Control of supersaturation in batch cooling crystallization by robust state feedback linearization

We describe the application of model predictive control (MPC) using state mapping to the automatic landing system of a spaceplane. The controller has to be designed to enable the vehicle to follow reference signals with respect to trajectory and velocity, which are expressed as functions of the downrange. To track the reference signals, a control input is generally designed so that one or more ideal transient responses are realized. We also have developed a flight control system based on this concept. However, it was not satisfactory for use as the controller of an actual vehicle due to the lack of consideration of the input and state constraints. A controller that considers these constraints can be designed by applying MPC. On the other hand, it is difficult to predefine the transient responses necessary to track the reference signals, which vary with the current downrange. In this paper, a new approach using state mapping and feedback linearization is proposed to improve the control performance of tracking the reference signals. State mapping is derived to describe a system in which the reference signals can be handled as a constant set point, and the described system is linearized using state feedback. The proposed system is applied to the Japanese Automatic Landing Flight Experiment (ALFLEX) vehicle. A numerical simulation is performed to verify the validity of the proposed method based on MPC.

Gain scheduled controllers for dynamic systems using sector nonlinearities

This paper deals with the design and the robustness analysis of a model predictive control (MPC) for the position tracking of primary flight movables driven by electro-mechanical actuators. This study is, in particular, focused on a rotary electro-mechanical actuator (EMA) by UMBRAGROUP, employing a patented mechanical transmission based on a differential ball-screw mechanism characterized by a huge gear ratio. To obtain a baseline reference, conventional PID regulators were initially optimized by using multi-objective cost functions based on tracking accuracy, load disturbance rejection, and power consumption. The position regulator was then replaced by an MPC regulator, designed to balance performance, computational resources, and safety constraints. A nonlinear physics-based simulation model of the EMA, entirely developed in the Matlab–Simulink environment and validated with experiments, was used to compare the two control strategies. The simulation results in both the time and frequency domains highlight that the MPC solution provides faster and more accurate position tracking, improved dynamic stiffness, and reduced power absorption. Finally, the robustness against model uncertainties of the MPC was addressed by imposing random and combined deviations of model parameters from the nominal values (via Monte Carlo analysis). The results demonstrate that the implementation of MPC control laws could enhance the stability and the reliability of EMAs, thus supporting their application for safety-critical flight control functions.

Explicit model predictive control of gas–liquid separation plant via orthogonal search tree partitioning

This study examines implementation of a Model Predictive Controller (MPC) to a new concept in active suspension design. Active and passive components are placed in series to mitigate both high and low frequency disturbance inputs at the tire-road interface. This is modelled using an additional mass spring damper tuned to regulate high frequency inputs, leaving the active components to respond to low frequency inputs. A generic half car model for such a system is developed and subjected to various disturbance inputs at constant velocity and output to verify the system dynamics. Inputs include step, multimodal, and random disturbances as well as a step input that returns to zero. These trials serve as a baseline to evaluate the performance of the passive suspension as well as a Model Predictive Controller. Current research that uses MPC in active suspension design focuses heavily on the traditional half car model with 4 DOF[4]. MPC is applied to this new 6 DOF model and incorporates preview information into the controller response for each of the test cases. The cost function for the MPC places penalties on the translational and rotational position and velocity of the chassis relative to a reference state that is based on each disturbance profile. Parameters of interest are driver absorbed power due to both linear and rotational movement of the chassis. The results for each test case demonstrate the utility of MPC. For every response, there is a decrease in the absorbed power due to rotational and linear sources on the magnitude of 98–100%. The incorporation of preview information also removed the rotation of the chassis for each test case by placing a heavy weight upon its movement. For the step input, the controller reduced the peak rate of change of the chassis by 71.4%. For the multi-mode input, the low frequency sinusoidal inputs showed a dramatic reduction in vertical displacement in the steady state behavior as the MPC will produce an output that is tuned to cancel the disturbance. The high frequency effects are also effectively removed by the passive components of the suspension. This ability to mitigate both sources of disturbance is a marked advantage of the double-stacked suspension design. MPC allowed for the overall reduction of chassis movement by 54.0% with preview information. This improvement is due to the ability of the double stacked suspension with MPC to use the additional degrees of freedom to attenuate disturbances at more than one frequency. The random input demonstrates the ability of the controller to maintain a smooth chassis trajectory even with a chaotic road profile. Finally, the step up-down input demonstrates the ability of the controller to use other components of the suspension system to mitigate a disturbance in order to keep the chassis stable. These results demonstrate that preview information can be used to take full advantage of double stacked, active suspensions and further enhance mobility over different kinds of terrain. Future work includes investigating the effectiveness of other predictive control methods such as two-point boundary value problem or dynamic programming, optimizing the weights used, or adding constraints to the model.

New technological advances are changing the way robotics are designed for safe and dependable physical human–robot interaction and human-like prosthesis. Outstanding examples are the adoption of soft covers, compliant transmission elements, and motion control laws that allow compliant behavior in the event of collisions while preserving accuracy and performance during motion in free space. In this scenario, there is growing interest in variable stiffness actuators (VSAs). Herein, we present a new design of an anthropomorphic elbow VSA based on an architecture we developed previously. A robust dynamic feedback linearization algorithm is used to achieve simultaneous control of the output link position and stiffness. This actuation system makes use of two compliant transmission elements, characterized by a nonlinear relation between deflection and applied torque. Static feedback control algorithms have been proposed in literature considering purely elastic transmission; however, viscoelasticity is often observed in practice. This phenomenon may harm the performance of static feedback linearization algorithms, particularly in the case of trajectory tracking. To overcome this limitation, we propose a dynamic feedback linearization algorithm that explicitly considers the viscoelasticity of the transmission elements, and validate it through simulations and experimental studies. The results are compared with the static feedback case to showcase the improvement in trajectory tracking, even in the case of parameter uncertainty.

This study deals with the synchronization problem of the stochastic fractional-order biomathematical model of muscular blood vessels (SFOMBVs) with nonlinear inputs using a state-feedback adaptive control law, in which the effects of uncertainties and external disturbances are considered in the modeling. The linear state feedback and adaptive laws are combined via an adaptive update law, leading to a simple and robust adaptive feedback scheme. The synchronization and tracking performances of the SFOMBV master and slave systems are investigated, and the stability of the proposed control system is proved based on stochastic analysis techniques and Lyapunov theory. The simulation results show that the proposed control method can lead an abnormal muscular blood vessel to a normal trajectory with good robustness by reducing the tracking error.

The author presents a robust technique for designing compensators for a certain class of nonlinear systems following the philosophy behind input-output linearization and sliding mode control. The technique takes advantage of a robust equivalent feedback linearization using sliding mode theory and then superimposes linear design algorithms in order to shape the loop operator (loop transfer function) of the feedback linearized system. Robustness issues are addressed; when the external disturbances to the system and modeling parameter uncertainties are bounded and satisfy the matching conditions, the nonlinear system can be robustly linearized. The proposed scheme has enough parameters to give flexibility in the choice of the desired closed-loop characteristics. At the same time, it leaves the designer with the responsibility of selecting the following parameters: boundary layer, strength of attraction to the sliding surface, and bandwidth.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Levitation control is a core technique of magnetic levitation (Maglev) trains, whose performance has a significant impact on the driving safety and ride comfort during the operation of Maglev trains. With the rapid development of high temperature superconducting (HTS) materials, a novel hybrid levitation system for Maglev trains, composed of HTS and normal conducting electromagnets, is becoming a more promising alternative to the conventional levitation system, due to a lager levitation air gap and lower energy consumption. The controller of the hybrid levitation system is hard to design due to strong nonlinearity, open-loop instability and fast-response requirements. In this study, we propose a robust model predictive control (MPC) strategy for the novel hybrid levitation system in which state constraints are taken into account, including the air gap, and the velocity and acceleration of the hybrid magnet. In the MPC strategy, the prediction model employs a stabilized model through nonlinear and linear state feedback. With regard to the online computational load, the primal-dual interior-point (PDI) algorithm is adopted to solve the optimization problem with high efficiency to deal with constraints in a real-time manner. Finally, simulation results are demonstrated to verify the effectiveness of the proposed MPC-PDI control strategy for the hybrid levitation system, and the significances considering state constraints are revealed. This study provides an engineering realization solution to the novel hybrid levitation system of a Maglev train.

Discussion on: “Improved MPC Design based on Saturating Control Laws”

Chance-constrained stochastic MPC of greenhouse production systems with parametric uncertainty

On input-to-state stability of min–max nonlinear model predictive control

The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steadystates. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input-multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control. Linear Quadratic Regulator (LQR) with integral action.

The authors provide an alternative solution to the problem of semiglobal stabilization of a class of minimum phase nonlinear systems that was considered by A.R. Teel (1991). The method used yields a stabilizing linear state feedback law in contrast to a nonlinear state feedback law proposed by Teel. The peaking phenomenon is eliminated by inducing a specific time-scale structure in the linear part of the closed-loop system. This structure consists of a very slow and a very fast time scale. The crucial component in the method is the relation between the slow and the fast time-scales. The proposed linear state feedback control law has a single tunable gain parameter that allows for local asymptotic stability and regulation to the origin for any initial condition in some a priori given (arbitrarily large) bounded set. >

This work proposes a nonlinear modeling of a permanent magnet synchronous motor (PMSM) based on state space neural networks. The state space neural network is trained and the state variables (currents in a direct–quadrature frame and the rotational speed) are estimated by considering a robust Unscented Kalman Filter (UKF). Two contributions are presented in this work: the fist one is a nonlinear modeling structure for a PMSM based on a state space neural network that allows real-time parameter identification, and the second one is PMSM neural network training and state estimation based on a robust UKF. The robustness of the UKF is obtained by using a singular value decomposition of the covariance matrix. A comparison analysis is performed over a real PMSM motor by considering the proposed approach and a linear approximation of the nonlinear model where the states and parameters are computed by using an Extended Kalman Filter. The identified model is validated in closed loop by considering a nonlinear control strategy based on state feedback linearization.