Constrained model predictive force control of an electrohydraulic actuator

An analytical MPC controller was designed for force control of a single-rod electrohydraulic actuator. The controller based on a difference equation uses short control horizon. The constraints on both input and output variables are taken into consideration by the controller. The mechanism of output constraints satisfaction uses output prediction and makes possible to constrain the output values many sampling instants ahead. Thus, it extends capabilities of the analytical MPC controllers to the field reserved so far for much more computationally expensive numerical MPC algorithms. Results of real life experiments illustrate efficiency of the proposed controller. The results also show that the MPC controller has better tracking performance than conventional P and PI controllers. The MPC controller with the constraint handling mechanisms, though relatively simple, offers very good performance. As the design process is detailed, it is possible to relatively easy adapt the proposed approach to other control plants.     

Computation delay compensation for real time implementation of robust model predictive control

The implementation of model predictive control (MPC) requires to solve an optimization problem online. The computation time, often not negligible especially for nonlinear MPC (NMPC), introduces a delay in the feedback loop. Moreover, it impedes fast sampling rate setting for the controller to react to uncertainties quickly. In this paper, a dual time scale control scheme is proposed for linear/nonlinear systems with external disturbances. A pre-compensator works at fast sampling rate to suppress uncertainty, while the outer MPC controller updates the open loop input sequence at a slower rate. The computation delay is explicitly considered and compensated in the MPC design. Four robust MPC algorithms for linear/nonlinear systems in the literature are adopted and tailored for the proposed control scheme. The recursive feasibility and stability are rigorously analysed. Three simulation examples are provided to validate the proposed approaches.     

Pathways for optimization-based drug delivery

An overview of our research results on the implementation of model predictive control (MPC) on-chip is presented, with central focus the development of small-size, energy efficient controllers suitable for drug delivery systems and devices. Profiling simulations coupled with codesign techniques are used in order to reveal algorithmic bottlenecks and to effectively customize implementation designs. Hardware in-the-loop simulations using a general purpose processor and a field programmable gate array, and emulations of an application specific processor are provided. The performance measurements and estimates illustrate that MPC is suitable for on-chip real-time optimal control of complex systems with fast dynamics.     

Enhanced predictive ratio control of interacting systems

Ratio control for two interacting processes is proposed with a PID feedforward design based on model predictive control (MPC) scheme. At each sampling instant, the MPC control action minimizes a state-dependent performance index associated with a PID-type state vector, thus yielding a PID-type control structure. Compared to the standard MPC formulations with separated single-variable control, such a control action allows one to take into account the non-uniformity of the two process outputs. After reformulating the MPC control law as a PID control law, we provide conditions for prediction horizon and weighting matrices so that the closed-loop control is asymptotically stable, and show the effectiveness of the approach with simulation and experiment results.     

Distributed model predictive control of constrained nonlinear systems with communication delays

Distributed model predictive control (MPC), having been proven to be efficient for large-scale control systems, is essentially enabled by communication network connections among involved subsystems (agents). This paper studies the distributed MPC problem for a class of continuous-time decoupled nonlinear systems subject to communication delays. By using a robustness constraint and designing a waiting mechanism, a delay-involved distributed MPC scheme is proposed. Furthermore, the iterative feasibility and stability properties are analyzed. It is shown that, if the communication delays are bounded by an upper bound, and the cooperation weights and the sampling period are designed appropriately, the overall system state converges to the equilibrium point. The theoretical results are verified by a simulation study.     

A method of MPC model error detection

This work introduces a method of multivariable model error detection in model prediction control (MPC). The idea is to use non-disturbing small sinusoidal test signals to obtain accurate estimates of process frequency responses at several frequency points. Then, the differences between estimated frequency responses and the frequency responses of current MPC model are used to form the model error index matrix which is used to access the model error of the MPC controller. An upper error bound is developed for quantifying the error of frequency response estimation. The method works in closed-loop operation with the MPC controller online. Simulation studies are used to demonstrate the use of the method.     

Analytical results for the multi-objective design of model-predictive control

In model-predictive control (MPC), achieving the best closed-loop performance under a given computational capacity is the underlying design consideration. This paper analyzes the MPC tuning problem with control performance and required computational capacity as competing design objectives. The proposed multi-objective design of MPC (MOD-MPC) approach extends current methods that treat control performance and the computational capacity separately – often with the latter as a fixed constraint – which requires the implementation hardware to be known a priori. The proposed approach focuses on the tuning of structural MPC parameters, namely sampling time and prediction horizon length, to produce a set of optimal choices available to the practitioner. The posed design problem is then analyzed to reveal key properties, including smoothness of the design objectives and parameter bounds, and establish certain validated guarantees. Founded on these properties, necessary and sufficient conditions for an effective and efficient optimizer are presented, leading to a specialized multi-objective optimizer for the MOD-MPC being proposed. Finally, two real-world control problems are used to illustrate the results of the tuning approach and importance of the developed conditions for an effective optimizer of the MOD-MPC problem.     

A fixed-point iteration scheme for real-time model predictive control

A simple model predictive control (MPC) concept for nonlinear systems under input constraints is considered. The presented algorithm takes advantage of an MPC formulation without terminal constraints in order to solve the optimality conditions by a fixed-point iteration scheme that is easy to implement and of algorithmic simplicity. Sufficient conditions for the contraction of the fixed-point iterations are derived. To allow for a real-time implementation within an MPC scheme, a constant number of fixed-point iterations is used in each sampling step and sufficient conditions for asymptotic stability and incremental reduction of the suboptimality are presented.     

Incorporating state estimation into model predictive control and its application to network traffic control

Model predictive control (MPC) is of interest because it is one of the few control design methods which preserves standard design variables and yet handles constraints. MPC is normally posed as a full-state feedback control and is implemented in a certainty-equivalence fashion with best estimates of the states being used in place of the exact state. This paper focuses on exploring the inclusion of state estimates and their interaction with constraints. It does this by applying constrained MPC to a system with stochastic disturbances. The stochastic nature of the problem requires re-posing the constraints in a probabilistic form. Using a gaussian assumption, the original problem is approximated by a standard deterministically-constrained MPC problem for the conditional mean process of the state. The state estimates’ conditional covariances appear in tightening the constraints. ‘Closed-loop covariance’ is introduced to reduce the infeasibility and the conservativeness caused by using long-horizon, open-loop prediction covariances. The resulting control law is applied to a telecommunications network traffic control problem as an example.     

Model predictive control of continuous-time nonlinear systems with piecewise constant control

A new model predictive control (MPC) algorithm for nonlinear systems is presented. The plant under control, the state and control constraints, and the performance index to be minimized are described in continuous time, while the manipulated variables are allowed to change at fixed and uniformly distributed sampling times. In so doing, the optimization is performed with respect to sequences, as in discrete-time nonlinear MPC, but the continuous-time evolution of the system is considered as in continuous-time nonlinear MPC.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Predictive control of a real-world Diesel engine using an extended online active set strategy

In order to meet tight emission limits Diesel engines are nowadays equipped with additional hardware components like an exhaust gas recirculation valve and a variable geometry turbocharger. Conventional engine control units use two SISO control loops to regulate the exhaust gas recirculation valve and the variable geometry turbocharger, although their effects are highly coupled. Moreover, these actuators are subject to physical constraints which seems to make an advanced control approach like model predictive control (MPC) the method of choice. In order to deal with MPC sampling times in the order of milliseconds, we employed an extension of the recently developed online active set strategy for controlling a real-world Diesel engine in a closed-loop manner. The results show that predictive engine control based on online optimisation can be accomplished in real-time – even on cheap controller hardware – and leads to increased controller performance.     

On real-time robust model predictive control

High-speed applications impose a hard real-time constraint on the solution of a model predictive control (MPC) problem, which generally prevents the computation of the optimal control input. As a result, in most MPC implementations guarantees on feasibility and stability are sacrificed in order to achieve a real-time setting. In this paper we develop a real-time MPC approach for linear systems that provides these guarantees for arbitrary time constraints, allowing one to trade off computation time vs. performance. Stability is guaranteed by means of a constraint, enforcing that the resulting suboptimal MPC cost is a Lyapunov function. The key is then to guarantee feasibility in real-time, which is achieved by the proposed algorithm through a warm-starting technique in combination with robust MPC design. We address both regulation and tracking of piecewise constant references. As a main contribution of this paper, a new warm-start procedure together with a Lyapunov function for real-time tracking is presented. In addition to providing strong theoretical guarantees, the proposed method can be implemented at high sampling rates. Simulation examples demonstrate the effectiveness of the real-time scheme and show that computation times in the millisecond range can be achieved.     

A General Robust MPC Design for the State‐Space Model: Application to Paper Machine Process

Applying model predictive control (MPC) in some cases such as complicated process dynamics and/or rapid sampling leads us to poorly numerically conditioned solutions and heavy computational load. Furthermore, there is always mismatch in a model that describes a real process. Therefore, in this paper in order to prevail over the mentioned difficulties, we design a robust MPC using the Laguerre orthonormal basis in order to speed up the convergence at the same time with lower computation adding an extra parameter “a” in MPC. In addition, the Kalman state estimator is included in the prediction model and accordingly the MPC design is related to the Kalman estimator parameters as well as the error of estimations which helps the controller react faster against unmeasured disturbances. Tuning the parameters of the Kalman estimator as well as MPC is another achievement of this paper which guarantees the robustness of the system against the model mismatch and measurement noise. The sensitivity function at low frequency is minimized to tune the MPC parameters since the lower the magnitude of the sensitivity function at low frequency the better command tracking and disturbance rejection results. The integral absolute error (IAE) and peak of the sensitivity are used as constraints in optimization procedure to ensure the stability and robustness of the controlled process. The performance of the controller is examined via the controlling level of a Tank and paper machine processes.     

Nonlinear model predictive control of a magnetic levitation system

The paper presents a fast nonlinear model predictive control (MPC) scheme for a magnetic levitation system. A nonlinear dynamical model of the levitation system is derived that additionally captures the inductor current dynamics of the electromagnet in order to achieve a high MPC performance both for stabilization and fast setpoint changes of the levitating mass. The optimization algorithm underlying the MPC scheme accounts for control constraints and allows for a time and memory efficient computation of the single iteration. The overall control performance of the levitation system as well as the low computational costs of the MPC scheme is shown both in simulations and experiments with a sampling frequency of 700 Hz on a standard dSPACE hardware.     

Multiobjective model predictive control

This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying, state-dependent decision criterion. Compared to standard single-objective MPC formulations, such a criterion allows one to take into account several, often irreconcilable, control specifications, such as high bandwidth (closed-loop promptness) when the state vector is far away from the equilibrium and low bandwidth (good noise rejection properties) near the equilibrium. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear or quadratic program, we show that it is possible to compute each Pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular Pareto optimal solution. Furthermore, we provide conditions for selecting Pareto optimal solutions so that the MPC control loop is asymptotically stable, and show the effectiveness of the approach in simulation examples.     

Contractive model predictive control for constrained nonlinearsystems

This paper addresses the development of stabilizing state and output feedback model predictive control (MPC) algorithms for constrained continuous-time nonlinear systems with discrete observations. Moreover, we propose a nonlinear observer structure for this class of systems and derive sufficient conditions under which this observer provides asymptotically convergent estimates. The MPC scheme proposed consists of a basic finite horizon nonlinear MPC technique with the introduction of an additional state constraint, which has been called a contractive constraint. The resulting MPC scheme has been denoted contractive MPC. This is a Lyapunov-based approach in which a Lyapunov function chosen a priori is decreased, not continuously, but discretely; it is allowed to increase at other times. We show in this work that the implementation of this additional constraint into the online optimization makes it possible to prove strong nominal stability properties of the closed-loop system     

在线优化线性反馈增益的非线性鲁棒预测控制方法

以鲁棒控制不变集作为预测控制的终端约束集,设计了一种新的鲁棒预测控制算法.将预测控制在不同采样点的待优化控制律考虑为线性反馈控制律,并通过在线优化求解线性反馈增益.从理论上证明了若采用所设计的鲁棒预测控制器,则系统是输入状态稳定的.最后通过计算机仿真验证了所提出设计方法的可行性.