Enlarging the domain of attraction of stable MPC controllers, maintaining the output performance

This work presents an alternative way to formulate the stable Model Predictive Control (MPC) optimization problem that allows the enlargement of the domain of attraction, while preserving the controller performance. Based on the dual MPC that uses the null local controller, it proposed the inclusion of an appropriate set of slacked terminal constraints into the control problem. As a result, the domain of attraction is unlimited for the stable modes of the system, and the largest possible for the non-stable modes. Although this controller does not achieve local optimality, simulations show that the input and output performances may be comparable to the ones obtained with the dual MPC that uses the LQR as a local controller.     

Uniting bounded control and MPC for stabilization of constrained linear systems

In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a logic-based supervisor that constantly monitors the plant, are derived to orchestrate the transition between the two controllers in a way that safeguards against any possible instability or infeasibility under MPC, reconciles the stability and optimality properties of both controllers, and guarantees asymptotic closed-loop stability for all initial conditions within the stability region of the bounded controller. The hybrid control scheme is shown to provide, irrespective of the chosen MPC formulation, a safety net for the practical implementation of MPC, for open-loop unstable plants, by providing a priori knowledge, through off-line computations, of a large set of initial conditions for which closed-loop stability is guaranteed. The implementation of the proposed approach is illustrated, through numerical simulations, for an exponentially unstable linear system.     

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.     

A practical multiple model adaptive strategy for single-loop MPC

This paper details a multiple model adaptive control strategy for model predictive control (MPC). To maintain performance of this linear controller over a wide range of operating levels, a multiple model adaptive control strategy for dynamic matrix control (DMC), the process industry's standard for MPC, is presented. The method of approach is to design multiple linear DMC controllers. The tuning parameters for the linear controllers are obtained using novel analytical expressions. The controller output of the adaptive DMC controller is a weighted average of the multiple linear DMC controllers. The capabilities of the multiple model adaptive strategy for DMC are investigated through computer simulations and an experimental system.     

Model predictive controller with average emissions constraints for diesel airpath

Diesel airpath controllers are required to deliver good tracking performance whilst satisfying operational constraints and physical limitations of the actuators. Due to explicit constraint handling capabilities, model predictive controllers (MPC) have been successfully deployed in diesel airpath applications. Previous MPC implementations have considered instantaneous constraints on engine-out emissions in order to meet legislated emissions regulations. However, the emissions standards are specified over a drive cycle, and hence, can be satisfied on average rather than just instantaneously, potentially allowing the controller to exploit the trade-off between emissions and fuel economy. In this work, an MPC is formulated to maximise the fuel efficiency whilst tracking boost pressure and exhaust gas recirculation (EGR) rate references, and in the face of uncertainties, adhering to the input, safety constraints and constraints on emissions averaged over some finite time period. The tracking performance and satisfaction of average emissions constraints using the proposed controller are demonstrated through an experimental study considering the new European drive cycle.     

Reference trajectory tuning of model predictive control

An approach to minimize tuning effort of nominal Model Predictive Control algorithms is proposed. The algorithm dynamically calculates output set points to accommodate user-defined output importance, which is more intuitive than selecting values for the MPC weighing matrices. Instead of tuning the weights on the outputs deviations from their set points, weights on the input values and input increments, which are the usual tuning parameters of MPC, the desired output control performance of the MPC can be specified by performance factors. The proposed method extends the existing methods that consider a reference trajectory for the output tracking to the case of zone control and input targets. The proposed method also assumes that, as in most commercial MPC packages, the controller has two layers: a static layer and an extended dynamic layer. The method is illustrated by three case studies, contemplating both SISO and MIMO systems. It is observed that: the output set point tracking performance can be changed without modifying the MPC tuning weights, the approach is capable of achieving similar performance to conventional MPC tuned by multiobjective optimization techniques from the literature, with a fraction of computer effort, and it can be integrated with Real Time Optimization algorithms to control complex systems, always respecting output constraints.     

Use of model predictive controller in dual-loop control of three-phase PWM AC/DC converter

In the classical dual-loop voltage control scheme for an AC/DC converter, this paper proposes a simple stabilizing inner-loop model predictive controller (MPC) to regulate the output current and q-frame current to their references. The proposed MPC minimizes a cost function of the tracking error without any use of numerical methods using the specific property of the input matrix of the converter. It is shown that this MPC globally stabilizes the converter in the presence of input constraints. As the same manner of the classical dual-loop control scheme, PI controllers are adopted in the outerloop to regulate the output voltage while maintaining the maximum power factor. The simulation results show that the proposed inner-loop MPC considerably enhances the closed-loop performance despite the load changes.     

Robust distributed model predictive control of linear systems with structured time-varying uncertainties

In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min–max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.     

Least-restrictive move-blocking model predictive control

Move-blocking lowers the computational complexity of model predictive control (MPC) problems by reducing the number of optimization variables. However, this may render states close to constraints infeasible. Thus move-blocking generally results in control laws that are restrictive; the controller domains may be unacceptably and unnecessarily small. Furthermore, different move-blocking strategies may result in controller domains of different sizes, all other factors being equal. In this paper an approach is proposed to design move-blocking MPC control laws that are least-restrictive, i.e. the controller domain is equal to the maximum controlled invariant set. The domains of different move-blocking controllers are then by design equal to each other. This allows comparison of differing move-blocking strategies based on cost performance only, without needing to consider domain size also. Thus this paper is a step towards being able to derive optimal move-blocking MPC control laws.     

Stable MPC for tracking with maximal domain of attraction

In this work, a stable MPC that maximizes the domain of attraction of the closed-loop system is proposed. The proposed approach is suitable to real applications in the sense that it accounts for the case of output tracking, it is offset free if the output target is reachable and minimizes the offset if some of the constraints are active at steady state. The new approach is based on the definition of a Minkowski functional related to the input and terminal constraints of the stable infinite horizon MPC. It is also shown that the domain of attraction is defined by the system model and the constraints, and it does not depend on the controller tuning parameters. The proposed controller is illustrated with small order examples of the control literature.     

Performance analysis of a dynamic phenomenological controller for a pellet cooling process

The cooling zone of an induration furnace exhibits a nonlinear dynamic behavior in addition to a strong coupling between output pressure and temperature. Simulation studies show that linear controller performance is unacceptable from an industrial point of view. In order to obtain adequate performance on a wide operating range, a nonlinear predictive controller (NLMPC) based on a phenomenological process model is proposed. Since the furnace simulation model shows that the equipment behaves as a Hammerstein model, a variable change is performed and a linear model predictive controller (MPC) is developed for the cooling zone. Both controllers are tested for set-point changes and disturbance rejection and give relatively similar performances. It is concluded that for processes having structured nonlinearities, as the cooling zone considered here, linear MPC should be preferred to NLMPC since the computation time is far less demanding and the industrial implementation easier.     

An improved state-space model structure and a corresponding predictive functional control design with improved control performance

Conventional state-space model predictive control requires a state estimator/observer to access the state information for feedback controller design. Its drawbacks are the numerical convergence stability of the observer and closed-loop control performance deterioration with activated plant input/output constraints. The recent direct use of measured input and output variables to formulate a non-minimal state-space (NMSS) model overcomes these problems, but the subsequent controller is too sensitive to model mismatch. In this article, an improved structure of NMSS model that incorporates the output-tracking error is first formulated and then a subsequent predictive functional control design is proposed. The proposed controller is tested on both model match and model mismatch cases for comparison with previous controllers. Results show that control performance is improved. In addition, a linear programming method for constraints dealing and a closed form of transfer function representation of the control system are provided for further insight into the proposed method.     

Synthesis of Mixed Objective Output Feedback Robust Model Predictive Control

Aiming at the constrained polytopic uncertain system with energy‐bounded disturbance and unmeasurable states, a novel synthesis scheme to design the output feedback robust model predictive control(MPC)is put forward by using mixed H₂/H_∞ design approach. The proposed scheme involves an offline design of a robust state observer using linear matrix inequalities(LMIs)and an online output feedback robust MPC algorithm using the estimated states in which the desired mixed objective robust output feedback controllers are cast into efficiently tractable LMI‐based convex optimization problems. In addition, the closed‐loop stability and the recursive feasibility of the proposed robust MPC are guaranteed through an appropriate reformulation of the estimation error bound (EEB). A numerical example subject to input constraints illustrates the effectiveness of the proposed controller.     

Supervisory nonlinear MPC for emergency voltage control using pattern search

The design of a higher-layer controller using model predictive control (MPC) is considered. The higher-layer controller uses MPC to determine set-points for controllers in a lower control layer. In this paper the use of an object-oriented model of the system for making predictions is proposed. When employing such an object-oriented prediction model the MPC problem is a nonlinear, non-smooth optimization problem, with an objective function that is expensive to evaluate. Multi-start pattern search is proposed as approach to solving this problem, since it deals effectively with the local minima and the non-smoothness of the problem, and does not require expensive estimation of derivatives. Experiments in an emergency voltage control problem on a 9-bus dynamic power network show the superior performance of the proposed multi-start pattern-search approach when compared to a gradient-based approach.     

Multi-objective constraint optimizing IOL control of distillation column with nonlinear observer

Performance of input–output linearizing (IOL) controllers suffers due to constraints on input and output variables. This problem is successfully tackled by augmenting IOL controllers with quadratic dynamic matrix controller (QDMC). However, this has created a constraint-mapping problem for coupled MIMO systems like distillation column. A multi-objective optimization problem needs to be solved to map the constraints on inputs. A suitable transformation technique is proposed to convert this multi-objective optimization problem to a single objective one. This makes the controller less computationally intensive and easy to implement. This controller (IOL-QDMC) along with nonlinear observer is implemented on a binary distillation column for dual composition control. Its performance is evaluated against a quadratic dynamic matrix controller (QDMC) and input–output linearization with PI controller (IOL-PI).     

Optimal MPC for tracking of constrained linear systems

Model predictive control (MPC) is one of the few techniques which is able to handle constraints on both state and input of the plant. The admissible evolution and asymptotic convergence of the closed-loop system is ensured by means of suitable choice of the terminal cost and terminal constraint. However, most of the existing results on MPC are designed for a regulation problem. If the desired steady-state changes, the MPC controller must be redesigned to guarantee the feasibility of the optimisation problem, the admissible evolution as well as the asymptotic stability. Recently, a novel MPC has been proposed to ensure the feasibility of the optimisation problem, constraints satisfaction and asymptotic evolution of the system to any admissible target steady-state. A drawback of this controller is the loss of a desirable property of the MPC controllers: the local optimality property. In this article, a novel formulation of the MPC for tracking is proposed aimed to recover the optimality property maintaining all the properties of the original formulation.     

Comparison of PI and MPC for control of a gas recovery unit

This study compares PI and MPC controls via a computer simulation for a gas recovery unit (GRU), which consists of three distillation columns operated in series: a de-ethanizer, a depropanizer and a debutanizer. In addition, the de-ethanizer feed is preheated by the bottoms product from the de-ethanizer, which causes additional process coupling. Rigorous models are developed for the columns including column pressure dynamics and heat transfer dynamics. The process is a highly coupled system and has interactive constraints that determine the feasible operating regions. A decentralized PI control system with override controls for the constraints was designed and implemented on the GRU simulator and was compared with an industrial MPC controller. The MPC controller was observed to outperform the decentralized control system due to its multivariable constraint control capability. Since the simulator is available to other university researchers, it can serve as a challenge problem for multivariable control and identification. Three MPC controllers with different strategies for controlling the bottom level of the first column were implemented on the GRU process. The first MPC controller does not directly control the level, the second one moves the setpoint to the PI level controller, and the third one controls the level directly by manipulating the flow. The results show that including level into the MPC controller improves composition control for cases in which the manipulated variable for the level control has a significant impact on compositions.     

Predictive metamorphic control

In spite of its easy implementation, ability to handle constraints and nonlinearities, etc., model predictive control (MPC) does have drawbacks including tuning difficulties. In this paper, we propose a refinement to the basic MPC strategy by incorporating a tuning parameter such that one can move smoothly from an existing controller to a new MPC strategy. Each change of this tuning parameter leads to a new stabilising control law, therefore, allowing one to gradually move from an existing control law to a new and better one. For the infinite horizon case without constraints and for the general case with state and input constraints, stability results are established. We also examine the practical applicability of the proposed approach by employing it in the nominal prediction model of the tube-based output feedback robust MPC method. The merits of the proposed method are illustrated by examples.     

Multi-input single-output control for extending the operating range: Generalized split range control using the baton strategy

Split range control is used to extend the steady-state operating range for a single output (controlled variable) by using multiple inputs (manipulated variables). The standard implementation of split range control uses a single controller with a split range block, but this approach has limitations when it comes to tuning. In this paper, we introduce a generalized split range control structure that overcomes these limitations by using multiple independent controllers with the same setpoint. Undesired switching between the controllers is avoided by using a baton strategy where only one controller is active at a time. As an alternative solution we consider model predictive control (MPC), but it requires a detailed dynamic model and does not allow for using only one input at a time.     

Control of ball mill grinding circuit using model predictive control scheme

Ball mill grinding circuits are essentially multivariable systems with high interaction among process variables. Traditionally grinding circuits are controlled by detuned multi-loop PI controllers that minimize the effect of interaction among the control loops. Detuned controllers generally become sluggish and a close control of the circuit is not possible. Model Predictive Controllers (MPC) can handle such highly interacting multivariable systems efficiently due to its coordinated approach. Moreover, MPC schemes can handle input and output constraints more explicitly and operation of the circuits close to their optimum operating conditions is possible. Control studies on a laboratory ball mill grinding circuit are carried out by simulation with detuned multi-loop PI controllers, unconstrained and constrained model predictive controllers and their performances are compared.