Non-minimal State Space 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.

A two-dimensional model predictive iterative learning control based on the set point learning strategy for batch processes

Although conventional two-dimensional model predictive iterative learning control (2D-MPILC) based on an extended non-minimum state space (ENMSS) model can avoid designing an observer, it only relies on feedback to passively deal with time delay. This passive treatment for time delay hinders the further improvement of control performance. To address this shortcoming, a two-dimensional model predictive iterative learning control strategy based on the set point learning (2D-SPL-MPILC) is proposed. Firstly, a set point learning strategy is developed to improve the ability to deal with time delay. Based on the error of the previous batch, the set point learning strategy perceives the system dynamics in advance, and then outputs this advance perception in the form of the predictive set point. Secondly, a novel ENMSS model is constructed on the basis of the predictive tracking error between the predictive set point and the actual output. Since the predictive tracking error integrates the predictive set point, this novel ENMSS model has certain predictive ability. Finally, based on this novel ENMSS model, a novel two-dimensional model predictive iterative learning control (2D-MPILC) method, which is called 2D-SPL-MPILC method, is designed. Because this controller contains the perception of future process dynamics, it can reduce the impact of time delay and improve the control performance. The case studies on the packing pressure control in injection molding process and batch reactors demonstrate the effectiveness of the presented 2D-SPL-MPILC strategy.

Adaptive Model Predictive Control Scheme Based on Non-Minimal State Space Representation

The model predictive control (MPC) technique is widely employed in process industries as a control scheme. The quality of the model used greatly influences the performance of the MPC. In time-varying systems, the plant model plays a critical role in determining the controller’s performance, as the controller’s control action relies on an adaptive model. Therefore, updating the system parameters rapidly and symmetrically in time-varying systems becomes necessary. To address this need, in the proposed work, a non-minimal state space model of a time-varying system is utilized for parameter estimation, and these parameters are updated at every sampling instant using a multi-innovation recursive least squares (MIRLS) scheme, which enables the timely updates of system parameters. We have explored various extensions of the recursive least square (RLS) scheme, such as the multi-innovation recursive least squares (MIRLS) method. This extension aims to achieve a higher convergence rate for parameter estimation. Furthermore, we have focused on the parameter estimation of a non-minimal state space time-varying system, where the system parameters change at each time interval. Additionally, we have incorporated a time-varying objective function into the MPC formulations, which enables adaptability to change the system dynamics. To demonstrate the applicability of our proposed approach, we have conducted simulation experiments using a benchmark time-varying model. These experiments showcase the effectiveness and benefits of our proposed methodology in dealing with time-varying systems.

Optimal metaheuristic state-dependent parameter proportional-integral-plus control: Alternative to gain-scheduled controller for control of a nonlinear continuous stirred tank reactor

The continuous stirred-tank reactors have complex dynamic behavior. In the reactor, the residual concentration decreases during an exothermic chemical reaction. In this transition proper cooling is essential to stabilize the reaction, and to prevent reactor overheating. This paper presents the data-driven metaheuristic state-dependent parameter proportional-integration-plus (M-SDP-PIP) control as an alternative of gain-scheduled control for adjusting the coolant temperature of the reactor. In fact, the parameters of the discrete transfer function were identified in the non-minimal state space using state-dependent parameter which is a nonlinear method; and weighting matrixes of linear quadratic servomechanism cost function of the optimal controller were achieved by metaheuristic methods, genetic algorithm, and particle swarm optimization, according to the minimization of the integral absolute error index and energy consumption. The proposed controller was compared to gain-scheduled and non-gain-scheduled controllers in the closed-loop condition in terms of tracking performance. The results show particle swarm optimization algorithm converge to the same optimal solution as genetic algorithm using fewer number of function evaluation, so that proposed controller has more effective offset-free servo-regulatory performance than other control schemes. In addition, it is simpler and more comprehensible because it requires no auxiliary equations and models to determine and manage the control gain, as opposed to the gain-scheduled structure.

Disturbance Observer-Based Repetitive Control System With Nonminimal State-Space Realization and Experimental Evaluation

This brief develops a disturbance observer-based repetitive control system using a non-minimal state-space (NMSS) realization where all state variables correspond to the system’s input and output variables and past values. Tracking a periodic reference signal or rejection of a periodic disturbance signal is achieved by including a disturbance observer to estimate an input disturbance containing the same frequency characteristics. This new approach differs from previously published designs because it separates the design procedure into two tasks: first, stabilization via state feedback control; second, independent incorporation of the periodic modes via estimation of the disturbance. Moreover, the new design naturally contains an anti-windup mechanism when the control signal reaches its maximum or minimum value. Results from the experimental evaluation are given, including a comparison against a design that constructs a minimal state controller using an observer. These results demonstrate that the new method can deliver significant performance improvement, with excellent disturbance rejection and reference tracking.

Modeling and Finite-Horizon MPC for a Boiler-Turbine System Using Minimal Realization State-Space Model

This paper aims to address a finite-horizon model predictive control (MPC) for non-linear drum-type boiler-turbine system using a system-identification method. Considering that the strong state coupling of a non-linear mechanism model, the subspace identification method is first utilized to obtain a linear state-space model, and transformed into an input–output model. By taking the inputs and outputs of the input–output model as system states, an augmented non-minimal state-space (NMSS) model of state measurable is constructed. In order to reduce the computation burden, the augmented NMSS model is further transformed into a canonical formulation by adopting a Kalman decomposition. Based on the minimal realization state-space model, the MPC controller is parameterized as a finite-horizon optimization problem. Finally, simulations are performed and evaluated the performance of the proposed method, and the simulation results show that: the linear model approximate the non-linear system accurately; the proposed MPC method can achieve a satisfactory stable control performance; and the computation time 18.388 s for the overall optimization problem also illustrates the real-time performance effectively.

Improved Constrained Predictive Functional Control Using Extended Non-Minimal State Space Formulation for the Cement Production Process

In this article, an improved constraint dealing method and an extended state space model-based constrained predictive functional control (PFC) approach is developed for the denitration process in cement production. To improve the control effect of the presented strategy, first, an enhanced form-based state space model in which the changes of the output predictions can be regulated to achieve smoother system dynamics is constructed. Then, a modified constraint dealing scheme, which integrates the relaxation factors to improve the success probability of solving the relevant optimization, is also introduced for the proposed method. On the basis of the two merits, better ensemble control performance is anticipated. Simulations on the regulation of the NOx concentration in the denitration process prove the validity of the proposed constrained PFC strategy.

Two-Dimensional Iterative Learning Model Predictive Control for Batch Processes: A New State Space Model Compensation Approach

To achieve improved control performance of batch processes under uncertainty, a novel two-dimensional model predictive iterative learning control (2D-MPILC) scheme is proposed. First, a new two-dimensional (2-D) extended nonminimal state space model is formulated where more degrees of freedom are offered for further controller design; second, a new error compensation strategy is introduced in the controller design to improve the ensemble control performance. The two merits are combined together to form a new control strategy where the model predictive control and iterative learning control are united based on the 2-D framework. By employing the novel model formulation and the system error compensation approaches, the effects caused by uncertainty in the batch processes can be eliminated gradually from cycle-to-cycle such that the desired control performance will be obtained finally. The effectiveness of the proposed 2D-MPILC is tested on the packing pressure in the injection molding batch process.

The Multivariable Control of Carbon Dioxide Absorption System using the Proportional Integral Plus (PIP) Controller

The present article investigates the implementation of non-minimal state space (NMSS) representation with proportional-integral-plus (PIP) controller for the carbon dioxide absorption process of Shiraz petrochemical ammonia unit. The PIP controller is a logical extension of conventional PI/PID controllers with additional dynamic feedback and input compensators. PIP controller is used for multivariable control without limitation on the number of controlled variables. A Multi Input - Multi Output (MIMO) square model was extracted from step response test. In this way, input water flow rate to carbon dioxide absorption system, the heat duty of input absorbent cooler to tray (1) of absorption tower and re-boiler heat duty of stripping tower are chosen as manipulated variables (inputs), while carbon dioxide mole fraction in absorption tower vapor product, the water mole fraction in absorption tower liquid product and tray temperature No. 36 of stripping tower are determined as controlled ones (outputs). The system identification is performed with three input and three output variables using step response test. As a result, continuous and discrete time transfer function matrices and suitable NMSS model for PIP controller are reported. Finally, in order to evaluate the PIP control performance, the feed flow rate increases by 2%. The results show the proper performance of designed PIP controller for both disturbance rejection and set point tracking.

Non‐minimal state space model predictive control using Laguerre functions for reference tracking

AbstractThis paper presents a new design of model predictive control which combines non‐minimal state space (NMSS) and Laguerre functions. The utilization of NMSS omits the observer design process and brings convenience to multi‐input, multi‐output systems with time delay. But the dimensions of NMSS are high, which is harmful to online computation. The use of Laguerre functions helps reduce the data required in the optimization algorithm and makes up for the deficiency of NMSS. A modified solution for the optimal tracking problem using NMSS and Laguerre functions is proposed. Although the choice of the parameters in Laguerre functions needs experiments and experience, the method presented in this paper brings convenience to MPC design. Simulation results show that this approach not only reduces the computing effort without sacrificing the control performance significantly, but also has a good robustness to interference when tracking.

Improved LQ Tracking Control Design for Industrial Processes Under Uncertainty: The Extended Nonminimal State Space Approach

Improved LQ Tracking Control Design for Industrial Processes Under Uncertainty: The Extended Nonminimal State Space Approach

Robust Nonminimal State Feedback Control for a Furuta Pendulum With Parametric Modeling Errors

Nonminimal state feedback control, also known as proportional-integral-plus control, together with antiwindup integrator, is applied, for the first time, to stabilize a Furuta pendulum (FP). The key elements in the nonminimal state space (NMSS) state transition matrix is obtained directly from the original minimal state space model. The NMSS model is proved to be controllable if the controllability conditions are met. In order to demonstrate the potential robustness of NMSF control, the controller is designed based on the model with two deliberate plant parameter mismatches. The feedback gains are optimized in an eigenvalue assignment way by minimizing a robust cost function, which is related to the closed-loop state matrix's eigenvalues' sensitivities to the two mismatched plant parameters. The sum of the normalized eigenvalue sensitivities (NES) is defined as cost function. In this article, multiple simulations with different plant parameters are implemented to evaluate the robustness. The optimized FP control system shows smaller envelope of multiple time responses compared to the one before optimization. Experimental results also confirm the optimized controller's improved robustness under parametric mismatches.

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.

Disturbance Observer Based Repetitive Control System with Non-minimal State Space Realization and Anti-windup Mechanism

This paper develops a disturbance observer-based repetitive control system using a non-minimal state-space realization in which all state variables are chosen to correspond to the system’s input and output variables and their past values. To enable the repetitive control system to follow a periodic reference signal or reject a disturbance signal of the same nature, a disturbance observer is used to estimate an input disturbance that contains the same frequency characteristics. This new approach differs from previously published design in repetitive control because it separates the design procedure into two simple tasks: first, stabilization by the design of a non-minimal state feedback control; and second, to independently incorporate the periodic modes via the estimation of the disturbance. Moreover, because this design ensures the stability of the disturbance observer, its implementation contains an anti-windup mechanism when the control signal reaches its maximum or minimum value. Without the complication of an observer for the state variables, the detection of a disturbance occurs earlier and the repetitive controller acts much faster than in the case of minimal state controller incorporating an observer. This leads to considerable performance improvement, with excellent disturbance rejection achieved with smaller control signal variations.

A New Minimax Optimization Design of H∞ LQ Fault-Tolerant Tracking Control for Multi-Phase Batch Processes

For multi-phase batch processes with partial failure of the actuator and unknown disturbance, this paper proposes a minimax optimization design method for H ∞ linear quadratic fault-tolerant tracking control based on switching strategy. Firstly, a non-minimum state space model is constructed based on the input-output model given by the batch process, and then a discrete switched model consisting of state errors, tracking errors and new state variables containing tracking errors is constructed. In this model, the antidisturbances performance index function with terminal constraint is selected, and the controller and the external disturbances are obtained by using the optimization theory. Then, under the acquired control law, the switching signal is designed and the range of uncertainty caused by the fault is given to realize the robustness of the system. The advantage of this design is that the system is tracking fast and the tracking error is small. Finally, by taking the parameters such as speed and pressure in the process of injection molding as examples, and comparing with the traditional control methods, the method presented in this paper is proved to be effective.

Model predictive control of laser metal deposition

Laser metal deposition (LMD) is one of the efficient processes in laser additive manufacturing (LAM) systems that uses metallic materials to produce metallic components additively. One of the remaining challenges for this type of systems is its product quality control. This paper proposes automatic control of melt pool size during the process of laser metal deposition. Using a low-cost near-infrared monochrome (NIRM) camera, the melt pool size is measured from grey melt pool image and is modelled by a first-order transfer function with time delay where the laser power is chosen to be the manipulated variable. Experimental data are used to identify the first-order plus delay model, which is then converted to a non-minimal state space realisation that accurately captures the time delay in discrete time with all state variables being measurable. A model predictive controller (MPC) is designed and implemented for controlling the melt pool size with the state space model. Experimental results are conducted on the platform TruLaser Cell 7020 from Trumpf, showing that the melt pool size has been successfully controlled to their desired specifications and the product quality measured by the variations of the brick height has been significantly improved.

A two-dimensional design of model predictive control for batch processes with two-dimensional (2D) dynamics using extended non-minimal state space structure

A modified two-dimensional (2D) structure based control strategy that incorporates model predictive control (MPC) and iterative learning control (ILC) in 2D sense is developed for batch processes in this article. To enhance the control effect of the conventional 2D model predictive iterative learning control (2D-MPILC), an improved non-minimal form of state space model is utilized in the developed method. Through employing such model, the dynamics of the closed-loop system can be regulated by tuning extra process variables. In other words, additional degrees of freedom are achieved in the novel controller design, and the modified control performance is expected for the proposed algorithm. The simulation results on two processes evaluate the effectiveness of the presented 2D-MPILC strategy finally.

A New control structure for tert-amyl methyl ether production using reactive distillation

The aim of this paper is to introduce new control structures in both centralized and decentralized scheme for tert-amyl methyl ether (TAME) production unit using reactive distillation which developed as a benchmark by Luyben (2005). Steady state and dynamic simulation was performed based on the case study data using Aspen® simulator. Dynamic simulation shows that control performance of the plant has oscillatory behavior using conventional PI controllers. Hence, a proper modification on the process flow sheet was carried out in order to remove oscillatory behavior of the process. Although, the new structure has better dynamic performance than the previous one using PI controller, it is not capable of eliminating the oscillations completely. Non-minimal state space with proportional integral plus controller (NMSS–PIP) controller was applied to dynamic model of the modified process. In this way, the system identification was carried out using refined instrumental variable (RIV) method and state matrices was obtained as left matrix fraction description (LMFD). The control performance of the PI and PIP controller for the modified structure revealed that the NMSS–PIP, completely eliminates the process oscillations while it has smoother responses with better settling time than the PI configuration. Furthermore, comparison of the ITAE criterion between main case and modified process indicates that the ITAE for PI and PIP control decreased by about 20% and 88%, respectively.

The design of NMSS fractional-order predictive functional controller for unstable systems with time delay

Open-loop unstable systems are more difficult to control than stable processes. In presence of time delay and uncertainty, the complexity of problem increases. In this paper, non-minimal state space predictive functional control (NMSS-PFC) infrastructure has been generalized for control of unstable systems with time delay. At first, NMSS system representation has been extended for a so-called coprime-factorized equivalent model of the unstable processes. Then, the proposed NMSS-fractional-order PFC (NMSS-FOPFC) has been formulated via a fractional order cost function in terms of the output tracking error vector. In the developed formulation and via the NMSS structure, the constraints on inputs of the system could be easily formulated and employment of fractional order cost function led to improved performance even in case of disturbances, perturbations or uncertainties. Closed loop robust stability analysis was also performed based on small gain theorem and verified via simulations. Simulation examples show that the proposed NMSS-FOPFC results in improved nominal and perturbed responses compared to conventional methods. Comparison has been carried out by considering integral of absolute error (IAE) and integral of squared error (ISE) as well as step response transient and steady state properties and the control effort.

Design of the Linear Quadratic Structure Based Predictive Functional Control for Industrial Processes Against Partial Actuator Failures Using GA Optimization

This paper addresses the genetic algorithm (GA) optimization and the linear quadratic (LQ) structure based predictive functional control (PFC) for batch processes under non-repetitive unknown disturbances and partial actuator faults. First, by adopting the extended non-minimal state space (ENMSS) model in which the state variables and the tracking error are united, the new state vector with more degrees is provided for the controller design. In order to enhance the ensemble control performance under the PFC structure, GA is adopted for the optimization of the weighting matrix in the controller. The case study on the injection velocity control in an injection molding machine demonstrates the effectiveness of the proposed PFC scheme against various disadvantages.