Predictive Functional Control Research Articles

Deep Learning based Model Predictive Controller on a Magnetic Levitation Ball System

The magnetic levitation (maglev) ball system is a prototypical Single-Input-Single-Output (SISO) system, characterized by its pronounced nonlinearity, rapid response, and open-loop instability. It serves as the basis for many industrial devices. For describing the dynamics of the maglev ball system precisely in the pseudo linear model, the long short-term memory (LSTM) based auto-regressive model with exogenous input variables (LSTM-ARX) is proposed. Firstly, the LSTM network is modified by incorporating the auto-regressive structure with respect to sequence input, allowing it to deduce a locally linearized model without the need for Taylor expansion. Then, the LSTM-ARX model is transformed into a linear parameter varying (LPV) state space model, and upon this foundation, a model predictive controller (MPC) is proposed. Specifically, when deducing the MPC, the deep learning-based model is linearized by fixing its state input at the current state, so that the nonlinear, non-convex optimization problem can be converted to a finite-horizon quadratic programming problem, thereby deriving the explicit form of MPC. To further enhance the efficiency of the controller in real-time control tasks, a predictive functional controller (PFC) is proposed. It employs multiple nonlinear functions to fit the control sequence, thereby reducing the number of decision variables of the on-line optimization problem in MPC. The proposed controller was successfully applied to the real-time control of the maglev ball system. Simulation and real-time control experiments have validated the improvement in transient performance and efficiency of the LSTM-ARX model-based PFC (LSTM-ARX-PFC).

Predictive functional control for separation processes by liquid-liquid extraction

A separation process by liquid-liquid extraction is a well-known and widespread industrial technology implemented to quantitatively recover valuable chemical elements. In the nuclear industry, such processes have been used for decades to recover uranium and plutonium from spent fuel. The process is non-linear and time constants vary over a wide range. Former studies on a simplified model showed linear controllers such as PID were not adapted to regulate these separation processes. The objective of this study is to propose process monitoring by using available physical models within the PAREX code and to validate the feasibility to monitor a separation process by using directly the PAREX code as a black box. The Predictive Functional Control (PFC) command law manages to monitor non-linear separation processes by liquid-liquid extraction, when using an existing physical model implemented in the PAREX code. An online alignment of the model on process values is necessary to keep the model sufficiently representative to predict the future behaviour of the process. As a reference benchmark, the PID control loop is also simulated with the physical model. The PFC and PID regulations are compared to evaluate the gain of using physical models implemented in the PAREX code. A simulation tool has been developed to implement the PID and Predictive Functional Control (PFC) controllers for separation processes by liquid-liquid extraction. The PFC command law manages to monitor non-linear separation processes, when using a physical model connected to the PAREX code. Even if the PID controller may be locally more efficient, the great strength of the PFC controller is to enable good performances on wider operating conditions, with an easier parametrization. The PFC algorithm is a mean to deal with the process characteristic features, like non-linearity and time constant change. The PFC controller appears to be a good candidate for experimental tests. A mid-term objective is to include the state estimator tool in the control loop to consolidate the controlled variable measurements. These developments may be regarded as an add-on module in a digital factory concept. Results shown in this article are only from simulation. For the sake of data confidentiality, studies with the PAREX code cannot be published and numerical parameters of the process are normalized. These simulations will be validated during further experimental tests.

Design of a model‐free controller based on predictive functional control

AbstractIntelligent‐PID (i‐PID) control proposed by Fliess is a simple control algorithm. The controller is designed based on ultra‐local model, and consisted of PID type controller and derivatives of reference signal and controlled variables. Authors have considered discrete i‐PID controller and its properties, and one of the result was that PD controller was sufficient in discrete time domain. In discrete i‐PID controller, PD type controller is still required to ensure convergence of controlled error to zero, and PD type parameters affects convergence property, fast‐response property and stability. In this paper, predictive functional control (PFC) based on an ultra‐local model is proposed. By introducing of PFC, controlled variable converge to reference value without PD type controller. User‐specified parameters of the proposed controller is smaller than the conventional i‐PID controller. Characteristics of the proposed controller are compared with discrete i‐PID controller by numerical examples.

Autonomous predictive maintenance of quadrotor UAV with multi-actuator degradation

Abstract With the wide application of quadrotor unmanned aerial vehicles (UAVs), the requirements for their safety and reliability are becoming increasingly stringent. In this paper, based on the feedback of airframe performance health perception information and the predictive function control strategy, the autonomous maintenance of a quadrotor UAV with multi-actuator degradation is realised. Autonomous maintenance architecture is constructed by the predictive maintenance (PdM) idea and the Laguerre function model predictive pontrol (LF-MPC) strategy. Using the two-stage Kalman filter (TSKF) method, based on the established UAV degradation model, the aircraft state and actuator degradation state are predicted simultaneously. For the predictive perception of system health, on the one hand, the system health degree (HD) based on Mahalanobis distance is defined by the degree of airframe state deviation from the expected state, and then the failure threshold of the UAV is obtained. On the other hand, according to the degradation state of each actuator, a comprehensive degradation variable fused with different weight coefficients of multiple actuators degradation is used to obtain the probability density function (PDF) of remaining useful life (RUL) prediction. For the autonomous maintenance of system health, the LF-MPC weight matrixes are adjusted adaptively in real-time based on the HD evaluation, to achieve a compromise balance between UAV performance and control effect, and greatly extend the working time of UAV. Simulation results verified the effectiveness of the proposed method.

Improved Two-Dimensional Design of Iterative Learning Predictive Functional Control for Batch Processes

Improved Two-Dimensional Design of Iterative Learning Predictive Functional Control for Batch Processes

Improving the Feedforward Component for Recent Variants of Predictive Functional Control

A recent study demonstrated that the use of feedforward information with conventional Predictive Functional Control (PFC) leads to unexpected inconsistencies, with subsequent negative impacts on tuning and behaviour. A proposal was made to define the coincident point differently and shown to reduce the lag in the closed-loop PFC responses and applied to some systems with benign dynamics. Other recent work has looked at parameterisations of the future input to deal with challenging open-loop dynamics and significantly extended the range of problems for which PFC can be effective. This paper combines the two concepts, and thus proposes an algorithm that has both more effective and simple tuning than original PFC as well as being applicable to a range of challenging dynamics.

Performance Comparison Between Centralized and Hierarchical Predictive Functional Control for Adaptive Cruise Control Application

This paper presents a performance comparison between two different control structures of Predictive Functional Control (PFC), namely centralized and hierarchical architectures for an Adaptive Cruise Control (ACC) system. Centralized PFC utilizes a linearized model of the vehicle longitudinal dynamics to compute the control law, while hierarchical PFC uses a simple kinematic model with inverse vehicle longitudinal dynamics. Based on the simulation results, both control structures produced a satisfactory performance. However, in the presence of disturbances such as road slopes and wind gusts, the centralized PFC becomes more sensitive and conservative than the hierarchical PFC. The main reason is that the linearization model used in centralized PFC is only effective around the selected nominal operating points. Since the decision-making process depends on the internal model performance, centralized PFC cannot compensate for this effect. Besides, it also takes a longer computation time than hierarchical PFC since more mathematical operations must be solved than the kinematic model, especially when physical and operational constraints are considered. The standard performance parameters such as Root Mean Squared Error (RMSE), settling time, and rise time are also used for the analysis. These findings can become a solid justification for using the hierarchical PFC structure in designing an ACC system for future work.

Application of Feedforward Cascade Compound Control Based on Improved Predictive Functional Control in Heat Exchanger Outlet Temperature System

Aiming at the problems of large delay and poor anti-disturbance ability in the outlet temperature control system of the heat exchanger to optimize the control accuracy of the system and improve the control performance, this paper proposes a control scheme combining predictive functional control with proportional-integral-derivative control. Using the incremental proportional-integral-derivative control algorithm to improve the optimization objective function of the predictive functional control algorithm, a predictive functional control optimization model with a proportional-integral-derivative structure is established. The feedforward compensation control is adopted to eliminate the influence of external disturbances on the heat exchanger temperature control system. Through simulation, the proposed control scheme is compared with the feedforward cascade compound control scheme based on a proportional-integral-derivative main controller. The results show that the scheme has a small over harmonic and strong anti-interference ability. The adaptability and stability of the system are significantly improved, and the exit temperature of the heat exchanger can be effectively controlled.

Speed Control for Variable Speed PMSM Drive System Using Nonlinear Variable-Horizon Predictive Functional Control

Electrohydrostatic actuators (EHAs) adopted variable speed permanent magnet synchronous motor (PMSM) drive systems are widely used by surface actuation systems in more electrical aircraft. However, the dynamic performance and the antidisturbance performance of EHA need to be improved due to the limited dynamic response of variable speed PMSM drive systems and uncertain aerodynamic disturbance. To improve the transient-state operation, nonlinear variable-horizon predictive functional control (NVHPFC) is proposed for the speed controller of the variable speed PMSM drive system. By analyzing the relationship between the prediction horizon and the electromagnetic torque, a nonlinear variable predictive horizon strategy is presented, which replaces the fixed predictive horizon in classical PFC. Aiming to improve the prediction accuracy and antidisturbance performance of NVHPFC, a discrete prediction error compensation strategy is incorporated with the NVHPFC. Meanwhile, the stability of the proposed method is verified by the Lyapunov function in the discrete domain. Finally, simulation and experimental results of the proposed method show stronger antidisturbance, smaller overshoot, and shorter settling time performance compared with the classical PFC method based on a field-programmable gate array (FPGA) test bench.

Predictive Functional Controller Design with Disturbance Observer and Its Application

Predictive Functional Controller Design with Disturbance Observer and Its Application

Performance Analysis of Predictive Functional Control for Automobile Adaptive Cruise Control System

This paper presents the performance analysis of Predictive Functional Control (PFC) for Adaptive Cruise Control (ACC) application. To cope with multiple driving objectives of modern ACC systems such as passenger comfort, safe distancing, and fast time response, an advanced optimal controller such as Model Predictive Control (MPC) is often used. Nevertheless, MPC requires a high computation load due to its complex formulation and may overload the processing power of a microcontroller. Thus, the prime objective of this work is to propose a PFC algorithm as an alternative controller, while providing a formal comparison between MPC and the traditional Proportional Integral (PI) controller. A standard kinematic model for vehicle longitudinal dynamics was modelled and used to derive the control law of PFC. Since the open-loop dynamic of the derived transfer function is not stable, the second objective is to propose a pre-stabilized loop or cascade PFC structure for the system. A complete tuning procedure and analysis were presented. The simulation result shows that although MPC performance is the best for the ACC application with Root Mean Square Error (RMSE) of 1.4873, PFC has shown a promising response with RMSE of 1.5501, which is better compared to the PI controller with RMSE of 1.6219. All the imposed driving constraints such as maximum acceleration, maximum deceleration and safe distance were satisfied in the car following application. Thus, the findings from this work can become a good initial motivation to further explore the capability of the PFC algorithm for future ACC development.  ABSTRAK: Kajian ini adalah berkenaan analisis prestasi Kawalan Fungsi Ramalan (PFC) aplikasi Kawalan Mudah Suai (ACC). Bagi memenuhi pelbagai keperluan objektif sistem pemanduan moden ACC seperti keselesaan penumpang, penjarakan selamat dan tindak balas pantas, kawalan optimum terbaru seperti Model Kawalan Ramalan (MPC) sering digunakan. Walau bagaimanapun, MPC memerlukan beban pengiraan tinggi kerana rumusnya yang kompleks dan mungkin mengakibatkan beban berlebihan kuasa pemprosesan mikrokawalan. Oleh itu, matlamat utama kajian ini adalah bagi mencadangkan algoritma PFC yang mempunyai pengiraan mudah sebagai kawalan alternatif, sementara menyediakan perbandingan formal antara MPC dan kawalan tradisional Berkadar Keseluruhan (PI). Oleh kerana model ini tidak stabil, objektif kedua adalah mencadangkan penggunaan struktur PFC berlapis bagi menstabilkan sistem terlebih dahulu sebelum algorithma kawalan digunakan atau dengan menggunakan struktur PFC secara berturut pada sistem. Prosedur lengkap dan terperinci untuk analisis PFC dibentangkan. Dapatan simulasi kajian menunjukkan walaupun prestasi MPC adalah baik bagi aplikasi ACC dengan Ralat Punca Min Kuasa Dua (RMSE) bernilai 1.4873, namun PFC menunjukkan tindak balas baik dengan RMSE bernilai 1.5501 berbanding kawalan PI yang mempunyai RMSE sebanyak 1.6219. Kesemua kekangan seperti pecutan dan nyahpecutan maksima, dan penjarakan selamat bertepatan dengan aplikasi kenderaan ini. Dengan itu, penemuan ini adalah motivasi awal yang baik bagi meneroka lebih jauh keupayaan algoritma PFC bagi membangun ACC pada masa hadapan.

Lyapunov-based model predictive control for a single-phase grid-connected cascaded multilevel asymmetrical inverter

This paper proposes an N-step ahead model predictive controller for a multilevel asymmetric cascade grid-connected inverter. To this goal, a predictive function controller has been designed based on the Lyapunov theory. First, the equations of the N-step ahead predictive sequence have been derived for the reference current as well as the reference voltage using first-order linear interpolation considering the mean of previous values. Second, the current, voltage, current error, and Lyapunov function have been calculated for the N-samples ahead. Then, the switching scenario has been determined such that it minimizes the derivation of the Lyapunov function. Moreover, the effect of the number of prediction steps on the unwanted harmonic reduction, switching average, grid power injection, and inverter efficiency has been investigated. Finally, The proposed controller is implemented on a 19-level asymmetric cascaded inverter. The results show that by increasing the prediction steps from 1 to 5, the harmonic distortion and the number of switches are reduced.

Generalized fuzzy cascade predictive functional control design for different types of challenging dynamics systems

This paper introduces a generalized form of cascade predictive functional control. The inner loop includes a state feedback controller, which aims to increase damping and stabilize the system. The outer loop utilizes an output feedback controller (OFC) to track reference and reject disturbance. The gains of the proposed controller structure are obtained optimally concerning to a specified prediction horizon through the predictive functional controller (PFC) method, which is improved by a fuzzy logic controller (FLC). The designed FLC plays a trade-off role between inner loop and outer loop gains values by tuning weighting factors in the PFC approach. In this paper, the proposed solution is formulated to convert the tracking problem into a regulation problem which results in complexity reduction and lower computational cost. Moreover, based on the proposed solution, a generalized form of OFC is obtained concerning to disturbance and reference characteristics. As a comparative study, the proposed controller is applied to the different types of challenging dynamics systems and compared to the discrete-time linear quadratic regulator (DLQR) control technique to reveal the benefits and reliable performance of the proposed control structure.

Recent Developments in Tuning Methods for Predictive Functional Control

Predictive functional control (PFC) is a popular alternative to PID because it exploits model information better and enables systematic constraint handling while also being cheap and computationally efficient. A recent overview paper reviewed some recent proposals for improving the tuning efficacy. This paper extends and develops upon that review paper by introducing some exciting new proposals for how to making tuning more intuitive and, thus, easier for unskilled operators. Moreover, there are early indications that these proposals are easily modified for use in nonlinear cases while maintaining a very low cost and a simple and fast online computation.

Improved Constrained Predictive Functional Control Using Extended Non-Minimal State Space Formulation for the Cement Production Process

In this article, an improved constraint dealing method and an extended state space model-based constrained predictive functional control (PFC) approach is developed for the denitration process in cement production. To improve the control effect of the presented strategy, first, an enhanced form-based state space model in which the changes of the output predictions can be regulated to achieve smoother system dynamics is constructed. Then, a modified constraint dealing scheme, which integrates the relaxation factors to improve the success probability of solving the relevant optimization, is also introduced for the proposed method. On the basis of the two merits, better ensemble control performance is anticipated. Simulations on the regulation of the NOx concentration in the denitration process prove the validity of the proposed constrained PFC strategy.

Predictive functional control for challenging dynamic processes using a simple prestabilization strategy

AbstractPredictive functional control (PFC) is a straightforward and cheap model‐based technique for systematic control of well‐damped open‐loop processes. Nevertheless, its oversimplified design characteristics are often the cause of diminished efficacy in more challenging applications; processes involving lightly damped and/or unstable dynamics have been particularly difficult to control with PFC. This paper presents a more sustainable solution for such applications by integrating the concept of prestabilization within the predictive functional control formulation. This is essentially a two‐stage synthesis wherein the undesirable open‐loop dynamics are first compensated, using a well‐understood classical approach such as proportional integral derivative (PID), before implementing predictive control in a cascade structure. The proposal, although comes with significant implications for tuning and constraint handling, is, nonetheless, straightforward and provides improved closed‐loop control in the presence of external perturbations compared to the standard PFC and the PID algorithms, as demonstrated with two industrial case studies.

Performance Comparison Between Predictive Functional Control and PID Algorithms for Automobile Cruise Control System

This work presents a performance comparison between a Predictive Functional Control (PFC) and a traditional Proportional Integral Derivative (PID) controller specifically for a cruise control application. The tuning efficacy, constraints handling, and disturbance rejection features of both controllers are analysed by comparing their closed-loop response. A simplified nonlinear vehicle longitudinal dynamics model is derived and utilised as a plant to simulate the control response from a real car. For a fair comparison, both PFC and PID are tuned to achieve the similar desired closed-loop time response. Qualitatively, the results show that PFC provides a better closed-loop response, constraints handling, and disturbance rejection compared to PID. Besides, it is also found that the tuning approach of PFC is more intuitive and practical in nature which can be very handy for the future development of an autonomous cruise control application.

Fuzzy decoupling predictive functional control for nonlinear hydro-turbine governing systems with mechanical time delay of the hydraulic servo system

This study presents fuzzy decoupling predictive functional control for nonlinear hydro-turbine governing systems with time delay and strong coupling. Here, the Takagi–Sugeno fuzzy approach and fuzzy neural network decoupling algorithm are implemented in the pretreatment of a four-dimensional time delay hydro-turbine governing system model, aiming to solve the nonlinearity and separate coupling variables of the hydro-turbine governing system effectively. Then, a new fuzzy decoupling predictive functional control strategy proposed by combining the simplified hydro-turbine governing system model and predictive function control as well as the robustness and stability of the designed controller are verified by theoretical derivation. Numerical experiment demonstrates effectiveness and superiority of the proposed approach in comparison with fuzzy control under different operation conditions.

Indoor temperature regulation and energy consumption inside a working office in building system using a predictive functional control

ABSTRACT This paper presents a novel control approach for indoor temperature regulation in tertiary buildings, based on predictive functional control. The main control objective is to reduce the energy consumption while ensuring the desired thermal comfort of the occupants. The novelty of this approach may perform in the presence of disturbances such occupancy profile, electrical equipment, indoor temperature, surrounding temperatures and weather data. Predictive functional control algorithm consists in using a dynamic model of the process inside the controller in real time in order to anticipate the future behavior of the system. The proposed method is successfully illustrated using an example of temperature control of a working office which is implemented in the SIMBAD toolbox (SIMulator of Buildings and Devices) integrated into the Matlab/Simulink environment. The proposed control compromises a class of control algorithms that utilizes an online process model to optimize the future response of a plant. The efficiency of the proposed control has been validated using good performance indexes for various scenarios. Simulation results revealed a good level of comfort is ensured with a minimum energy (3.2015 kWh), temperature regulation with a very low error, a high level of comfort is generated in the office room during working hours. Thus, demonstrating the validity and effectiveness of this control strategy.

General regression neural network-based data-driven model-free predictive functional control for a class of discrete-time nonlinear systems

General regression neural network-based data-driven model-free predictive functional control for a class of discrete-time nonlinear systems