Nonlinear Model-based Control Research Articles

Nonlinear model-based predictive control of a yeast fermentation bioreactor using new bee colony-WNN modelling structure

This paper concentrates on the application of a newly developed model for the nonlinear control of a yeast fermentation bioreactor. The primary control objectives are the maintenance of temperature and product concentration within the desired range. So, having an accurate model in control strategy is not ignorable and this model influences on close-loop controllability. In the context of online control, the parameters are changed (the system is time varying) and precision of extracted model is more important. Moreover, there is a demand for a computationally efficient model, and the convergence speed during the training of the neural network is significant. To overcome the challenges associated with slow convergence, the risk of being trapped in local minima, and the imperative of achieving computational efficiency, this study introduces a novel combination of a pruned Bee Colony Wavelet Neural Network for the online modeling of the bioreactor. The method's superiority lies in its ability to conduct searches in multiple sections independently, thereby avoiding local minima. The hybrid model controllability is further investigated using Dynamic Matrix Control (DMC) and Generalized Matrix Control (GPC) techniques. Subsequently, the paper explores the application of Nonlinear Model Predictive Control (NMPC) by solving a Gauss-Newton quadratic programming problem online, followed by a comparative analysis of the results. It is demonstrated that the precision of the model closely influences profitability and enhances product yields.

Fault-Tolerant Control for Aircraft with Structural Damage Using Sparse Online Gaussian Process Regression

This paper presents the design of data-driven fault-tolerant control using sparse online Gaussian process regression (SOGPR) to stabilize an aircraft with left-wing damage. The structural damage causes changes in mass, moment of inertia, center of gravity, and aerodynamic coefficients. These parameter variations deteriorate the performance of model-based nonlinear control methods. Hence, Gaussian process-based nonlinear dynamic inversion (GP-NDI) is proposed to compensate for uncertainties in situations of structural damage. Unlike parametric adaptive control approaches, Gaussian process regression is a non-parametric method that does not need prior information about uncertainties. And the proposed method implements SOGPR to reduce computational time and memory by incrementally updating the mean and variance. To compensate for the error in the estimated uncertainty, a robust control input is designed. In addition, a weighted delete score is used to improve the transient response. Numerical simulation results are compared with model reference adaptive control (MRAC) and nonlinear disturbance observer (NDO) to analyze a stabilizing and tracking performance in a structural damage situation.

Addressing Actuator Saturation during Fault Compensation in Model-Based Underwater Vehicle Control

Robust control systems are a necessity for autonomous underwater vehicle (AUV) systems due to the challenges they face during operation. Many AUV control-design methods have been developed for different actuator configurations, with robustness against model parameter uncertainties, environmental disturbances, and system faults. Actuator faults can reduce the physical capabilities of a system, which can be compensated for through control re-allocation. However, the increased control allocation to the remaining actuators may cause actuator saturation and reduce controller performance. In this work, we present a depth-pitch model-based nonlinear control law that directly considers actuator saturation, and a fault-tolerant control allocation method for a hybrid AUV actuator configuration. Two types of actuator faults are considered for an underwater vehicle with a hybrid actuator configuration. The proposed controller is implemented in a simulated system, and its trajectory tracking performance is compared with a baseline system without fault or saturation tolerance. To determine the utility of the proposed saturation and fault tolerance control methods, the tracking performance in these simulations is quantified in terms of the settling time, post-fault peak values, and root mean square of the depth and pitch errors.

Non-linear Model-based Predictive Control for Trajectory Tracking and Control Effort Minimization in a Smartphone-based Quadrotor

In this paper, the design and implementation of a non-linear model-based predictive controller (NMPC) for predefined trajectory tracking and to minimize the control effort of a smartphone-based quadrotor is carried out. The optimal control actions are calculated in each iteration by means of an optimal control algorithm based on the non-linear model of the quadrotor, considering some aerodynamic effects. Control algorithm implementation and simulation tests are executed on a smartphone using the CasADi framework. In addition, a technique for estimating the energy consumed based on control signals is presented. NMPC controller performance is compared to an H-infinity controller and an LQI controller, using three predefined trajectories, where the NMPC average tracking error was around 50\% lower, and average estimated power and energy consumption slightly higher, with respect to the H-infinity and LQI controllers.

Nonlinear Closed-Loop Predictive Control of Heart Rate and Blood Pressure Using Vagus Nerve Stimulation: An In Silico Study.

We propose a nonlinear model-based control technique for regulating the heart rate and blood pressure using vagus nerve neuromodulation. The closed-loop framework is based on an in silico model of the rat cardiovascular system for the simulation of the hemodynamic response to multi-location vagal nerve stimulation. The in silico model is derived by compartmentalizing the various physiological components involved in the closed-loop cardiovascular system with intrinsic baroreflex regulation to virtually generate nominal and hypertension-related heart dynamics of rats in rest and exercise states. The controller, using a reduced cycle-averaged model, monitors the outputs from the in silico model, estimates the current state of the reduced model, and computes the optimum stimulation locations and the corresponding parameters using a nonlinear model predictive control algorithm. The results demonstrate that the proposed control strategy is robust with respect to its ability to handle setpoint tracking and disturbance rejection in different simulation scenarios.

The future of control of process systems

This paper provides a perspective on the major challenges and directions in academic process control research over the next 5–10 years, and its industrial implementation. Large-scale systems control and identification, nonlinear model-based and model-free control, and controller performance monitoring and diagnosis are discussed as major directions for future research, along with control technology and industry workforce challenges and opportunities.

Nonlinear model predictive control of crystal size in batch cooling crystallization processes

The paper proposes a model-based nonlinear model predictive control (NMPC) method for online control of crystal mean size and standard deviation in cooling crystallization process. Image analysis method using deep learning neural network and mathematical statistical method are performed to obtain the mean size and standard deviation of crystal population. The nonlinear prediction model for the NMPC is derived from the input and output data. The effectiveness of the proposed NMPC method is evaluated by the alum cooling crystallization experiments. Experimental results demonstrate the benefits of the proposed combination of image analysis and feedback control of the crystal mean size and standard deviation. The control performance of NMPC is superior to model-free path following control (PFC) method due to the prediction and optimization capabilities of NMPC.

Design and stability analysis of a nonlinear controller for MRI-compatible pneumatic motors

Among permissible magnetic resonance imaging (MRI) compatible actuators for surgical robots, turbine-based pneumatic motors are noticeably favorited due to its compact size, simpler structure, fast additively manufacturability, and continuous bidirectional motion ability. Yet, the system dynamics of pneumatic motors, especially pneumatic nonlinearity, is often neglected and simple PID control is used, resulting in low system bandwidth (~0.5 Hz). To tackle this obstacle, this paper proposes a model-based nonlinear control method for MRI-compatible pneumatic motors. Dynamic models for a pneumatic motor previously designed by the author are developed first, followed by establishment of the nonlinear feedback controller. An error based Lyapunov candidate function is designed and mathematically proved to be globally uniformly asymptotically stable, guaranteeing desired accuracy. Experiment control tests demonstrate that the proposed control method can achieve satisfactorily better tracking accuracy than a conventional model-independent PID controller with respect to amplitude attenuation and phase delay.

A Survey on Model-Based Control and Guidance Principles for Autonomous Marine Vehicles

With the increasing number of applications for both surface and underwater autonomous vehicles, a great amount of control methods and guidance principles has been developed over the years. This work proposes a review of the most common of these methods. It is mainly focused on model-based nonlinear control methods and guidance principles. Notably, this work details examples and variations of model-based linearizing controllers, applications of line of sight guidance, sliding mode controllers and several other less common control methods for both fully-actuated and underactuated vehicles. Additionally, this work proposes an alternative definition of underactuation with respect to the task allowing for a better understanding of the consequences of underactuation on control. Comparison of fully-actuated and underactuated cases shows how control laws can be used to solve the problems of underactuation and what mechanisms can be used to compensate for the lack of actuation on a degree of freedom. The reviewed methods are compared and discussed with respect to their capabilities, limitations and suitability for typical tasks.

Nonlinear Model-Based Control of a Pneumatically Driven Robot

In robotics, pneumatic drives are an interesting alternative to classic electric drives, as their physical properties enable the design of safe, lightweight and intuitively operable robots. In this work, a nonlinear model-based feedback control concept for a robot with 4 compressed-air-driven rotary joints is presented. The robot model comprising kinetics and pressure dynamics is formulated. For this drive type, significant nonlinear friction effects are present, which is known to be challenging for controller design, especially since there is no output-side measurement of the effective drive torque after subtracting friction. A control concept based on differential flatness, here with the particular case of feedback linearization, is derived, which is particularly well suited for a system with such effects. The algorithm contains both kinetics and pressure dynamics in one central controller, and its working principle and practical implications are discussed. With experimental results, the effectiveness of the trajectory tracking controller is demonstrated and insights into the components of this controller are provided.

Mechatronic design of dynamically decoupled manipulators based on the control performance improvement

AbstractThe control of industrial robot manipulators presents a difficult problem for control engineers due to the complexity of their nonlinear dynamics models. Nonlinear controls based on feedback linearization are developed to meet control requirements. Model-based nonlinear control is highly sensitive to parameter errors and leads to problems of robustness for tracking trajectories at high speeds, and there is the additional problem of a heavy computational burden to consider in the design of nonlinear controllers. In this paper, a mechatronic design approach is proposed, which aims to facilitate controller design by redesigning the mechanical structure. The problem is approached in two steps: first, the dynamic decoupling conditions of manipulators are described and discussed, involving redistribution of the moving mass, which leads to the decoupling of motion equations. A classical linear control law is then used to track the desired efficient bang-bang profile trajectory. Then, in the presence of parameter uncertainty and external disturbances, the nonlinear controls with simple structures are adopted to stabilize the decoupled system asymptotically. An analysis of the results from a simulation of this approach demonstrates its effectiveness in controller design. The proposed improvement in control performance is illustrated via two spatial manipulators.

Nonlinear feedback control of bimodality in the wake of a three-dimensional bluff body

The turbulent wake behind a square-back Ahmed body in close proximity to the ground exhibits bimodal switching. This manifests as the center of the wake randomly switching side-to-side between one of two asymmetric positions. This work is the first attempt to employ nonlinear model-based feedback control to suppress this wake bimodality. High fidelity simulations are used to develop and implement the control strategy and investigate the resulting effect on the wake and aerodynamic drag.

On nonlinear model predictive direct yaw moment control for trailer sway mitigation

In car–trailer combinations, the hitch angle is the relative yaw angle between towing car and trailer. The literature has shown that the inclusion of the hitch angle measurement for the feedback control of trailer oscillations can bring safety benefits, compared with conventional trailer sway mitigation algorithms based on the yaw rate of the car. Given the nonlinearity of the vehicle system in the typical conditions requiring the hitch angle control function intervention, nonlinear model-based controllers could be an effective solution. This paper presents four real-time implementable nonlinear model predictive control (NMPC) formulations, using the hitch angle measurement for the torque-vectoring (TV) control of an electric front-wheel drive car towing a trailer. The simulation results show that: (i) the active safety is enhanced by the proposed NMPC TV formulations, with respect to a benchmarking NMPC TV controller only based on the control of the towing car; (ii) the NMPC formulations that directly constrain the hitch angle error, or perform continuous hitch angle tracking, outperform those that modify the reference yaw rate or yaw rate error based on the hitch angle error; and (iii) the NMPC approaches including a dynamic model of the trailer are robust with respect to variations of trailer parameters.

Toward a Data-Driven Template Model for Quadrupedal Locomotion

This work investigates a data-driven template model for trajectory planning of dynamic quadrupedal robots. Many state-of-the-art approaches involve using a reduced-order model, primarily due to computational tractability. The spirit of the trajectory planning approach in this work draws on recent advancements in the area of behavioral systems theory. Here, we aim to capitalize on the knowledge of well-known template models to construct a data-driven model, enabling us to obtain an information rich reduced-order model. In particular, this work considers input-output states similar to that of the single rigid body model and proceeds to develop a data-driven representation of the system, which is then used in a predictive control framework to plan a trajectory for quadrupeds. The optimal trajectory is passed to a low-level and nonlinear model-based controller to be tracked. Preliminary experimental results are provided to establish the efficacy of this hierarchical control approach for trotting and walking gaits of a high-dimensional quadrupedal robot on unknown terrains and in the presence of disturbances.

Implementable MPC-based surge avoidance nonlinear control strategies for non-ideally modeled natural gas compression systems

The surge avoidance control plays a pivotal role in a centrifugal compression process to maintain safety and high efficiency. In the literature, MPC-like schemes have shown promise for use in such tasks given that they can systematically deal with several process constraints. However, to obtain a good performance in the compression process with a significant deviation of gas ideality, the model used in MPC formulations has to be able to predict the process behavior correctly. This paper proposes surge avoidance feasible optimization-based MPC schemes for non-ideally modeled natural gas compression systems. Its pivotal contributions are: (i) extension of the isothermal and ideal gas thermodynamic behaviors commonly adopted in models of surge prevention MPC schemes to a non-isothermal flow and non-ideally behaved gas-like more realistic compression system; (ii) formulation of a proposed nonlinear model-based MPC control law with surge protection being managed by slacked nonlinear constraints; (iii) synthesis of an adaptive infinite horizon MPC-based surge avoidance scheme that relies upon the successive linearization of the proposed rigorous model for the compression system. From simulations carried out with a plant-model mismatch oriented by distinct equations of state, results obtained from the proposed rigorous model-based surge avoidance NMPC strategy are favorably compared to those obtained with the simplified model widely used in the literature. Finally, the proposed adaptive MPC-based surge prevention scheme showed convergence towards the corresponding NMPC with a drastically reduced computational cost.

Anti-disturbance composite tracking control for a coupled two-tank MIMO process with experimental studies

Coupled multiple-tank systems are very important for a wide range of industrial applications due to their unique uses. However, the liquid level control for the coupled two-tank multi-input multi-output (MIMO) system is quite challenging because it has strong nonlinearity and coupling, and it is susceptible to multiple external disturbances. For this process, this paper proposes a novel anti-disturbance control strategy consisting on a nonlinear composite hierarchical anti-disturbance predictive control (CHADPC). First, a model-based explicit nonlinear model predictive controller (ENMPC) is designed assuming that all disturbances are measurable and its global exponential stability is proved. Then, a nonlinear disturbance observer (DO) is designed to estimate the lumped disturbances. The composite controller handling the estimated disturbances is then proposed. Finally, simulation and experimental tracking control tests under perturbations and comparisons with recently reported works have been carried out to highlight the promising performance of the proposed ENMPC and CHADPC schemes.

Reduction of the CO emission from wood pellet small-scale boiler using model-based control

The paper presents new approach in reducing of the CO emission in exhaust gases from small-scale wood pellet boilers. The results are obtained by control of the airflow to the boiler using a model-based nonlinear predictive controller. The complex-structure nonlinear model designed, and simplified to the nonlinear block-oriented Hammerstein system. Finally, the Hammerstein system is used to design the nonlinear predictive controller of the combustion process. The effectiveness analysis of the designed control algorithm under operating conditions at nominal heat power shows that 1) the airflow changes to the boiler is crucial for the CO concentration in the flue gasses and 2) accurate control of the airflow may lead to a significant reduction of the CO emission without any changes of the boiler design. The paper shows that reducing CO emissions from small-scale wood pellet boilers decreased by 35–50% of the original value with low implementation cost to fit industrial scale.

Optimization Based on Pattern Search Algorithm Applied to pH Non-Linear Control: Application to Alkalinization Process of Sugar Juice

In this paper, an approach for the tuning of a model-based non-linear predictive control (NMPC) is presented. The proposed control uses the pattern search optimization algorithm (PSM), which is applied to the pH non-linear control in the alkalinization process of sugar juice. First, the model identification is made using the Takagi Sugeno T-S fuzzy inference systems with multidimensional fuzzy sets; the next step is the controller parameters tuning. The PSM algorithm is used in both cases. The proposed approach allows the minimization of model uncertainty and decreases, in the response, the error in a steady state when compared with other authors who perform the same procedure but apply other optimization algorithms. The results show an improvement in the steady-state error in the plant response.

Accurate linear and nonlinear model-based feedforward deposition control for material extrusion additive manufacturing

Additive manufacturing (AM) is gaining attention as an alternative to traditional manufacturing processes. Of the available AM methods, material extrusion (ME) AM is predominant. High-quality ME AM demands accurate synchronization between positioning (motion) control and extrusion control, as poor synchronization leads to printing defects like over- and under-extrusion. Typically, extrusion control in ME AM is achieved via feedforward (FF) control techniques due to difficulties in sensing extrusion rate in real-time for feedback control. However, existing FF extrusion control techniques rely on simple linear models to control the highly nonlinear extrusion process, leading to quality issues like over- and under-extrusion. This paper presents two FF control strategies for mitigating over- and under-extrusion defects in ME AM. The first strategy uses a standard linear model of extrusion system but applies it to FF motion control rather than FF extrusion control. This has the net effect of synchronizing motion and extrusion control while avoiding some nonlinearities associated with the extrusion process. In the second approach, an empirical nonlinear model of the extrusion process is developed and adopted for the design of a nonlinear FF extrusion controller. Both approaches were validated experimentally on a fused filament fabrication (FFF) 3D printer, and respectively demonstrated up to 40.45% and 35.98% improvement in deposition accuracy (i.e., reduced over- and under-extrusion) compared to a standard FF extrusion control approach typically used in the literature. In addition, the proposed nonlinear FF controller was shown to be more versatile and lead to faster ME AM compared to the proposed linear FF motion control approach. A practical application of the proposed techniques for improving the quality of a variable-width pattern printed using a new concept of continuously varied extrusion was demonstrated.

An adaptive neural network-based controller for car driving simulators

The paper proposes an approach to deal with problems stemming from inaccurate elements of car driving simulators and the disadvantages of nonlinear model-based controllers, including the Backstepping and Sliding Mode Control. For this kind of model, it is challenging to design nonlinear model-based controllers to guarantee smooth and accurate movements due to unmodelled parts in the system dynamics and the appearance of external forces. Furthermore, there are well-known demerits in the aforementioned controls, such as ‘explosion of terms’ and chattering phenomena. The main contribution focuses on constructing an adaptive and robust neural network-based controller with online learning laws, which not only ensures the high accuracy of the robot’s motion under uncertain components and external factors but also mitigate the disadvantages of conventional controllers. The stability and convergence of the proposed method are proven by Lyapunov’s stability. The simulation results show the validity and efficiency of the proposed control algorithm.