Non-minimal state-space model-based continuous-time model predictive control with constraints

This article proposes a model predictive control scheme based on a non-minimal state-space (NMSS) structure. Such a combination yields a continuous-time state-space model predictive control system that permits hard constraints to be imposed on both plant input and output variables, whilst using NMSS output-feedback without the need for an observer. A comparison between the NMSS and observer-based approaches using Monte Carlo uncertainty analysis shows that the former design is considerably less sensitive to plant-model mismatch than the latter. Through simulation studies, the article also investigates the role of the implementation filter in noise attenuation, disturbance rejection and robustness of the closed-loop predictive control system. The results show that the filter poles become a subset of the closed-loop poles and this provides a straightforward method of tuning the closed-loop performance to achieve a reasonable balance between speed of response, disturbance rejection, measurement noise attenuation and robustness.     

An improved structure for model predictive control using non-minimal state space realisation

This paper describes a new method for the design of model predictive control (MPC) using non-minimal state space models, in which the state variables are chosen as the set of measured input and output variables and their past values. It shows that the proposed design approach avoids the use of an observer to access the state information and, as a result, the disturbance rejection, particularly the system input disturbance rejection, is significantly improved when constraints become activated. In addition, when there is no model/plant mismatch, the paper shows that the system output constraints can be realised in the proposed approach. Furthermore, closed-form transfer function representation of the model predictive control system enables the application of frequency response analysis tools to the nominal performance of the system.     

An improved model predictive control approach based on extended non-minimal state space formulation

This paper presents a new design method of model predictive control (MPC) based on extended non-minimal state space models, in which the measured input and output variables, their past values together with the defined output errors are chosen as the state variables. It shows that this approach does not need the design of an observer to access the state information any more and by augmenting the process model and its objective function to include the changes of the system state variables, the control performances are superior to those of the controller that does not bear this feature. Furthermore, closed-loop transfer function representation of the model predictive control system facilitates the use of frequency response analysis methods for the nominal control performances of the system.     

Input-output linearizing control of constrained nonlinear processes

An input-output linearization strategy for constrained nonlinear processes is proposed. The system may have constraints on both the manipulated input and the controlled output. The nonlinear control system is comprised of: (i) an input-output linearizing controller that compensates for processes nonlinearities; (ii) a constraint mapping algorithm that transforms the original input constraints into constraints on the manipulated input of the feedback linearized system; (iii) a linear model predictive controller that regulates the resulting constrained linear system; and (iv) a disturbance model that ensures offset-free setpoint tracking. As a result of these features, the approach combines the computational simplicity of input output linearization and the constraint handling capability of model predictive control. Simulation results for a continuous stirred tank reactor demonstrate the superior performance of the proposed strategy as compared to conventional input-output linearizing control and model predictive control techniques.     

Model predictive control of axial dispersion chemical reactor

This paper discusses the development of model predictive control algorithm which accounts for the input and state constraints applied to the parabolic partial differential equations (PDEs) system describing the axial dispersion chemical reactor. Spatially varying terms arising from the nonlinear PDEs model are accounted for in model development. Finite-dimensional modal representation capturing the dominant dynamics of the PDEs system is derived for controller design through Galerkin's method and modal decomposition technique. Tustin's discretization and Cayley transform are used to obtain infinite-dimensional discrete-time dynamic modal representations which are used in subsequent constrained controller design. The proposed discrete-time constrained model predictive control synthesis is constructed in a way that the objective function is only based on the low-order modal representation of the PDEs system, while higher-order modes are utilized only in the constraints of the PDEs state. Finally, the MPC formulations are successfully applied, via simulation results, to the PDEs system with input and state constraints.     

线性自抗扰控制的抗饱和补偿措施

控制输入约束是实际工业过程中普遍存在的现象,然而控制器设计中通常都假设执行机构动态是线性的,因此当执行机构存在约束时,执行机构输出信号与控制器输出信号不一致,使系统的动态性能降低,甚至导致系统不稳定.本文针对线性自抗扰控制(linearactive disturbance rejection control,LADRC)执行机构的约束问题,提出两种抗饱和补偿方案,利用LADRC扩张状态观测器估计控制器状态或者控制器输出与执行器输出的误差,从而使LADRC能快速消除饱和.将这两种方法用到含执行机构饱和的一阶惯性加迟延被控对象进行仿真研究,结果表明两种补偿措施下线性自抗扰控制器能得到较好的控制性能.随后本文将LADRC抗饱和思想推广到负荷频率控制系统(load frequency control,LFC)中,仿真表明基于误差补偿的抗饱和方案对于LFC系统更为有效.     

Output feedback model predictive control for LPV systems based on quasi-min–max algorithm

This paper proposes a robust output feedback model predictive control (MPC) scheme for linear parameter varying (LPV) systems based on a quasi-min–max algorithm. This approach involves an off-line design of a robust state observer for LPV systems using linear matrix inequality (LMI) and an on-line robust output feedback MPC algorithm using the estimated state. The proposed MPC method for LPV systems is applicable for a variety of systems with constraints and guarantees the robust stability of the output feedback systems. A numerical example for an LPV system subject to input constraints is given to demonstrate its effectiveness.     

六自由度机械臂约束预测控制系统的设计

本文提出了一种基于约束预测控制的机械臂实时运动控制方法.该控制方法分为两层,分别设计了约束预测控制器和跟踪控制器.其中,约束预测控制器在考虑系统物理约束的条件下,在线为跟踪控制器生成参考轨迹;跟踪控制器采用最优反馈控制律,使机械臂沿参考轨迹运动.为了简化控制器的设计和在线求解,本文采用输入输出线性化的方式简化机械臂动力学模型.同时,为了克服扰动,在约束预测控制器中引入前馈策略,提出了带前馈一反馈控制结构的预测控制设计.因此,本文设计的控制器可以使机械臂在满足物理约束的条件下快速稳定地跟踪到目标位置.通过在PUMA560机理模型上进行仿真实验,验证了预测控制算法的可行性和有效性.     

Time‐varying input delay compensation for nonlinear systems with additive disturbance: An output feedback approach

This paper addresses the output feedback tracking control of a class of multiple‐input and multiple‐output nonlinear systems subject to time‐varying input delay and additive bounded disturbances. Based on the backstepping design approach, an output feedback robust controller is proposed by integrating an extended state observer and a novel robust controller, which uses a desired trajectory‐based feedforward term to achieve an improved model compensation and a robust delay compensation feedback term based on the finite integral of the past control values to compensate for the time‐varying input delay. The extended state observer can simultaneously estimate the unmeasurable system states and the additive disturbances only with the output measurement and delayed control input. The proposed controller theoretically guarantees prescribed transient performance and steady‐state tracking accuracy in spite of the presence of time‐varying input delay and additive bounded disturbances based on Lyapunov stability analysis by using a Lyapunov‐Krasovskii functional. A specific study on a 2‐link robot manipulator is performed; based on the system model and the proposed design procedure, a suitable controller is developed, and comparative simulation results are obtained to demonstrate the effectiveness of the developed control scheme.     

Robust output feedback model predictive control of constrained linear systems

This paper provides a solution to the problem of robust output feedback model predictive control of constrained, linear, discrete-time systems in the presence of bounded state and output disturbances. The proposed output feedback controller consists of a simple, stable Luenberger state estimator and a recently developed, robustly stabilizing, tube-based, model predictive controller. The state estimation error is bounded by an invariant set. The tube-based controller ensures that all possible realizations of the state trajectory lie in a simple uncertainty tube the ‘center’ of which is the solution of a nominal (disturbance-free) system and the ‘cross-section’ of which is also invariant. Satisfaction of the state and input constraints for the original system is guaranteed by employing tighter constraint sets for the nominal system. The complexity of the resultant controller is similar to that required for nominal model predictive control.     

Experimental quadrotor flight performance using computationally efficient and recursively feasible linear model predictive control

A new linear model predictive control (MPC) algorithm in a state-space framework is presented based on the fusion of two past MPC control laws: steady-state optimal MPC (SSOMPC) and Laguerre optimal MPC (LOMPC). The new controller, SSLOMPC, is demonstrated to have improved feasibility, tracking performance and computation time than its predecessors. This is verified in both simulation and practical experimentation on a quadrotor unmanned air vehicle in an indoor motion-capture testbed. The performance of the control law is experimentally compared with proportional-integral-derivative (PID) and linear quadratic regulator (LQR) controllers in an unconstrained square manoeuvre. The use of soft control output and hard control input constraints is also examined in single and dual constrained manoeuvres.     

离散时间部分状态反馈模型参考自适应控制

本文针对线性不确定性系统, 给出了部分状态反馈直接模型参考自适应控制设计方案以及详细的系统稳 定性、输出跟踪性能分析. 控制器设计基于降维观测器和参数化方法. 此方案采用反馈控制, 反馈信号不仅仅依赖 全状态信息或者输出信号, 而是任意不超过系统维数的可测信号. 因此, 部分状态反馈控制是包含状态反馈、输出 反馈控制的新的控制方案, 缓解了状态反馈对状态信息的限制, 降低了输出反馈控制结构的复杂性. 通过引入辅助 信号, 本文证明了输出匹配条件的存在性、所有闭环系统信号的有界性以及渐近输出跟踪性能. 仿真结果验证了该 方案的有效性.     

基于扩张状态观测器的车辆横摆稳定模型预测控制器设计

针对车辆横摆稳定性控制问题,本文提出一种基于扩张状态观测器的线性模型预测控制器设计方法.首先,将非线性车辆模型线性化,建立带有模型误差干扰项的线性模型,其中线性化导致的模型误差采用扩张状态观测器估计得到,并证明了观测器的稳定性.然后基于此模型设计线性预测控制器,近似实现了非线性预测控制器的控制效果,同时降低了计算量.最后,通过不同路况下的仿真实验结果,验证了所提方法的计算性能和控制效果.     

State space model predictive fault-tolerant control for batch processes with partial actuator failure

This paper presents a state space model predictive fault-tolerant control scheme for batch processes with unknown disturbances and partial actuator faults. To develop the model predictive fault-tolerant control, the batch process is first treated into a non-minimal representation using state space transformation. The relevant concepts of the corresponding model predictive fault-tolerant control is thus introduced through state space formulation, where improved closed-loop control performance is achieved even with unknown disturbances and actuator faults, because, unlike traditional model predictive fault-tolerant control, the proposed control method can directly regulate the process output/input changes in the design. For performance comparison, a traditional model predictive fault-tolerant control is also designed. Application to injection velocity control shows that the proposed scheme achieve the design objective well with performance improvement.     

Optimal digital controller and observer design for multiple time-delay transfer function matrices with multiple input–output time delays

In this article, we address the optimal digital design methodology for multiple time-delay transfer function matrices with multiple input–output time delays. In our approach, the multiple time-delay analogue transfer function matrix with multiple input–output time delays is minimally realised using a continuous-time state-space model. For deriving an explicit form of the optimal digital controller, the realised continuous-time multiple input–output time-delay system is discretised, and an extended high-order discrete-time state-space model is constructed for discrete-time LQR design. To derive a low-order optimal digital observer for the multiple input–output time-delay system, the multiple time-delay state obtained from the multiple time-delay outputs is discretised. Then, the well-known duality concept is employed to design an optimal digital observer using the low-order discretised multiple input time-delay system together with the newly discretised multiple time-delay state. The proposed approach is restricted to multiple time-delay systems where multiple time delays arise only in the input and output, and not in the state.     

A control matching model predictive control approach to string stable vehicle platooning

A predictive control strategy for vehicle platoons is presented in this paper, accommodating both string stability and constraints (e.g., physical and safety) satisfaction. In the proposed design procedure, the two objectives are achieved by matching a model predictive controller (MPC), enforcing constraints satisfaction, with a linear controller designed to guarantee string stability. The proposed approach neatly combines the straightforward design of a string stable controller in the frequency domain, where a considerable number of approaches have been proposed in literature, with the capability of an MPC-based controller enforcing state and input constraints.A controller obtained with the proposed design procedure is validated both in simulations and in the field test, showing how string stability and constraints satisfaction can be simultaneously achieved with a single controller. The operating region that the MPC controller is string stable is characterized by the interior of feasible set of the MPC controller.     

High performance nonlinear adaptive control of temperature in cryogenic wind tunnel

A new nonlinear adaptive control method based on Immersion and Invariant (I&I) approach is proposed for the temperature control of a cryogenic wind tunnel. The proposed control method can be applied to wide range temperature operation of the tunnel by incorporating the nonlinear dynamic model of temperature into the controller design. By constructing globally stable nonlinear observer, and rendering an invariant and attractive manifold in the state space of plant and observer, the uncertain gain of known disturbance and unknown wind tunnel wall temperature are considered in the same manner within the adaptive I&I control frame. In the design, nominal heat transfer coefficient is deployed to avoid complicated design process involving nonlinear parameterization. This design leads to an adaptive output feedback stabilization control law for the temperature with guaranteed transient and steady performance, which exhibits reasonable robustness to time delay in the control input channel and other uncertainties. The analysis and simulation show the effectiveness of the proposed control methodology.     

Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control

This work considers the problem of stabilization of nonlinear systems subject to state and control constraints, for cases where the state constraints need to be enforced at all times (hard constraints) and where they can be relaxed for some time (soft constraints). We propose a Lyapunov-based predictive control design that guarantees stabilization and state and input constraint satisfaction for all times from an explicitly characterized set of initial conditions. An auxiliary Lyapunov-based analytical bounded control design is used to characterize the stability region of the predictive controller and also provide a feasible initial guess to the optimization problem in the predictive controller formulation. For the case when the state constraints are soft, we propose a switched predictive control strategy that reduces the time during which state constraints are violated, driving the states into the state and input constraints feasibility region of the Lyapunov-based predictive controller. We demonstrate the application of the Lyapunov-based predictive controller designs through a chemical process example.     

Design of robust model predictive control with input constraints

This article addresses the problem of designing a robust output feedback model predictive control (MPC) with input constraints, which ensures a parameter-dependent quadratic stability and guaranteed cost for the case of linear polytopic systems. A new heuristic method is introduced to guarantee input constraints for the MPC. To reject disturbances and maintain the process at the optimal operating conditions or setpoints, the integrator is added to the controller design procedure. Finally, some numerical examples are given to illustrate the effectiveness of the proposed method.     

Adaptive receding horizon control for constrained MIMO systems

An adaptive control algorithm for open-loop stable, constrained, linear, multiple input multiple output systems is presented. The proposed approach can deal with both input and output constraints, as well as measurement noise and output disturbances. The adaptive controller consists of an iterative set membership identification algorithm, that provides a set of candidate plant models at each time step, and a model predictive controller, that enforces input and output constraints for all the plants inside the model set. The algorithm relies only on the solution of standard convex optimization problems that are guaranteed to be recursively feasible. The experimental results obtained by applying the proposed controller to a quad-tank testbed are presented.