Non-minimal State Space Model Research Articles

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.

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.

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.

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.

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.

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.

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.

Fractional order MPC design using improved state space model

Abstract In order to improve the performance of control systems, a fractional order model predictive control (FMPC) algorithm using extended non-minimal state space (ENMSS) model is presented in this paper. For this propose, the fractional order model that describes the characteristics of practical processes more accurate than integer order model and the model predictive control (MPC) method based on ENMSS model that includes the state variable and output tracking error are considered. In this paper, the Grunwald-Letnikov (GL) definition is used to discretize the fractional order model and the fractional order cost function. This algorithm inherits the advantages of integer order extended non-minimal state space model predictive control (ENMSSMPC) with more adjustable parameters and better disturbance rejection, such that the controller tuning is more flexible. By comparing with the integer order ENMSSMPC, the results of the temperature control of an industrial heating furnace indicate the performance improvement of the proposed method.

New Minmax Linear Quadratic Fault-Tolerant Tracking Control for Batch Processes

A new design of linear quadratic control (LQ) is proposed for batch processes with partial actuator faults and unknown disturbance. The autoregressive model built through input-output process data is transformed into a new non-minimal state space (NMSS) model in which the process state variables and tracking error are combined, then a new LQ control scheme is derived based on minimax optimization. Unlike LQ based on traditional NMSS model (TNMSSLQ), the process state variables and tracking error can both be regulated in the proposed method. Monotonic situations of optimal performance cost are further derived to yield sufficient conditions for both nominal and robust system stability. Finally, an injection velocity control example is illustrated to show the effectiveness.

Multivariable PID Control Using Improved State Space Model Predictive Control Optimization

In this paper, an improved proportional-integral-derivative (PID) controller optimized by extended nonminimal state space (ENMSS) model based model predictive control (MPC) is proposed for a typical multivariable process in the distillation column. The MPC optimized PID controller inherits the advantages of both methods, i.e., the simple structure of PID controller and good performance of MPC in dealing with industrial processes of coupling and time delay dynamics. In the ENMSS model constructed for MPC, the state variables and tracking error are combined and regulated separately, so that more freedom can be provided during the controller design and better performance can be acquired finally. A case study of a typical multivariable process in the distillation column under model/plant mismatches, disturbances, and measurement noises is introduced to demonstrate the effectiveness of the proposed method. In order to verify the improved performance of the proposed approach, a nonminimal state space model pred...

Improved Decoupled Nonminimal State Space Model Based PID for Multivariable Processes

In this paper, a decoupled nonminimal state space model based PID is proposed. The proposed decoupling structure follows the nonzero-pole cancellations design and the subsequent PID is obtained thr...

Tuning of PI–PD controller using extended non-minimal state space model predictive control for the stabilized gasoline vapor pressure in a stabilized tower

Nonlinearities, uncertainties and large time delay widely exist in the industrial processes, which pose great difficulty to traditional proportional-integral-derivative (PID) control. Proportional-integral–proportional-derivative (PI–PD) controller, which is a modified form of PID controller, can get a better performance than PID control. However, due to the fact that PI–PD controller has an extra parameter, the difficulty of parameter adjustment is a major problem. In this paper, a new PI–PD method optimized by the extended non-minimal state space model predictive control (ENMSSMPC) is proposed to get the optimal parameters of PI–PD controller for dealing with the process complexity. The proposed PI–PD controller combines the advantage of ENMSSMPC and the simple structure of the PID controller and is tested on the stabilized gasoline vapor pressure in a stabilized tower. Results show that it outperforms traditional controllers such as PID controller, PI–PD controller, traditional model predictive control based PID and PIPD controllers (TPFC-PID and TPFC-PIPD) and IMC based Robust PID controller (Robust IMC-PID).

PFC based PID design using genetic algorithm for chamber pressure in a coke furnace

This paper proposes a genetic algorithm (GA) optimization based PID controller design using non-minimal state space model. This strategy is inspired by the lack of analytical tuning guideline of weighting matrices for state space model based controller design. The strategy consists of two steps. First, a PID controller is designed using a non-minimal state space model through predictive functional control optimization. Then the weighting matrices in the controller design are optimized through GA to achieve the desired closed-loop control performance. The performance of the proposed method is tested on the chamber pressure of an industrial coke furnace and compared with the recent extended non-minimal state space predictive functional control (ENMSSPFC) based PID controller, where results demonstrate that the proposed PID shows better performance than ENMSSPFC based PID control.

Predictive control optimization based PID control for temperature in an industrial surfactant reactor

Due to the character of nonlinearity, uncertainties, time delays and so on in the industrial reactors, the performance of proportional-integral-derivative (PID) control cannot always achieve the desired effect. Model predictive control (MPC) is a useful control strategy in the fact that the process models do not need to be accurately known. However, limited by the cost, hardware and so on, the application of MPC is less convenient than PID. In this paper, the temperature control in an industrial surfactant reactor is studied, where an improved PID controller optimized by extended non-minimal state space model predictive control (ENMSSMPC) framework is employed. The temperature in the surfactant reactor is first modeled as a typical step-response model and then a corresponding improved state space transformation with subsequent MPC design is done. The overall strategy combines the advantages of both PID's simple structure and MPC's good control performance. The proposed method is compared with traditional PID and MPC controllers and results show that it provides improved performance.

New PID Controller Design Using Extended Nonminimal State Space Model Based Predictive Functional Control Structure

Proportional-integral-derivative (PID) controller is widely adopted in practice. However, model predictive control (MPC) generally shows improved control performance for industrial processes with delays. In this paper, an improved PID using extended nonminimal state space model based predictive functional control (ENMSSPFC) is proposed and tested on the chamber pressure in an industrial coke furnace. Based on the state space formulation of the process model, ENMSSPFC and PID control strategies are combined to obtain an improved PID control, where the proposed PID has simultaneously the same performance as ENMSSPFC and the same simple structure as traditional PID control. The proposed PID allows the implementation of MPC in a PID form and thus avoids the issues of hardware and of costs caused by MPC implementation. Performance of the proposed PID is compared with several traditional PID controllers. Results show that it provides improved performance than traditional PID control methods.

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.

Output feedback adaptive stabilization and command following for minimum phase dynamical systems with unmatched uncertainties and disturbances

In this article, we develop an output feedback adaptive control framework for continuous-time minimum phase multivariable dynamical systems for output stabilisation and command following. The approach is based on a nonminimal state-space realisation that generates an expanded set of states using the filtered inputs and filtered outputs and their derivatives of the original system. Specifically, a direct adaptive controller for the nonminimal state-space model is constructed using the expanded states of the nonminimal realisation and is shown to be effective for multi-input, multi-output linear dynamical systems with unmatched disturbances, unmatched uncertainties and unstable dynamics. The proposed adaptive control architecture requires only knowledge of the open-loop system's relative degree as well as a bound on the system's order. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach.

Robust MPC with Output Feedback of Integrating Systems

In this work, it is presented a new contribution to the design of a robust MPC with output feedback, input constraints, and uncertain model. Multivariable predictive controllers have been used in industry to reduce the variability of the process output and to allow the operation of the system near to the constraints, where it is usually located the optimum operating point. For this reason, new controllers have been developed with the objective of achieving better performance, simpler control structure, and robustness with respect to model uncertainty. In this work, it is proposed a model predictive controller based on a nonminimal state space model where the state is perfectly known. It is an infinite prediction horizon controller, and it is assumed that there is uncertainty in the stable part of the model, which may also include integrating modes that are frequently present in the process plants. The method is illustrated with a simulation example of the process industry using linear models based on a real process.

Output feedback adaptive command following and disturbance rejection for nonminimum phase uncertain dynamical systems

AbstractIn this paper, we develop an output feedback adaptive control framework for continuous‐time nonminimum phase multivariable systems for output stabilization, command following, and disturbance rejection. The approach is based on a nonminimal state space realization that generates an expanded set of states using the filtered inputs and filtered outputs and their derivatives of the original system. Specifically, a direct adaptive controller for the nonminimal state space model is constructed using the expanded states of the nonminimal realization and is shown to be effective for multi‐input, multi‐output nonminimum phase systems with unstable dynamics. The adaptive controller does not require any model information nor does it require information of the system poles and system zeros or estimation of the system Markov parameters. Several illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.