Observer-based prescribed performance attitude control for flexible spacecraft with actuator saturation

This paper investigates the prescribed performance attitude control problem for flexible spacecraft subject to external disturbances and actuator constraints. By using a new performance function and an error transformation, the attitude control system is transformed into an error system which will be kept bounded to ensure expected dynamic and steady-state responses. Compared with the commonly used performance function, the modified one has an explicit prespecified terminal time which determines the maximum convergence time of the attitude control system. A modal observer and a disturbance observer are designed to deal with the flexible vibration and disturbances, respectively. Furthermore, when considering actuator saturation, an improved control strategy is developed with an auxiliary system utilized to compensate the saturation. The stability of the closed-loop system is analyzed by Lyapunov theory. Simulation results show the effectiveness and performance of the proposed methods.     

Position control of a rodless cylinder in pneumatic servo with actuator saturation

In this paper, positioning control of a rodless cylinder in pneumatic servo systems with actuator saturation is investigated via an active disturbance rejection control. A linear extended state observer is designed to estimate and compensate strong friction force and other nonlinearities in the pneumatic rodless cylinder system. An actuator saturation linear feedback control law is developed to further improve the control performance. Furthermore, a linear matrix inequality-based optimization algorithm is employed to estimate a strictly invariance set for the closed-loop system. Experiment results with response time 0.5 s and accuracy 0.005 mm for a 200 mm step signal demonstrate the effectiveness of the proposed control strategy.     

Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints

This paper focuses on the problem of adaptive neural network tracking control for a class of discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints. Two novel state-feedback and output-feedback dynamic control laws are established where the function tanh() is employed to solve the saturation constraint problem. Implicit function theorem and mean value theorem are exploited to deal with non-affine variables that are used as actual control. Radial basis function neural networks are used to approximate the desired input function. Discrete Nussbaum gain is used to estimate the unknown sign of control gain. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of control schemes proposed in this paper.     

Solution of low-dimensional constrained model predictive control problems

Large benefits are possible by utilizing the solution of the constrained optimization problem involved in model predictive control. For a special case of these problems, the solution can be obtained relatively easily from its relationship with the unconstrained optimum. In this paper, a visualization of the relationship between the constrained and unconstrained optimum is presented. Based upon this relationship, a method for finding the constrained optimum is proposed that is suitable for low-dimensional control systems. A comparison with a linear programming formulation on 2 × 2 and 3 × 3 problems shows that the computational effort can be 10–35 times lower. For such processes, the proposed approach may allow one to avail the benefits of optimization by using the small process control systems already present in many plants.     

A new continuous sliding mode control approach with actuator saturation for control of 2-DOF helicopter system

The 2-degree of freedom (DOF) helicopter system is a typical higher-order, multi-variable, nonlinear and strong coupled control system. The helicopter dynamics also includes parametric uncertainties and is subject to unknown external disturbances. Such complicated system requires designing a sophisticated control algorithm that can handle these difficulties. This paper presents a new robust control algorithm which is a combination of two continuous control techniques, composite nonlinear feedback (CNF) and super-twisting control (STC) methods. In the existing integral sliding mode (ISM) based CNF control law, the discontinuous term exhibits chattering which is not desirable for many practical applications. As the continuity of well known STC reduces chattering in the system, the proposed strategy is beneficial over the current ISM based CNF control law which has a discontinuous term. Two controllers with integral sliding surface are designed to control the position of the pitch and the yaw angles of the 2- DOF helicopter. The adequacy of this specific combination has been exhibited through general analysis, simulation and experimental results of 2-DOF helicopter setup. The acquired results demonstrate the good execution of the proposed controller regarding stabilization, following reference input without overshoot against actuator saturation and robustness concerning to the limited matched disturbances.     

Model predictive control for a class of systems with isolated nonlinearity

The paper is concerned with an overall convergent nonlinear model predictive control design for a kind of nonlinear mechatronic drive systems. The proposed nonlinear model predictive control results in the improvement of regulatory capacity for reference tracking and load disturbance rejection. The design of the nonlinear model predictive controller consists of two steps: the first step is to design a linear model predictive controller based on the linear part of the system at each sample instant, then an overall convergent nonlinear part is added to the linear model predictive controller to combine a nonlinear controller using error driven. The structure of the proposed controller is similar to that of classical PI optimal regulator but it also bears a set-point feed forward control loop, thus tracking ability and disturbance rejection are improved. The proposed method is compared with the results from recent literature, where control performance under both model match and mismatch cases are enlightened.     

Model predictive control of discrete-time hybrid systems with discrete inputs

This paper proposes and discusses a model predictive control approach to hybrid systems with discrete inputs only. The algorithm, which takes into account a model of a hybrid system, described as a mixed logical dynamical system, is based on a performance-driven reachability analysis. The algorithm abstracts the behavior of the hybrid system by building a "tree of evolution." The nodes of the tree represent the reachable states of a process, and the branches connect two nodes if a transition exists between the corresponding states. A cost-function value is associated with each node, and based on this value the exploration of the tree is driven. As soon as the exploration of the tree is finished, the corresponding input is applied to the system and the procedure is repeated.     

Static and low order anti-windup synthesis for cascade control systems with actuator saturation: An application to temperature-based process control

In this paper, a new framework for designing static and low order anti-windup compensator (AWC) for industrial cascade control systems with actuator saturation constraint is presented. Based on less conservative block diagonal quadratic Lyapunov function, sector boundedness, decoupled architecture, norm reduction and cascade loop compensation, linear matrix inequalities are developed which guarantee stability and suitable performance for overall closed-loop system. Static AWC parameters are obtained by comparing the full order AWC architecture with generalized architecture for cascade control system. Low order AWC is designed by sub-optimal approach in which AWC weights are tuned by designer. Anti-windup compensator is divided into inner and outer loop compensators which compensate the effect of saturation at each level. It is observed that the proposed methodology is less conservative than the traditional AWC schemes when applied to cascade control systems. The proposed scheme is successfully tested experimentally on a temperature-based process control system and results are outlined.     

Model predictive control helps to regulate slow processes--robust barrel temperature control

Slow temperature control is a challenging control problem. The problem becomes even more challenging when multiple zones are involved, such as in barrel temperature control for extruders. Often, strict closed-loop performance requirements (such as fast startup with no overshoot and maintaining tight temperature control during production) are given for such applications. When characteristics of the system are examined, it becomes clear that a commonly used proportional plus integral plus derivative (PID) controller cannot meet such performance specifications for this kind of system. The system either will overshoot or not maintain the temperature within the specified range during the production run. In order to achieve the required performance, a control strategy that utilizes techniques such as model predictive control, autotuning, and multiple parameter PID is formulated. This control strategy proves to be very effective in achieving the desired specifications, and is very robust.     

Extended state observer based output control for spacecraft rendezvous and docking with actuator saturation

This paper investigates the relative position tracking and attitude synchronization problem of a chaser spacecraft rendezvous and docking with an uncontrolled tumbling target in the presence of external disturbances and actuator saturation. By combining the extended state observer technique with backstepping control methodology, a robust output-feedback control strategy with no precise motion information of the tumbling target is proposed. Moreover, a particular Nussbaum-type function is introduced to compensate for the nonlinear terms arising for actuator saturation. Within the Lyapunov framework, it is then shown that the proposed control strategy can guarantee the relative position and attitude errors converge into small regions containing the origin. Finally, numerical simulations are carried out to verify the effectiveness of the designed control strategy.     

Improved state space model predictive fault-tolerant control for injection molding batch processes with partial actuator faults using GA optimization

A novel model predictive fault-tolerant control (MPFTC) strategy adopting genetic algorithm (GA) is proposed for batch processes under the case of disturbances and partial actuator faults. Based on the extended state space model in which the tracking error is contained, there are more degrees of freedom provided for the controller design and better control performance is obtained. In order to enhance the control performance further, the GA is introduced to optimize the relevant weighting matrices in the cost function. The effectiveness of the proposed MPFTC approach is tested on the injection velocity regulation of the injection molding process.     

Model predictive control for systems with fast dynamics using inverse neural models

In this work, a novel model predictive control (MPC) scheme is introduced, by integrating direct and indirect neural control methodologies. The proposed approach makes use of a robust inverse radial basis function (RBF) model taking into account the applicability domain criterion, in order to provide a suitable initial starting point for the optimizer, thus helping to solve the optimization problem faster. The performance of the proposed controller is evaluated on the control of a highly nonlinear system with fast dynamics and compared with different control schemes. Results show that the proposed approach outperforms the rivaling schemes in terms of response; moreover, it solves the optimization problem in less than one sampling period, thus effectively rendering MPC-based controllers capable of handling systems with fast dynamics.     

Model predictive control of non-linear systems over networks with data quantization and packet loss

This paper studies the approach of model predictive control (MPC) for the non-linear systems under networked environment where both data quantization and packet loss may occur. The non-linear controlled plant in the networked control system (NCS) is represented by a Tagaki-Sugeno (T-S) model. The sensed data and control signal are quantized in both links and described as sector bound uncertainties by applying sector bound approach. Then, the quantized data are transmitted in the communication networks and may suffer from the effect of packet losses, which are modeled as Bernoulli process. A fuzzy predictive controller which guarantees the stability of the closed-loop system is obtained by solving a set of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed method.     

A PSO-based optimal tuning strategy for constrained multivariable predictive controllers with model uncertainty

This paper describes the development of a method to optimally tune constrained MPC algorithms with model uncertainty. The proposed method is formulated by using the worst-case control scenario, which is characterized by the Morari resiliency index and the condition number, and a given nonlinear multi-objective performance criterion. The resulting constrained mixed-integer nonlinear optimization problem is solved on the basis of a modified version of the particle swarm optimization technique, because of its effectiveness in dealing with this kind of problem. The performance of this PSO-based tuning method is evaluated through its application to the well-known Shell heavy oil fractionator process.     

Adaptive control for spacecraft rendezvous subject to actuator faults and saturations

An adaptive saturated fault-tolerant controller is proposed for a spacecraft rendezvous maneuver with a cooperative target spacecraft. The six-degree-of-freedom (6-DOF) relative dynamics subject to unknown inertial parameters, external disturbances, actuator faults and saturations are formulated in the pursuer's body-fixed frame. To design controller satisfying asymmetric magnitude constraints, a modified smooth hyperbolic tangent function is applied to approximate the non-differentiable saturation function. Based on the augmented system technique, an adaptive fault-tolerant saturated controller is designed for the pursuer by using a Nussbaum function matrix compensating for the nonlinear term arising from the input saturations. In addition, a Levant differentiator is introduced to obtain the derivative of the virtual control in finite time that avoids the complicated calculation. It is proved via Lyapunov stability theory that all the signals in the closed-loop augmented system are bounded and the relative errors asymptotically converge to zero. Numerical simulations are performed to illustrate effectiveness of the proposed controller.     

Robust model predictive control design with input constraints

The paper addresses the problem of designing a robust output/state model predictive control for linear polytopic systems with input constraints. The new predictive and control horizon model is derived as a linear polytopic system. Lyapunov function approach guarantees the quadratic stability and guaranteed cost for closed-loop system. The invariant set and an algorithm approach similar to Soft Variable-Structure Control (SVSC), ensures input constraints for the model predictive plant control system. In the proposed control scheme, the required on-line computation load is significantly less than in MPC literature, which opens the possibility to use these control design schemes not only for plants with slow dynamics, but also for faster ones.     

Modeling a multivariable reactor and on-line model predictive control

A nonlinear first principle model is developed for a laboratory-scaled multivariable chemical reactor rig in this paper and the on-line model predictive control (MPC) is implemented to the rig. The reactor has three variables-temperature, pH, and dissolved oxygen with nonlinear dynamics-and is therefore used as a pilot system for the biochemical industry. A nonlinear discrete-time model is derived for each of the three output variables and their model parameters are estimated from the real data using an adaptive optimization method. The developed model is used in a nonlinear MPC scheme. An accurate multistep-ahead prediction is obtained for MPC, where the extended Kalman filter is used to estimate system unknown states. The on-line control is implemented and a satisfactory tracking performance is achieved. The MPC is compared with three decentralized PID controllers and the advantage of the nonlinear MPC over the PID is clearly shown.     

基于广义预测控制算法的水槽液位控制系统

为提高液位系统控制的可靠性和安全性,引入了广义预测控制算法。首先介绍了广义预测控制的基本算法,包括其基本理论、算法的优点及一些重要参数的选取标准。然后以水槽液位控制装置为控制对象建立了一个控制系统的数学模型,并对应用广义预测控制算法的该模型进行了仿真验证。仿真结果表明,所提出的算法具有良好的动态响应性能和快速跟踪设定值,并具有较好的控制效果。无论系统是否存在模型失配,只要控制系统是稳定的,就不会有静差。