Non-minimal State Space Research Articles

Combined pole assignment and mean value engine model multivariable decoupling control

This article considers a combined pole assignment and multivariable decoupling control algorithm using discrete-time, non-minimum state space (NMSS) methods. In contrast to earlier research based on low-order linear models, the approach is applied to a nonlinear mean value internal combustion engine model with three control inputs, namely the throttle plate angle, injected fuel mass flow and spark advance angle. The controlled outputs are the air mass flow pressure, crank shaft speed and air–fuel ratio (AFR). It is well known that, for example, regulating the AFR to the stoichiometric value (i.e. [Formula: see text]) leads to a desirable balance between power output and fuel consumption, while reducing pollutant emissions. In this regard, the linear NMSS approach is straightforward to design for a range of performance requirements and yields comparable results to a more complex benchmark sliding mode control system. Furthermore, it retains a similar implementation structure to current production units, which are typically based on conventional proportional-integral compensation. The robustness to changing operating levels and disturbances, including an air leakage signal, are evaluated in simulation.

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.

Control of Nonlinear Biological Systems by Non-minimal State Variable Feedback

We contrast biostatistical methods for optimal treatment determination with optimal control methodology, originally developed in the engineering literature but now used more widely. We describe non-minimal state space (NMSS) control methods for biological systems, with a particular focus on the use of state-dependent parameter models to represent system nonlinearities. Three examples are considered, namely the control of (i) a nonlinear forced logistic function implemented with a time delay; (ii) athletic horse heart rate with potential application for training improvement; and (iii) a physically-based simulation model for the uptake of CO2 by plant leaves in response to light intensity, with application to closed-environment grow cells. Although all three examples have been extensively studied in the literature, the novelty of the present article is in the NMSS formulation and in the application of a recently developed state-dependent (nonlinear) control algorithm. In the case of the leaf photosynthesis simulation, however, the linear NMSS algorithm yields satisfactory results, illustrating the inherent robustness of feedback.

Improved Nonminimal State Space Model Predictive Control for Multivariable Processes Using a Non-Zero–Pole Decoupling Formulation

In this article, a decoupling approach is first formulated, and then a corresponding nonminimal state space predictive control is proposed. The proposed decoupling structure can avoid zero–pole cancellations between the decoupler and the process, and thus, realization is guaranteed. Consequently, a systematic design of nonminimal state space predictive control can be designed in terms of a SISO procedure. Simulation results of a typical multivariable process are provided to demonstrate the effectiveness of the proposed method. In addition, a closed-form transfer function representation that facilitates frequency analysis of the control system is also provided to give further insight into the proposed strategy.

Multivariable decoupling predictive functional control with non-zero–pole cancellation and state weighting: Application on chamber pressure in a coke furnace

Based on the multivariable description of processes in industry, a non-zero–pole cancellation decoupling strategy is first proposed and then used for state space predictive functional control (PFC) design. The proposed decoupling guarantees realization and enables the control system design to be based on single-input single-output (SISO) process formulations. To facilitate the closed-loop control performance improvement, the subsequent controller design adopts an extended non-minimal structure that can regulate the process state dynamics, which provides more degrees compared with traditional state space methods. By interpretations of the proposed performance through process transfer function formulations, relationship with and superiority to traditional state space PFC are further revealed. Finally, the effectiveness and merits of the proposed are illustrated by application to a typical industrial chamber pressure process, in comparison with a typical non-minimal state space PFC method recently developed.

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.

A Control Systems Approach to Input Estimation with Hydrological Applications

This paper demonstrates the feasibility of a new approach to system inversion and input signal estimation based on the exploitation of non-minimal state space feedback control system design methods that can be applied to non-minimum phase and unstable systems. The real and simulated examples demonstrate its practical utility and show that it has particular relevance in a hydrological systems context.

Partially decoupled approach of extended non-minimal state space predictive functional control for MIMO processes

This paper presents a partially decoupled design of the state space predictive functional control for MIMO processes. The multivariable process is first treated into MISO process by a simple Cramer's rule solution to linear equations which provides a balance between model complexity and control system design, and then the derived MISO process based extended state space predictive functional control is presented. The overall design of the controller enables the controller to consider both the process state dynamics and the output dynamics, thus improved control performance for tracking set-points and disturbance rejection is resulted. The proposed controller is tested on both model match and model mismatch cases to demonstrate its superiority. In addition, a closed-form of transfer function representation that facilitates frequency analysis of the control system is provided to give further insight into the proposed method.

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.

An improved model predictive control approach based on extended non-minimal state space formulation

This paper presents a new design method of model predictive control (MPC) based on extended non-minimal state space models, in which the measured input and output variables, their past values together with the defined output errors are chosen as the state variables. It shows that this approach does not need the design of an observer to access the state information any more and by augmenting the process model and its objective function to include the changes of the system state variables, the control performances are superior to those of the controller that does not bear this feature. Furthermore, closed-loop transfer function representation of the model predictive control system facilitates the use of frequency response analysis methods for the nominal control performances of the system.

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.

Non-minimal state-space model-based continuous-time model predictive control with constraints

This article proposes a model predictive control scheme based on a non-minimal state-space (NMSS) structure. Such a combination yields a continuous-time state-space model predictive control system that permits hard constraints to be imposed on both plant input and output variables, whilst using NMSS output-feedback without the need for an observer. A comparison between the NMSS and observer-based approaches using Monte Carlo uncertainty analysis shows that the former design is considerably less sensitive to plant-model mismatch than the latter. Through simulation studies, the article also investigates the role of the implementation filter in noise attenuation, disturbance rejection and robustness of the closed-loop predictive control system. The results show that the filter poles become a subset of the closed-loop poles and this provides a straightforward method of tuning the closed-loop performance to achieve a reasonable balance between speed of response, disturbance rejection, measurement noise attenuation and robustness.

Forward path model predictive control using a non-minimal state-space form

This paper considers model predictive control (MPC) using a non-minimal state-space (NMSS) form, in which the state vector consists only of the directly measured system variables. Two control structures emerge from the analysis, namely the conventional feedback form and an alternative forward path structure. There is a close analogy with proportional-integral-plus (PIP) control system design, which is also based on the definition of an NMSS model with two control structures. However, the MPC/NMSS approach has the advantage of handling system constraints at the design stage. Also, since the NMSS model is obtained directly from the identified transfer function model, the covariance matrix for the parameter estimates can be used to evaluate the robustness of the predictive control system to model uncertainty using Monte Carlo simulation. The effectiveness of the approach is demonstrated by means of simulation examples, including the IFAC′93 benchmark and the ALSTOM non-linear gasifier problem. For the simulation examples considered here, the forward path form preserves the good performance properties of the original MPC/NMSS controller, while at the same time yielding improved robustness.

Infinite horizon MPC with non-minimal state space feedback

In the MPC literature, stability is usually assured under the assumption that the state is measured. Since the closed-loop system may be nonlinear because of the constraints, it is not possible to apply the separation principle to prove global stability for the output feedback case. It is well known that, a nonlinear closed-loop system with the state estimated via an exponentially converging observer combined with a state feedback controller can be unstable even when the controller is stable. One alternative to overcome the state estimation problem is to adopt a non-minimal state space model, in which the states are represented by measured past inputs and outputs [P.C. Young, M.A. Behzadi, C.L. Wang, A. Chotai, Direct digital and adaptative control by input–output, state variable feedback pole assignment, International Journal of Control 46 (1987) 1867–1881; C. Wang, P.C. Young, Direct digital control by input–output, state variable feedback: theoretical background, International Journal of Control 47 (1988) 97–109]. In this case, no observer is needed since the state variables can be directly measured. However, an important disadvantage of this approach is that the realigned model is not of minimal order, which makes the infinite horizon approach to obtain nominal stability difficult to apply. Here, we propose a method to properly formulate an infinite horizon MPC based on the output-realigned model, which avoids the use of an observer and guarantees the closed loop stability. The simulation results show that, besides providing closed-loop stability for systems with integrating and stable modes, the proposed controller may have a better performance than those MPC controllers that make use of an observer to estimate the current states.

Continuous-time non-minimal state-space design

A continuous time non-minimal state-space (NMSS) representation is shown to be explicitly related to the underlying minimal state-space observer/state feedback design method and, moreover, the corresponding state feedback gains are explicitly related. This result provides a starting point for NMSS methods in the continuous-time domain. Numerical examples are given which illustrate the underlying relationship.

A robust sequential CO2 emissions strategy based on optimal control of atmospheric CO2 concentrations

This paper formally introduces the concept of mitigation as a stochastic control problem. This is illustrated by applying a digital state variable feedback control approach known as Non-Minimum State Space (NMSS) control to the problem of specifying carbon emissions to control atmospheric CO2 concentrations in the presence of uncertainty. It is shown that the control approach naturally lends itself to integrating both anticipatory and reflexive mitigation strategies within a single unified framework. The framework explicitly considers the closed-loop nature of climate mitigation, and employs a policy orientated optimisation procedure to specify the properties of this closed-loop system. The product of this exercise is a control law that is suitably conditioned to regulate atmospheric CO2 concentrations through assimilating online information within a 25-year review cycle framework. It is shown that the optimal control law is also robust when faced with significant levels of uncertainty about the functioning of the global carbon cycle.

Multivariable proportional-integral-plus (PIP) control of the ALSTOM nonlinear gasifier simulation

Multivariable proportional-integral-plus (PIP) control methods are applied to the nonlinear ALSTOM Benchmark Challenge II. The approach utilises a data-based combined model reduction and linearisation step, which plays an essential role in satisfying the design specifications. The discrete-time transfer function models obtained in this manner are represented in a non-minimum state space form suitable for PIP control system design. Here, full state variable feedback control can be implemented directly from the measured input and output signals of the controlled process, without resorting to the design and implementation of a deterministic state reconstructor or a stochastic Kalman filter. Furthermore, the non-minimal formulation provides more design freedom than the equivalent minimal case, a characteristic that proves particularly useful in tuning the algorithm to meet the Benchmark specifications. The latter requirements are comfortably met for all three operating conditions by using a straightforward to implement, fixed gain, linear PIP algorithm.

The data-based mechanistic approach to the modelling, forecasting and control of environmental systems

The paper presents a unified approach to the modelling, forecasting and control of natural and man-made environmental systems. The modelling approach exploits the author’s Data-Based Mechanistic (DBM) modelling philosophy, combined with powerful methods of recursive statistical estimation. These provide the basis for two major stages of model building: first, the critical evaluation of the over-parametrized simulation models that are currently the most common vehicle used in environmental planning and management studies; and second, the adaptive, data-based estimation of parsimonious, ‘top-down’ models that can be used for adaptive forecasting and data assimilation, as well as operational control and management system design. The associated control system design methodology is based on the Non-Minimal State Space (NMSS) approach to the design of Proportional-Integral-Plus (PIP) control systems, based on the DBM models obtained at the previous modelling stage. The paper includes a case study concerned with the modelling and control of globally averaged levels of CO 2 in the atmosphere.

Robust MPC with Output Feedback and Realigned Model

In this work, it is presented a contribution to the design of the robust MPC with output feedback and input constraints. This work extends existing approaches by considering a particular non-minimal state space model, which transforms the output feedback strategy into a state feedback strategy. The controller is developed to the case in which the system inputs may become saturated. We follow a two stages approach. In the off-line stage, a series of unconstrained robust MPCs is obtained by including in the control optimization problem, inequality constraints that force the state of the closed-loop system to contract along the time. Each of these controllers is associated to particular sets of manipulated inputs and controlled outputs. In the existing version of the method, the closed loop system involves a state observer that makes the solution to the robust MPC optimization problem a time consuming step. In the on-line step of the controller design proposed procedure, a sub optimal control law is obtained by combining control configurations that correspond to particular subsets of available manipulated inputs. The method is illustrated with a simulation example of the process industry.