Set-point Tracking Controller Research Articles

A hierarchical multi-parametric programming approach for dynamic risk-based model predictive quality control

In this work, we present a hierarchical batch quality control strategy with real-time process safety management. It features a multi-time-scale decision-making framework augmenting: (i) Risk-aware model predictive controller for short-term set point tracking and dynamic risk control under disturbances; (ii) Control-aware optimizer for long-term quality and safety optimization over the entire batch operation; (iii) Intermediate surrogate model to bridge the timescale gap by readjusting the optimizer operating decisions for the controller. All of the above problems are solved via multi-parametric mixed-integer quadratic programming with a key advantage to generate offline explicit control/optimization laws as affine functions of process and risk variables. This allows for the design of a fit-for-purpose risk management plan prior to real-time implementation, while reducing the need for repetitive online dynamic optimization. A unified process model is used to underpin the consistency of hierarchical operational optimization. The proposed approach offers a flexible strategy to integrate distinct decision-making time scales which can be selected separately tailored to the process-specific need of control, fault prognosis, and end-batch quality control. A T2 batch reactor case study is presented to showcase this approach to systematically address the interactions and trade-offs of multiple decision layers toward improving process efficiency and safety.

Intelligent MIMO ORFBLS-Based Setpoint Tracking Control with Its Application to Temperature Control of an Industrial Extrusion Barrel

Intelligent MIMO ORFBLS-Based Setpoint Tracking Control with Its Application to Temperature Control of an Industrial Extrusion Barrel

Event-Triggered Constrained Optimal Control for Organic Rankine Cycle Systems via Safe Reinforcement Learning.

The organic Rankine cycle (ORC) is an effective application for converting low-grade heat sources into power and is crucial for environmentally friendly production and energy recovery. However, the inherent complexity of the mechanism, its strong and unidentified nonlinearity, and the presence of control constraints severely impair the design of its optimal controller. To solve these issues, this study provides a novel event-triggered (ET) constrained optimal control approach for the ORC systems based on a safe reinforcement learning technique to find the optimal control law. Instead of employing the usual non-quadratic integral form to solve the control-limited optimal control problems, a constraint handling strategy based on a relaxed weighted barrier function (BF) technique is proposed. By adding the BF terms to the original value function, a modified value iteration algorithm is developed to make the control input solutions that tend to violate the constraints be pushed back and maintained in their safe sets. In addition, the ET mechanism proposed in this article is critically required for the ORC systems, and it can significantly reduce the computational load. The combination of these two techniques allows the ORC systems to achieve set-point tracking control and satisfy the control restrictions. The proposed approach is conducted based on a heuristic dynamic programming framework with three neural networks (NNs) involved. The safety and convergence of the proposed approach and the stability of the closed-loop system are analyzed. Simulation results and comparisons are presented to demonstrate its effectiveness.

Improved Set-point Tracking Control of an Unmanned Aerodynamic MIMO System Using Hybrid Neural Networks

Artificial neural networks (ANN), an Artificial Intelligence (AI) technique, are both bio-inspired and nature-inspired models that mimic the operations of the human brain and the central nervous system that is capable of learning. This paper is based on a system that optimizes the performance of an uncertain unmanned nonlinear Multi-Input Multi-Output (MIMO) aerodynamic plant called Twin Rotor MIMO System (TRMS). The pitch and yaw angles which are challenging to control and optimize in practice, are being used as the input to the Nonlinear Auto-Regressive with eXogenous (NARX) model, and eventually trained. The training features use the Matlab Deep Learning Toolbox. The NARX structure has its core in the neural networks’ architecture. Data is collected from the TRMS testbed which is used to train the network. ANN as a Hybrid intelligent control strategy of ANN in combination with Pattern Search and Genetic Algorithm, is then utilized to optimize the parameters of the neural networks. At the end it was validated, tested and the optimized system run in simulation and compared with other intelligent and conventional controllers, with the proposed controller outperforming them, giving a very fast tracking control, stable and optimal performance that satisfactorily met all our design requirements.

Relocated internal model control based cascade control strategy for stable and unstable systems with delay

To control unstable and stable plants a new series cascade control structure (SCCS) is proposed. The proposed SCCS incorporates two or three controllers (setpoint tracking controller, secondary disturbance rejection controller and stabilising controller for only unstable plants). Internal model control scheme (IMCS) augmented with integration of square error (ISE) minimisation along with robustness considerations are applied to design the secondary loop disturbance rejection controller. In contrast, relocated IMCS augmented with ISE minimisation is applied for the outer loop or setpoint tracking controller. Routh Hurwitz stability criteria and maximum sensitivity considerations are used to design the proportional-derivative (PD) controller, which stabilises the unstable plant. It is important to note that the suggested SCCS only needs four controller parameters to be tuned, which is less than the recently reported techniques. Robust stability analysis of the proposed SCCS is performed in the presence of uncertainty. The simulation results depict that the suggested approach imparts pre-eminent improvement in closed-loop performance such as faster setpoint tracking and better disturbance rejection for nominal and perturbed plants.

Combining [formula omitted] and resonant control to enable high-bandwidth measurements with a MEMS force sensor

We report high-performance control of a MEMS force sensor to provide high-bandwidth reference tracking under uncertain conditions. A key novelty is the implementation of a zero-displacement feedback control system that combines a mixed-sensitivity H∞ controller for setpoint tracking with a resonant controller to augment additional damping to the system. To make the device compatible with various samples, we propose a method to adaptively improve force tracking performance when the force sensor comes into contact with a relatively stiff sample. Performance of the closed-loop system is evaluated by conducting force tracking experiments on two samples with different stiffnesses. The results show that, when operated in closed loop, a resolution of 9.3 nN and a force tracking bandwidth of 1000 Hz can be achieved.

Generalized optimal 3-degree of freedom parallel cascade control strategy for stable, unstable and integrating chemical processes

To control stable, unstable and integrating chemical processes, a new three-degree of freedom (3DOF) decoupled parallel cascade control architecture (PCCA) is proposed. The proposed PCCA assimilates two/three controllers (secondary disturbance rejection controller, stabilizing controller for only unstable/integrating plants and set-point tracking controller). Internal model control approach (IMCA) augmented with integral of squared error (ISE) minimization and robustness considerations are adopted to design both the secondary loop disturbance rejection controller and the outer-loop set-point tracking controller with the satisfactory performance-robustness tradeoff. Maximum sensitivity constraints and Routh-Hurwitz stability criteria are applied to design the proportional-derivative (PD) controller which stabilizes the unstable and integrating primary plant. It is worth mentioning that the suggested decoupled 3DOF PCCA requires tuning of only two/three controller parameters which are less when compared to recently reported strategies. Robust stability of the suggested 3DOF PCCA is studied in the presence of uncertainty. The simulation results epitomize that the suggested methodology imparts pre-eminent enhancement in closed-loop performance (faster setpoint following and disturbance elimination) for both nominal as well as perturbed plants.

Data-driven worst case model predictive control algorithm for propylene distillation column under uncertainty of top composition

Composition soft sensors have wide application in the distillation process. In this study, considering the limitation of the prediction ability of the composition soft sensor, a data-driven worst case model predictive control of propylene distillation column is proposed to hedge against the uncertainty of top composition. Firstly, based on the compartmental method and the dynamic mechanism model, a linear state space model of the distillation column is constructed. Aiming at dealing with the uncertainty of top propylene content caused by composition soft sensor, the data-driven uncertainty set is constructed by the combination of principal component analysis and kernel density estimation based on the historical data. Then, the certainty equivalent, traditional worst case, data-driven worst case, set-point tracking and offset-free model predictive control algorithm are designed. Finally, a case study of composition control in a propylene distillation column is carried out. Compared with other strategies, the proposed algorithm ensures the quality of the product while achieving small quality surplus and low operating cost.

Real-time control and monitoring of drilling fluids density by fuzzy-based control system

The drilling fluids play a significant role in the oil drilling process, being its physicochemical properties the focus of the operation control. Nowadays, the control methods are usually based on manual dosing of additives by the specialized operators, where the recipes are obtained by pilot or bench tests, demanding a greater amount of raw material, increasing the operation time and costs. Control strategies of drilling fluids properties based on fuzzy logic may contribute to a high reliability and safety for human resources in drilling operations, a higher process efficiency and the mitigation of environmental impacts. This research aimed to propose and develop an automated flow loop system for fluid preparation with real-time monitoring, control, and self-correction of the drilling fluid density. The control strategy was based on fuzzy logic and used the Mamdani-type inference rules as the basis for developing a Fuzzy-PI controller. The performance of the proposed Fuzzy-PI controller was compared to a classic PI controller in disturbance-rejection and setpoint-tracking control problems. Beyond efficient control, the Fuzzy-PI controller enabled a reduction in raw material consumption of 63% for barite and 38% for water, in the disturbance-rejection control scenario; and 21% for barite and 47% for water, in the setpoint-tracking control scenario.

Optimal Sub-References for Setpoint Tracking: A Multi-level MPC Approach

We propose a novel method to improve the convergence performance of model predictive control (MPC) for setpoint tracking, by introducing sub-references within a multilevel MPC structure. In some cases, MPC is implemented with a short prediction horizon due to limited on-line computation capacity, which could lead to deteriorated dynamic performance. The introduced multi-level optimization method can generate proper sub-references for the MPC setpoint tracking problem, and efficiently improve the dynamic performance. In the higher level a specific performance criterion is taken as the objective, while explicit MPC is utilized in the lower level to represent the control input. The generated sub-references are then used in MPC for the real system with prediction horizon restrictions. Setpoint-tracking MPC for linear systems is used to illustrate the approach throughout the paper. Numerical simulations show that MPC with sub-references significantly improves the convergence performance compared with regular MPC with the same prediction horizon. Thus, it can be concluded that MPC with sub-references has a high potential to tackle more complicated control problems with limited computation capacity.

Design of I-PD Controller Based Modified Smith Predictor for Processes With Inverse Response and Time Delay Using Equilibrium Optimizer

In the process control industry, it is arduous to control some integrating or unstable processes since they involve time delays and have an inverse response. Conventional controllers such as PID cannot provide sufficient control performance alone in the control of these systems. This article proposes a control algorithm based on an I-PD-based Smith predictor for the control of time-delayed integrating or unstable inverse processes. The controller parameters are tuned by using the Equilibrium optimizer (EO) algorithm, which is presented in the literature in 2020, in the proposed control approach. The EO algorithm aims to determine the optimal controller parameters by minimizing the error and control signal using a multi-objective function based on ITAE performance criterion. Thus, the controller parameters that will provide the set-point tracking and disturbance rejection control most properly can be determined. Simulation studies are conducted based on different process structures to evaluate the performance of the proposed method. The proposed method is compared with studies from the literature in terms of set-point tracking, parameter uncertainties, control signals, and disturbance rejection. It is seen that the transient responses and disturbance rejection of the time-delayed and inverse response integrating or unstable processes are improved with the proposed method.

Observer-based Control Design for Overhead Crane Systems

This paper proposes an observer-based control design with Disturbance Feedback Control (DFC) for overhead crane systems. DFC is a technique to improve the disturbance rejection capabilities of existing control loops. The crane system is modelled with 3D dynamics and linearized. Payload sway angles are estimated by a Kalman Filter. A state feedback controller for setpoint tracking and a DFC for disturbance rejection are designed using Linear Matrix Inequalities. Both simulation and experimental results show that the observer-based control with DFC can estimate the sway angle and is able to attenuate disturbance inputs better than the conventional observer-based control. The proposed design can thus achieve practical angle sensor-less control with a retro-fit modification of an existing control.

On the Design of Constrained PI-Like Output Feedback Tracking Controllers via Robust Positive Invariance and Bilinear Programming

In this paper, we design a novel PI-like output feedback tracking controller for linear systems subject to state and input constraints. The proposed solution exploits the internal model principle to design via robust positive invariance and the Extended Farkas’ Lemma, a constrained set-point tracking controller. The considered polyhedral setup results in a bilinear optimization design problem that can be solved offline, allowing to simultaneously determine the sets of admissible set-points and plant’s initial conditions. The proposed solution guarantees asymptotic offset-free set-point tracking, local stability, and constraints fulfillment. Simulation results show the effectiveness of the proposed design and contrast it with an alternative scheme.

Coordinated control of heat-power integrated energy system using zone model predictive control with variable zone width

• Evaluation of the thermal-electric interactions within the IES. • Heat-power coordinated control scheme is proposed to improve the flexibility of IES. • Zone-MPC is developed for the heat control to unlock better power side performance. • Zone width variation function is designed to release optimization space flexibly. • The applicability of the proposed method is fully demonstrated in various scenarios. Integrated energy system (IES) with high-penetration of renewable energy is one of the important development directions of future energy systems. However, the fluctuations on both the source and load sides bring great challenges to the stable operating of IES, and the strong interactions between multiple types of energies further increase the control difficulties. This paper investigates the dynamic differences in the thermal and power processes of the IES by simulating a typical combined heat and power IES model. The response speed at the thermal side is found to be over five times slower than that at the power side. Further considering the different control requirements for the heat and power supply, a novel heat-power coordinated control strategy based on the idea of zone model predictive control is proposed to improve the flexibility of the IES. The conventional set-point tracking control is applied at the power side to eliminate the offset between the supply and demand quickly, while the thermal side control is relaxed to a variable-width zone control to unlock superior regulation performance at the power side. A series of simulation studies are carried out under normal, frequent electric-side disturbance, extreme weather and low-carbon operating scenarios. The results demonstrate that the proposed approach can greatly improve the electrical control performance of the IES with slight degradations on the thermal side. This paper points to a new way of using zone predictive control to exploit the differences between multiple forms of energies for the flexible operation of modern energy systems.

Reinforcement Learning and Optimal Setpoint Tracking Control of Linear Systems With External Disturbances

In order to deal with optimal setpoint tracking (OST) problems, a discounted cost function has been introduced in the existing work. However, the optimal tracking controllers developed according to the discounted cost function may not ensure asymptotic tracking and the stability of the closed-loop systems. To overcome these limitations, in this article, we propose a novel adaptive optimal control method to minimize a cost function without a discount factor. The proposed method starts from a reformulation of the infinite-horizon OST problem for linear discrete-time systems with external disturbances. We derive an algebraic Riccati equation for solving the OST problem, whose solution is uniquely determined under mild conditions. It is proved that the obtained controller accommodates the disturbance and realizes the output tracking with zero steady-state error. In the framework of reinforcement learning, a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> -learning algorithm is devised to learn the suboptimal control policy by using measured data. The present learning algorithm does not require that the disturbance is measurable and can be implemented completely model-free. Finally, two examples on dc motor system and F-16 aircraft plant are provided to corroborate our design methodology.

New LADRC scheme for fractional-order systems

Active Disturbance Rejection Control (ADRC) is a very promising recent concept for the design of controllers to control systems with uncertainties. Based on an extended state observer, this control structure allows both external disturbances and modeling uncertainties to be actively rejected. The use of the active rejection control of disturbances is gaining more and more interest among the system control community. This is mainly due to its easy design, undemanding implementation and robustness. In this paper, three solutions using the ARDC structure to control fractional-order system are discussed. Two methods taken from the literature are briefly introduced, namely, the fractional-order dynamics rejection scheme (FODRS) and the fractional linear active disturbance rejection control (FLADRC). The basic ideas and technical formulations of these two are presented. A third method, based on the robustness performance introduced by fractional-order controllers, is also proposed in this paper. The proposed design method of the set-point tracking controller is based on the Bode’s ideal transfer function (Bode’s ITF). This will improve the robustness of the control scheme.

An Improved Particle Swarm Optimization with Multiple Strategies for PID Control System Design

In this paper, an improved particle swarm optimization (PSO) with multiple subpopulations is developed for PID control system designs. The original single population needs to be divided into several subpopulations, and each subpopulation then tackles a corresponding performance index of the system. Under this proposed structure, several PID controllers can be simultaneously designed to meet different performance indexes when the algorithm is executed only one time. It is a great improvement because the general PSO algorithm with a single population can only deal with one performance index. To demonstrate the feasibility of the proposed scheme, a complicated chemical nonlinear process called the continuously stirred tank reactor (CSTR) is illustrated. Three different kinds of control operations are simulated including the step response control, set-point tracking control, and unstable equilibrium point control. For each control case five different performance indexes are assigned to guide the PID controller design combined with the nonlinear CSTR system. Simulation results will sufficiently confirm the superiority of the proposed algorithm.

Adaptive Internal Model Control of SCR Denitration System Based on Multi-Objective Optimization

Many thermal power plants use selective catalytic reduction (SCR) systems to complete flue gas denitration. The system has the characteristics of large inertia, large delay and nonlinearity. At the same time, it is difficult to use the controller under a single working condition to meet the control task of the system under the full working conditions. In order to solve the above control difficulties, This paper proposes a two-degree-of-freedom internal model control (2-DOF-IMC) method based on controller parameter adaptation and multi-model adaptation to realize the control of the full working conditions of the SCR system. First, the intelligent identification method based on Differential evolution quantum particle swarm optimization (DEQPSO) is used to obtain the sub-model of ammonia injection-SCR outlet Nitrogen Oxide (NOx) concentration in typical working conditions. A 2-DOF-IMC controller under each sub-model is established. Then, aiming at system set point tracking performance, anti-disturbance performance, and control energy consumption, the Pareto optimal solution of each controller is obtained by using the Non-dominated Sorting Genetic Algorithms-II (NSGA-II) algorithm based on chaotic mutation. Finally, the controller parameter adaptive strategy is designed based on the Takagi-Sugeno (T-S) fuzzy model, and the multi-model adaptive strategy is designed based on the recursive bayesian probability weighting. Through the dynamic performance test and the anti-disturbance performance test, it is verified that the 2-DOF-IMC based on controller parameter adaptation and multi-model adaptation has good control performance and adaptability to all working conditions. The method proposed in this paper combines the advantages of multi-parameter and multi-model strategies, further improves the control quality, and provides a new solution for the control of thermal power plant SCR system.

Linear Active Disturbance Rejection Control with a Fractional-Order Integral Action

Linear active disturbance rejection control (LADRC) is a powerful control structure thanks to its performance in uncertainties, internal and external disturbances estimation and cancelation. An extended state observer (ESO) based controller is the key to the LADRC method. In this article, the LADRC scheme combined with a fractional-order integral action (FOI-LADRC) is proposed to improve the robustness of the standard LADRC. Using the robust closed-loop Bode’s ideal transfer function (BITF), an appropriate pole placement method is proposed to design the set-point tracking controller of the FOI-LADRC scheme. Numerical simulations and experimental results on a cart-pendulum system will illustrate the effectiveness of the proposed FOI-LADRC scheme for the disturbance rejection, the set-point tracking and the improved robustness. To illustrate the LADRC control schemes and to verify the performance of the proposed FOI-LADRC, compared to the standard LADRC and IOI-LADRC structures, two tests will be carried out. First, simulation tests on an academic example will be presented to show the effect of the different parameters of the control law on the performance of the closed-loop system. Then, these three control structures are implemented on an experimental test bench, the cart-pendulum system, to show their efficiency and to show the superiority of the proposed method compared to the two other structures.

Constrained set-point tracking control via output feedback for a class of nonlinear cascaded systems

This article proposes a constrained set-point tracking control scheme via output feedback for a class of nonlinear cascaded systems. The system in question allows for input-to-state stable (ISS) unmodelled dynamics, uncertain nonlinearities, and additive nonvanishing disturbances in the input channel. A reduced-order extended state observer (RESO) is delicately constructed to observe unmeasured states and to estimate the external disturbances. ISS changing supply rates technique with uncertain supply pair is developed to deal with the unmodelled dynamics. The tan-type Barrier Lyapunov function (BLF) is introduced to guarantee the tracking error converge to the origin without violation of the output constraint and all the closed-loop signals are bounded in the semi-global sense. The numerical example of a simple-link robot arm (SLRA) with and without an output constraint illustrates our theoretical results.