecture based on Youla–Kucera controller parameterization. First, a coarse controller is designed to satisfy nominal performance of closed-loop system. Second, Youla parameter is used to construct an on-line and real-time fine tuning mechanism including a group of controller candidates under arbitrary switching strategy. The mechanism can adjust the control performance on-line to achieve the balance between dynamic and steady-state performance without resulting in any closed-loop stability problems.

A new computational approach for optimal control of switched systems

The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples.

Constrained minimum variance and covariance steering based on affine disturbance feedback control parameterization

AbstractThis paper deals with finite‐horizon minimum‐variance and covariance steering problems subject to constraints. The goal of the minimum variance problem is to steer the state mean of an uncertain system to a prescribed vector while minimizing the trace of its terminal state covariance whereas the goal in the covariance steering problem is to steer the covariance matrix of the terminal state to a prescribed positive definite matrix. The paper proposes a solution approach that relies on a stochastic version of the affine disturbance feedback control parametrization. In this control policy parametrization, the control input at each stage is expressed as an affine function of the history of disturbances that have acted upon the system. It is shown that this particular parametrization reduces the stochastic optimal control problems considered in this paper into tractable convex programs or difference of convex functions programs with essentially the same decision variables. In addition, the paper proposes a variation of this control parametrization that relies on truncated histories of past disturbances, which allows for sub‐optimal controllers to be designed that strike a balance between performance and computational cost. The suboptimality of the truncated policies is formally analyzed and closed form expressions are provided for the performance loss due to the use of the truncation scheme. Finally, the paper concludes with a comparative analysis of the truncated versions of the proposed policy parametrization and other standard policy parametrizations through numerical simulations.

Sequential time scaling transformation technique for time-delay optimal control problem

The time-scaling transformation technique used within the computational framework of control parameterization serves as an effective method for the optimization of control switching time as well as the control value for time-delay optimal control problems. However, the conventional time-scaling transformation stipulates that the switching times for all control components must be identical, which may not be feasible in real-world scenarios. To address this limitation, we introduce the sequential time-scaling transformation technique for solving time-delay optimal control problems. By sequentially applying control parameterization and time-scaling transformation to each of the control variable, the new technique enables the configuration of a varying number of segments for the control, and the switching time for each control component can be adaptively selected. Numerical results demonstrate that our approach not only achieves superior cost performance but also offers enhanced flexibility in control strategy.

Robust Adaptive Control of the Offshore Produced Water Treatment Process: An Improved Multivariable MRAC-Based Approach

The application of deoiling hydrocyclone systems as the downstream of three-phase gravity separator (TPGS) systems is one of the most commonly deployed produced water treatment processes in offshore oil and gas production. Due to the compact system’s complexity and tailor-made features, it is always challenging to develop some optimally coordinated control solution for the coupled hydrocyclone and TPGS systems. It is obvious that coordinated control can better fulfill legislative discharge regulation by robustly maintaining high separation efficiencies. This paper presents a new control solution for a set of integrated hydrocyclone and TPGS systems by applying an improved multi-variable model reference adaptive control (MV-MRAC) approach with the aim of achieving both asymptotic output tracking and unknown disturbance rejection. A robust MV-MRAC controller design is proposed based on a control parameterization derived from a factorization of a high-frequency gain matrix Kp=LDS as a product of three matrices, where L represents unity lower triangular, D=sign(D) represents diagonal, and S represents positive definite, and a teaching–learning-based optimization (TLBO) algorithm for optimizing the adaption rates. The developed solution is analyzed and compared with a commonly deployed PI control solution on a model that is derived from a lab-scale produced water treatment process. This simulation study demonstrates the promising potential of the proposed control solution compared with the currently deployed PI control solution.

Tracking Performance of Feedback Systems Over a Fading Channel With Limited Bandwidth.

In this study, we investigated the optimal tracking performance (OTP) of feedback control systems with limited bandwidth and colored noise in a fading channel. For the steady state of the feedback control systems, an equivalent average channel (EAC) model was developed by retaining the effects of the first and second moments of the multiplicative channel output, and on the basis of the coprime decomposition, all-pass factorization, and Youla parameterization of controllers, exact expressions for the OTP were derived by designing two compensators. The expressions quantitatively show the relationship between the OTP and inherent features of the plant. Specifically, the directions and locations of unstable poles (UPs) and nonminimum phase (NMP) zeros adversely affect the tracking performance. Furthermore, the bandwidth limitation and the presence of colored noise also degrade the tracking performance. Finally, our conclusions were verified by considering a numerical arithmetic example.

Sequential adaptive switching time optimization technique for maximum hands-off control problems

<abstract><p>In this paper, we consider maximum hands-off control problem governed by a nonlinear dynamical system, where the maximum hands-off control constraint is characterized by an $ L^{0} $ norm. For this problem, we first approximate the $ L^{0} $ norm constraint by a $ L^{1} $ norm constraint. Then, the control parameterization together with sequential adaptive switching time optimization technique is proposed to approximate the optimal control problem by a sequence of finite-dimensional optimization problems. Furthermore, a smoothing technique is exploited to approximate the non-smooth maximum operator and an error analysis is investigated for this approximation. The gradients of the cost functional with respect to the decision variables in the approximate problem are derived. On the basis of these results, we develop a gradient-based optimization algorithm to solve the resulting optimization problem. Finally, an example is solved to demonstrate the effectiveness of the proposed algorithm.</p></abstract>

Efficient tuning for motion control in diverse systems: a Bayesian framework

Feed-forward control is widely used in motion control systems that involve repetitive tasks, leading to substantial performance improvements. This paper presents a model-free feedforward optimization framework centred around Bayesian Optimization (BO). Bypassing the need for exhaustive system modelling, the method directly optimizes the Iterative Learning Control (ILC) degrees of freedom based on a user-defined parametrization of the feed-forward controller. Experimental results on a motion control application show significant improvements with respect to more classical ILC. A notable advantage emerges when dealing with an industrially relevant case with multiple similar plants; the optimizer is shown to adeptly adjust the feed-forward control to be compliant with the response of the measured system.

On the correlation of local collocation and control parameterization methods

On the correlation of local collocation and control parameterization methods

Cooperative optimal train operation algorithm for utilizing regenerative braking energy

The efficient use of regenerative braking energy between trains can significantly reduce the net traction energy consumption in urban rail transit systems, and has attracted considerable attention in recent years. An effective way of using regenerative braking energy is to adjust the train's coasting or cruising phase to an acceleration phase to match the braking phase of a nearby train within the same substation. This paper formulates the train driving phase adjustment problem as a cooperative optimal control problem, where a novel energy constraint is introduced to ensure efficient use of regenerative braking energy during the adjusted phase with optimal traction effort. By applying the control parameterisation method and elaborate handling of the energy constraint and the non-smooth control bound constraint, we transform the formulated problem into a nonlinear programming problem. We then use the sequential quadratic programming algorithm to solve the resulting problem, with the gradients of the cost and constraint functions computed using the sensitivity method. Numerical examples based on real-world data for a subway line show the effectiveness of the proposed method and its advantages over a genetic algorithm in terms of energy savings and computational efficiency.

Stability optimization of time-delay systems with zero-location constraints applied to non-collocated vibration suppression

We present an active control method for achieving non-collocated vibration absorption, implemented on a lumped mass system. The task of suppressing vibrations at a number of frequencies, at a target mass is recast into a problem of assigning zeros of the transfer function from the external excitation force to the position of the target mass. The controller design involves computing the controller parameters by utilizing the available output feedback to directly assign a set of zeros on the imaginary axis while simultaneously preserving the overall stability with a sufficient margin. The design also takes into account delays in the feedback path. The presence of delays leads to an infinite dimensional system for which, there exists in general, infinitely many characteristic roots. The requirement of achieving sufficient damping in the resulting closed-loop system together with suppressing vibrations of the desired frequency leads to a constrained optimization problem of minimizing the spectral abscissa function subject to zero-location constraints. These constraints exhibit polynomial dependence on the controller parameters. We present two approaches for controller parameterization for the single and multiple input case. Both approaches are based on constraint elimination and exploit the property that the constraints are affine in a selection of the gain parameters. Finally, the methodology is verified by simulating on a spring–mass–damper system following which, it is then validated experimentally on a laboratory setup.

Data-driven fixed-structure frequency-based [formula omitted] and [formula omitted] controller design

The frequency response data of a system is used to design fixed-structure controllers for the ℋ2 and ℋ∞ synthesis problem. The minimization of the two and infinity norm of the transfer function between the exogenous inputs and performance outputs is approximated by a convex optimization problem involving Linear Matrix Inequalities (LMIs). A very general controller parametrization is used for continuous and discrete-time controllers with a matrix transfer function or state-space representation. Numerical results indicate that the proposed data-driven method gives equivalent performance to model-based approaches when a parametric model is available.

Dynamic optimal control of flow front position in injection molding process: A control parameterization-based method

High dynamic and precise control of process variables within permissible limits is the key to high product quality in the injection molding industry. Among these variables, the injection flow rate of molten polymer is particularly significant. In this paper, an effective optimal open-loop and state feedback controller design method is designed to realize the optimal tracking control of the melt polymer flow front position flow of melt polymer fluid during injection molding. To this end, the dynamic model of the filling process is firstly established, taking into account the nonlinearity of hydraulic control system and the effect of molten polymer flow on the dynamics of the injection ram, and then the dynamic optimal tracking control problem of flow front position of molten polymer in injection molding machine is proposed. Then, an open-loop controller and a multi-level feedback control law are well designed, wherein the control signal and the control feedback kernels are parameterized by control parameterization. The controller design problems are transformed into sequential optimal parameter decision problems. The explicit expressions of the gradient information of the objective function and constraints on the parameters of the decision variables are solved by using the state sensitivity equation analysis method, and the gradient information is combined with the nonlinear programming algorithm to solve the optimization problems efficiently. Finally, the viability and effectiveness of the proposed design method are verified by numerical simulations.

Process optimization of microbial fermentation with parameter uncertainties via distributionally robust discrete control

There are some uncertain kinetic parameters in microbial fermentation system because of the unclear intracellular metabolic mechanisms. Considering the affection of these uncertain parameters on system performance, dynamic process optimization of the fermentation system can be modeled as a distributionally robust discrete control problem under moment uncertainty, which aims to maximize the mean productivity by optimizing the discrete-valued dilution rate function. Based on duality theory, the established min–max discrete optimal control problem is first transformed into a single level minimization problem, which is then discretized into a large-scale parameter optimization problem with semi-infinite constraint via time transformation and control parameterization. A new two-step estimation of distribution algorithm is developed to solve the obtained large-scale optimization problem. Numerical results show the feasibility and effectiveness of the proposed solution approach together with the superiority of the obtained control strategy considering parameter uncertainties.

Optimized parametrization of adaptive controllers for enhanced current regulation in grid‐tied converters

SummaryGrid‐connected converters play a significant role in renewable energy systems, acting as a crucial interface between the inverter and the electrical grid, often incorporating LCL filters. One of the primary challenges in controlling grid‐injected current is the grid uncertainty, which can have a direct impact on the resonance frequency of the LCL filter. Adaptive controllers are feasible to deal with this kind of situation. However, the setup of these controllers requires an experienced designer. This work proposes a novel approach for parametrization of adaptive controllers, as well as their gain initialization, using particle swarm optimization, considering performance indexes and stability constraints. The proposed approach improves the current tracking performance and avoids relevant overshoots during transient regimes. The experimental results of current regulation in a grid‐tied voltage source inverter with an LCL filter provide compelling evidence for the effectiveness of this method. The optimized control structure exhibits significantly lower regulation errors and demonstrates improved tracking dynamics when compared to non‐optimized control structures.

Parametrization and Optimal Tuning of Constrained Series PIDA Controller for IPDT Models

The new modular approach to constrained control of higher-order processes with dominant first-order dynamics using generalized controllers with automatic resets (ARCs) is addressed. The controller design is based on the multiple real dominant pole (MRDP) method for the integrator plus dead time (IPDT) process models. The controller output constraints are taken into account by inserting the smallest numerator time constant of the controller transfer function into the positive feedback loop representing the automatic reset (integral) term. In the series realization of the proportional–integral–derivative–acceleration (PIDA) controller (and other controllers with even derivative degree), the time constant mentioned is complex, so only the real part of the time constant has been used so far. Other possible conversions of a complex number to a real number, such as the absolute value (modulus), can be covered by introducing a tuning parameter that modifies the calculated real time constant and generalizes the mentioned conversion when designing controllers with constraints. In this article, the impact of the tuning parameter on the overall dynamics of the control loop is studied by simulation. In addition, an evaluation of the stability of the closed-loop control system is performed using the circle criterion in the frequency domain. The analysis has shown that the approximation of the complex zero by its real part and modulus leads to a near optimal response to the set point tracking. The disturbance rejection can be significantly improved by increasing the tuning parameter by nearly 50%. In general, the tuning parameter can be used to find a compromise between servo and regulatory control. The robustness and applicability of the proposed controller is evaluated using a time-delayed process with first-order dominant dynamics when the actual transfer function is much more complicated than the IPDT model. A comparison of the proposed MRDP-PIDA controller with series PI, PID and PIDA controllers based on a modified SIMC method has shown that the MRDP-PIDA controller performs better than the SIMC method, although the SIMC uses a more complex process model.

Reconfiguration for UAV Formation: A Novel Method Based on Modified Artificial Bee Colony Algorithm

The flight formation of unmanned aerial vehicles (UAVs) needs to be reconfigured whenever necessary to cope with complex environments and varying tasks. However, the continuity, nonlinearity and high dimensionality of the UAV formation control parameters bring significant challenges to the efficiency and safety of UAV formation reconfiguration. To this end, this paper proposes a reconfiguration strategy of the UAV formation based on a modified Artificial Bee Colony (ABC) algorithm, which ensures superior efficiency and safety level simultaneously. Specifically, we first formulate the formation reconfiguration problem minimizing the time consumed for reconfiguration under the constraints of safety and connection. Then the continuous optimization problem is discretized by using the control parameterization and time discretization (CPTD) method. Finally, we use a modified ABC algorithm to find the solution of formation reconfiguration. Extensive performance evaluations are conducted to verify the superiority of the proposed method. It is concluded that the proposed algorithm achieves a better performance than the existing approaches in literature in solving the problem of 3-D formation reconfiguration.

Enhanced affine formation maneuver control using historical acceleration command

SummaryHow a network of multiple vehicles gets to a goal formation from an initial formation is as important as reaching the goal formation. Despite that stress matrix has been well applied to construct distributed affine formation control, most works have focused on the stabilization or stability issues and paid little attention to the performance regulation or the control parameterization issues. In this paper, we aim to design an error‐model based distributed control for the affine formation maneuver of second‐order multi‐agent systems (MASs), and to demonstrate the advantages of the control approach in performance tuning. The basic idea behind the control design is to force the actual error‐trajectory dynamics of each controlled follower to approximate that of an ideal second‐order error model. The designed controller possesses a notable feature that the historical acceleration command (HAC) is used to enhance system performance during the formation maneuvers. By a theory tool of neutral functional differential equations, we develop a delay‐independent condition on the design parameters, under which the system stability is robust to the actively introduced HAC. Furthermore, we derive an inequality describe the relationship between the ultimate bounds of tracking errors and the delay parameter. This paper presents a clear mechanism to tune the comprehensive performance of affine formation control. Simulation results show the effectiveness of the stability condition and the performance‐tuning mechanism, as well as the possible fragility of the system stability to the delay when the condition is not satisfied.

Selection/control concurrent optimization of BLDC motors for industrial robots.

This paper aims to concurrently select and control off-the-shelf BLDC motors of industrial robots by using a synergistic model-based approach. The BLDC motors are considered with trapezoidal back-emf, where the three-phase (a,b,c) dynamics of motors are modeled in a mechatronic powertrain model of the robot for the selection and control problem, defining it as a multi-objective dynamic optimization problem with static and dynamic constraints. Since the mechanical and electrical actuators' parameters modify the robot's performance, the selection process considers the actuators' parameters, their control input, operational limits, and the mechanical output to the transmission of the robot joints. Then, three objective functions are to be minimized, the motor's energy consumption, the tracking error, and the total weight of installed motors on the robot mechanism. The control parameterization approach via a cascade controller with PI controllers for actuators' voltage and a PID controller for actuators' torque is used to solve the multi-objective dynamic optimization problem. Based on simulations of the closed-loop system, a Pareto front is obtained to examine trade-offs among the objective functions before implementing any actuators in the existing robotic system. The proposed method is tested on an experimental platform to verify its effectiveness. The performance of an industrial robot with the actuators originally installed is compared with the results obtained by the synergic approach. The results of this comparison show that 10.85% of electrical power can be saved, and the trajectory tracking error improved up to 57.41% using the proposed methodology.

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.