State Space Model Predictive Control Research Articles

An improved state space model predictive control for linear systems with input disturbance

This paper presents an improved model predictive control (MPC) algorithm for linear systems with input disturbance. Based on the developed extended non-minimum state space input disturbance (ENMSS-ID) model, the input disturbance model structure is incorporated into the MPC framework and the objective function of the MPC optimization problem is improved to weigh the system output increments. This enables the algorithm simultaneously to achieve good input disturbance rejection performance for systems with known input disturbances and reduce the controllers’ sensitivity to model mismatch. An existing optimal estimation method is introduced to estimate the input disturbance, together with the proposed strategy to improve estimation convergence. Offset-free property is also proven to show the steady-state performance of the designed control scheme. Finally, two benchmark plants are studied to illustrate the effectiveness and advantages of the proposed algorithm.

Improved Model Predictive Speed Control of a PMSM via Laguerre Functions

This paper proposes a model predictive speed control strategy for a surface-mounted permanent magnet synchronous motor by applying Laguerre functions. The model predictive controller (MPC) incorporates an integrator. A quadratic programming procedure is applied to solve the constrained optimization problem online. The paper also provides a solution for stability. The performance efficiency of the proposed scheme is validated by comparing the results with the performance of an optimal linear quadratic regulator, conventional state-space model predictive control, and a simple MPC algorithm with integral action. Extensive simulation results confirm the efficacy of the proposed scheme, showing that it achieves good steady-state performance while maintaining a fast dynamic response.

Modified Active Disturbance Rejection Predictive Control: A fixed-order state–space formulation for SISO systems

This paper presents a novel control strategy that provides active disturbance rejection predictive control on constrained systems with no nominal identified model. The proposed loop relaxes the modelling requirement to a fixed discrete-time state–space realisation of a first-order plus integrator plant despite the nature of the controlled process. A third-order discrete Extended State Observer (ESO) estimates the model mismatch and assumed plant states. Moreover, the constraints handling is tackled by incorporating the compensation term related to the total perturbation in the definition of the optimisation problem constraints. The proposal merges in a new way state–space Model Predictive Control (MPC) and Active Disturbance Rejection Control (ADRC) into an architecture suitable for the servo-regulatory operation of linear and non-linear systems, as shown through validation examples.

Explicitly incorporating surrogate safety measures into connected and automated vehicle longitudinal control objectives for enhancing platoon safety

The concepts of Connected and Automated Vehicles (CAV) and vehicle platooning have generated high expectations regarding the safety performance of future transportation systems. Existing CAV longitudinal control research primarily focuses on efficiency and control stability, by considering different inter-vehicle spacing policies. In very few cases, safety was also considered as a constraint, but not in the main control objectives. Theoretically, stability can only guarantee that CAV platoons eventually achieve an equilibrium state but is unable to promise safety along the process of achieving equilibrium. It is important to note that CAV does not mean absolutely safe, and its longitudinal or platoon control safety performance depends on how the control algorithms are designed, how accurately it can detect and predict its lead vehicle’s (could be a human-driven vehicle) next move, and other practical factors such as control and communication delays. To optimize CAV platoon safety, this study integrates surrogate safety measures (SSM) and model predictive control (MPC) into CAV longitudinal control for trajectory optimization. SSM has been widely adopted for modeling the safety consequences of various vehicle control strategies and identifying near-crash events from either simulated or field-captured traffic data. This study directly incorporates three typical SSM into the longitudinal control objectives of CAV and constructs a state-space MPC algorithm to model how these SSM vary as a result of CAV dynamics. Numerical examples are provided to show the performance of these SSM-based optimal CAV longitudinal control methods under traffic flow perturbations. To further confirm the necessity of explicitly considering SSM in CAV longitudinal control and its effectiveness in reducing rear-end collision risk, the proposed methods are compared with three classical longitudinal control models that do not consider SSM based on microscopic traffic simulation. It is noted that all SSM-based optimal control methods perform better than others as manifested by some key risk indicators, demonstrating the importance of explicitly considering SSM and safety in CAV longitudinal control.

An Adaptive Predictive Control Method Based on State-space Model

An adaptive state-space model predictive control strategy is proposed for complex industrial processes with nonlinear, time-varying and constrained characteristics. The state-space model obtained by on-line identification algorithm is used as the system model, and the indirect form is used to design the adaptive predictive controller. The controller includes quadratic programming solution to the constraint problem. The effectiveness of the proposed control strategy is verified by the simulation experiment of 2-CSTR process control.

Adaptive disturbance rejection model predictive control and its application in a selective catalytic reduction denitrification system

This study aims to increase the control performance of a selective catalytic reduction (SCR) denitrification system through modeling and disturbance rejection. The concept of converted ammonia flowrate is introduced to transform the nonlinear problem into a quasi-linear problem, so that transfer-function models can be used directly. The augmented process model is used to estimate the disturbance using the Kalman filter. Because of its superiority in time-series prediction, the online least-squares support vector machine is implemented to develop an adaptive disturbance model. State-space model predictive control with an adaptive disturbance model is presented. The simulation results show that the proposed control scheme can improve the control performance of the SCR denitrification system markedly. Based on simulations, this control structure has been used successfully in a real SCR denitrification process, which shows the effectiveness of the proposed control scheme further.

Model Predictive Control with a Relaxed Cost Function for Constrained Linear Systems

The Model Predictive Control technique is widely used for optimizing the performance of constrained multi-input multi-output processes. However, due to its mathematical complexity and heavy computation effort, it is mainly suitable in processes with slow dynamics. Based on the Exact Penalization Theorem, this paper presents a discrete-time state-space Model Predictive Control strategy with a relaxed performance index, where the constraints are implicitly defined in the weighting matrices, computed at each sampling time. The performance validation for the Model Predictive Control strategy with the proposed relaxed cost function uses the simulation of a tape transport system and a jet transport aircraft during cruise flight. Without affecting the tracking performance, numerical results show that the execution time is notably decreased compared with two well-known discrete-time state-space Model Predictive Control strategies. This makes the proposed Model Predictive Control mainly suitable for constrained multivariable processes with fast dynamics.

Multivariable non-minimum state space model predictive control based on disturbance observer

In order to suppress the influence of lumped system disturbance, such as external disturbance and internal disturbance caused by model mismatch and coupling between variables, more effectively, a multivariable non-minimum state space predictive control method based on disturbance observer (MNMSSPC-D) is proposed in this paper. Most of the existing methods based on the feedback control and feedforward compensation cannot guarantee optimal output. Unlike the existing methods, the proposed method extends the estimated disturbance and output variables into the state variables, forming a multivariable non-minimum state space (MNMSS) prediction model, and then uses the rolling optimization principle in predictive control to design the controller based on the formed prediction model. The main advantages of the proposed method are that the state can be guaranteed to be available to the MNMSS model and the optimal control performance and anti-disturbance ability of system can be obtained by the designed controller. The proposed MNMSSPC-D method is verified by the simulation with a heavy oil fractionator.

A hybrid control approach for the cracking outlet temperature system of ethylene cracking furnace

The main objective of this paper is to show the design and application on the cracking outlet temperature (COT) system using a hybrid control approach including non-minimal state-space model predictive control with an adjustable factor (AFNMSSMPC) and humanoid intelligent multimodality control (HIMMC) in two 100 k tone/year SC-1 ethylene cracking furnaces. Compared with the conventional control structure, the advanced control structure is designed based on the existing control problem. The advanced controller is developed at the platform of APC-ISYS software made by Zhejiang Supcon Company and implemented in an industrial upper computer which sets over and is connected with a CS3000 distributed control system (DCS) through OPCServer. In order to reduce the fluctuation of the COT, AFNMSSMPC is chosen as feedback controller, which guarantees system robustness together with tracking ability, and meanwhile HIMMC is as feed-forward controller based on the change in chamber temperature (measured disturbance), which can eliminate the effect on cracking outlet temperature (COT) in advance. The application results on COT of two ethylene cracking furnaces labeled M and N furnaces in practice using AFNMSSMPC-HIMMC compared to the traditional proportional–integral–differential (PID) control are presented. The standard deviation of COT reduces by 54.03% and 60.87% for M and N furnaces, respectively. The results show that the designed COT system has the capability of good tracking and strong disturbance rejection.

Event-based state-space model predictive control of a renewable hydrogen-based microgrid for office power demand profiles

This paper focuses on the design and implementation of an event-based control architecture to manage a renewable-based microgrid. This microgrid has renewable-energy generation and a hybrid energy storage system that uses electricity and hydrogen. The main load of the microgrid is the energy demand of an office. The primary control objective is to satisfy this load using the available renewable generation and stored energy while reducing the amount of energy purchased from the Utility Power Grid and the degradation of the electromechanical storage devices. To do that, the control architecture defined within an event framework, makes use of a set of state-space model predictive controllers which are selected as a function of a variable sampling period. To evaluate the performance of the proposed architecture, simulation tests for a summer day as well as an analytical study is performed. The obtained results show that the use of the event-based control architecture allows a significant reduction of the number of changes in the control action at the expense of an acceptable deterioration of set-point tracking for a microgrid with several types of electrochemical storage.

Low density polyethylene tubular reactor control using state space model predictive control

One of the conventional commodity polymers in the world is Low density polyethylene (LDPE). LDPE is mostly produced from free radical polymerization of ethylene gas under high pressure and temperature environment. However, the control of LDPE polymerization reactor is challenging due to the complexity of the polymerization process and the nature of the reactor itself. Thus, this study explores the application statespace model predictive control (SS-MPC) in controlling LDPE polymerization tubular reactor process. SS-MPC is a type of model predictive control (MPC) scheme which utilizes state space model as its process model. In general, MPC control scheme has a wide application in the industry due to its ability to handle multivariable control and optimize process performance. In order to implement the control scheme, a dynamic model of the reactor was developed using Aspen Dynamic. The dynamic model is then linked with MATLAB Simulink for online control implementation. The LDPE polymerization process was controlled by regulating the initiator and chain transfer agent (CTA) flowrate to control reactor temperature and polymer Melt Flow Index (MFI) grade. The state space model was identified using identification technique through two approaches; MIMO model and augmented SISO model. In order to evaluate the controller performance, MFI grade transition and disturbance rejection tests are conducted along with PID controller, as a comparison. Based on the tests, MPC had presented a notable performance in handling polymer grade transition (Integral squared error, ISE = 4530) and disturbance rejection (ISE = 99.03) in MFI profile compared to PID controller respond (ISE = 7003 for set point tracking and ISE = 12.66 for disturbance rejection). Nonetheless, PID controller had also presented a comparable performance in controlling maximum reactor temperature.

Offset-free state-space nonlinear predictive control for Wiener systems

This work is concerned with state space Multiple-Input Multiple-Output (MIMO) Wiener systems which consist of a linear dynamic block connected in series with a nonlinear steady-state (static) one. Model Predictive Control (MPC) algorithms with successive on-line model or trajectory linearisation for dynamic processes described by such Wiener systems are discussed. Advantages of the presented MPC algorithms are: (a) computational efficiency since quadratic optimisation problems are only solved on-line, nonlinear optimisation is not necessary, (b) very good quality of control, (c) offset-free control (no steady-state error in presence of disturbances) assured by a novel approach to disturbance modelling and state estimation, resulting in a simple design and a simple control structure. All features of the discussed algorithms are demonstrated and their performance is compared with that of the MPC algorithm with nonlinear optimisation as well as with the traditional offset-free state-space MPC approach.

Adaptive incremental state space MPC for collector defocusing of a parabolic trough plant

Commercial solar plants produce energy around a nominal operating point in which the solar field outlet temperature is high and close to the thermal limit of the heat transfer fluid. The main control of the temperature is carried out by means of the fluid flow-rate that circulates through the solar field. Defocusing the collectors is normally used as a safety mechanism to avoid exceeding the thermal limit. However, in situations in which the flow is saturated, the control of defocusing the collectors becomes of vital importance and is the system in charge of controlling the solar field outlet temperature.The paper presents an Adaptive State Space Model Predictive Control strategy with an incremental formulation to control the fourth and third collector defocus angles for field outlet temperature set-point tracking at the nominal operation point, avoiding the Heat Transfer Fluid temperature from exceeding the manufacturer thermal limit (oil degradation). The state space description uses an Unscented Kalman Filter for estimating the non-measurable states. A 50 MW parabolic solar trough plant nonlinear model has been used to design and validate the strategy. Simulation results are presented showing the advantages of using the proposed strategy.

State space model realization using step response data of MIMO system with input delays for model predictive control

This paper discusses state space realization algorithm from general multiple input multiple output (MIMO) step response data with or without input delays. It uses the factored form of the block Hankel matrix formed from the Markov parameters of the equivalent impulse response of the step response model to obtain an equivalent state space model. Though the state space model that best approximates the step response model has number of states equal to the rank of the block Hankel matrix, much lower rank state space model, adequate for use as internal model for model predictive control (MPC), can also be obtained. By using an empirical step response model of a pilot distillation plant, a simple state space MPC, which use a full rank, and then a low-rank approximation of the model as its internal model, is implemented on the plant model. The setpoint tracking trends of the control outputs of the two approximations match closely.

Linear Offset-Free Model Predictive Control in the Dynamic PLS Framework

This work addresses the model predictive control (MPC) of the offset-free tracking problem in the dynamic partial least square (DyPLS) framework. Firstly, state space MPC based on the DyPLS is proposed. Then, two methods are proposed to solve the offset-free problem. One is to reform the state space model as a velocity form. Another is to augment the state space model with a disturbance model and estimate the mismatch between system output and model output with an estimator. Both methods use the system output as a feedback in the control scheme. Hence, the offset-free tracking is guaranteed, and unmeasured step disturbance can be rejected. The results of two simulations demonstrate the effectiveness of proposed methods.

Incremental State-Space Model Predictive Control of a Fresnel Solar Collector Field

Model predictive control has been demonstrated to be one of the most efficient control techniques for solar power systems. An incremental offset-free state-space Model Predictive Controller (MPC) is developed for the Fresnel collector field located at the solar cooling plant installed on the roof of the Engineering School of Sevilla. A robust Luenberger observer is used for estimating the states of the plant which cannot be measured. The proposed strategy is tested on a nonlinear distributed parameter model of the Fresnel collector field. Its performance is compared to that obtained with a gain-scheduling generalized predictive controller. A real test carried out at the real plant is presented, showing that the proposed strategy achieves a very good performance.

Flight control and airwake suppression algorithm for carrier landing based on model predictive control

Carrier airwake will cause aircraft landing trajectory deviation from the reference glide path during the final precision approach and landing stage, hence exacerbating the operation load of pilots and increasing the risk of carrier landing. To address this issue, a flight control algorithm that employed state space model predictive control (MPC) to suppress the effect of airwake was presented for aircraft landing on the carrier in this article. The MPC controller was built on the basis of the small-disturbance motion equation of a carrier-based aircraft under the landing status. Meanwhile, in particular, the airwake model was introduced in MPC controller so that its influence could be mitigated promptly. The computer simulation experiments demonstrated that the proposed method could effectively reduce the trajectory deviation caused by airwake and improve the success rate of carrier landing.

A model predictive functional control based on proportional-integral-derivative (PID) and proportional-integral-proportional-derivative (PIPD) using extended non-minimal state space: Application to a molten carbonate fuel cell process

The performance of most controllers, including proportional-integral-derivative (PID) and proportional-integral-proportional-derivative (PIPD) controllers, depends upon tuning of control parameters. In this study, we propose a novel tuning strategy for PID and PIPD controllers whose control parameters are tuned using the extended non-minimal state space model predictive functional control (ENMSSPFC) scheme based on the auto-regressive moving average (ARMA) model. The proposed control method is applied numerically in the operation of the MCFC process with the parameters of PID and PIPD controllers being optimized by ENMSSPFC based on the ARMA model for the MCFC process. Numerical simulations were carried out to assess the set-point tracking performance and disturbance rejection performance both for the perfect plant model, which represents the ideal case, and for the imperfect plant model, which is usual in practical applications. When there exists uncertainty in the plant model, the PIPD controller exhibits better overall control performance compared to the PID controller.

Plant–Model Mismatch Estimation from Closed-Loop Data for State-Space Model Predictive Control

The area of controller performance monitoring, assessment, and diagnosis for model predictive control (MPC) has seen an increase in interest in recent years. A frequently identified cause of degraded performance is mismatch between the plant model used in the controller and the true dynamics of the plant. Most recent research focuses on locating plant–model mismatch in order to reduce the considerable effort required to re-identify the model. In this paper, we present a novel autocovariance-based plant–model mismatch estimation approach for unconstrained MPC based on linear state space models. We show that (additive) plant–model mismatch can be quantified as the solution of an optimization problem which minimizes the discrepancy between the sample autocovariance of plant outputs and the corresponding value obtained from theoretical predictions. We illustrate our theoretical results with two simulation case studies, demonstrating good performance in estimating parametric mismatch.

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.