State-space Control Research Articles

Fully symbolic-based technique for solving complex state-space control systems

Despite the superiority of symbolic approaches over the purely numerical approaches in many aspects, it does not receive the proper attention due to its significant complexity, high resources requirement and long drawn time which even grows significantly with the increase of model dimensions. However, its merits deserve every attempt to overcome the difficulties being faced. In this paper, a fully generic symbolic-based technique is proposed to deal with complex state space control problems. In this technique, depending on the model dimension if exceeds a predefined limit, the state space is solved using the partitioned matrices theory and block wise inversion formula. Experimental results demonstrate that the proposed technique overcomes all the previously mentioned barriers and gives the same results when compared to numerical methods (Simulink). Moreover, it can be used to gain useful information about the system itself, provides an indication of which parameters are more important and reveals the sensitivity of system model to single parameter variations.

Discrete Fundamental AC Voltage Controller for Three-Phase Standalone Converters

Voltage control of standalone converters with LC filter is usually based on proportional-resonant or proportional-integral controllers, which often require further active damping methods to achieve stability. These solutions place design constraints in the selection of the closed-loop pole locations which limit the achievable bandwidth and increase the design complexity. In contrast, in state-space based controllers, the closed-loop poles can be placed freely through state feedback, which makes them particularly suitable for high order plants and/or low sampling frequencies. Among the modern control methods, direct pole placement is a simple technique that enables the establishment of a straightforward relationship between outcome and design, as opposed to more advanced approaches. This paper presents a discrete state-space voltage controller for standalone converters with LC output filter. The proposed method combines the direct pole placement technique with a virtual disturbance observer in order to compensate the effects produced by the load and model mismatches. The design process takes into account both the filter parameters and the sampling frequency, rendering the performance of the obtained controller independent of both. The result is a streamlined design procedure that leads to consistent outcomes for a wide range of plant parameter variations, requiring only one input: the desired closed-loop bandwidth.

Novel Fractional-Order Model Predictive Control: State-Space Approach

This paper deals with a novel approach to the fractional-order model predictive control in state space. Except well-known fractional-order models of processes (plants) with arbitrary (real) order of the derivatives in fractional differential equations a new fractional performance index (cost function) and fractional control action are considered. Such combined approach to the model predictive control provides more degrees of freedom and incorporates fractional-order dynamics into the control in the form of memory due to the property of the fractional-order operator. An illustrative example of this approach is presented.

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.

Neural network predictive control of vibrations in tall structure: An experimental controlled vision

This article presents the use of neural network predictive controller as a novel technique for vibration control of tall structures employing single degree of freedom active tuned mass damper (ATMD). Additionally, the proposed technique is compared with two modern control techniques: pole-placement controller and adaptive neuro-fuzzy inference controller. A scaled-down laboratory model is used to validate the control techniques. A linear and a nonlinear auto-regressive exogenous (ARX) models are identified for the constructed structure. A neural network predictive controller is designed using the nonlinear ARX model. Polynomial and state-space pole-placement controllers are designed using the linear ARX model. A fuzzy logic controller is designed for the structure and trained using adaptive neuro fuzzy inference system (ANFIS). Hardware-in-the-loop implementation of these controllers demonstrates that the neural network predictive controller combines the advantages of both pole-placement and the ANFIS controllers and reduces the settling time of the mass damper six times with same amplitude mitigation.

Adaptive State-space Control of Under-actuated Systems Using Error-magnitude Dependent Self-tuning of Cost Weighting-factors

This article methodically constructs a novel adaptive self-tuning state-space controller that enhances the robustness of under-actuated systems against bounded exogenous disturbances. The generic Linear-Quadratic-Regulator (LQR) is employed as the baseline controller. The main contribution of this article is the formulation of a hierarchical online gain-adjustment mechanism that adaptively modulates the weighting-factors of LQR’s quadratic-performance-index by using pre-calibrated continuous hyperbolic scaling functions. The hyperbolic scaling functions are driven by the magnitude of system’s state-error variables. This augmentation dynamically updates the solution of the Matrix-Riccati-Equation which modifies the state-feedback gains after every sampling interval. The efficacy of the proposed adaptive controller is validated by conducting hardware-in-the-loop experiments on QNET Rotary Pendulum setup. The experimental outcomes show that the proposed adaptive control scheme yields stronger damping against oscillations and faster error-convergence rate, while maintaining the controller’s asymptotic-stability, under the influence of parametric uncertainties.

Modelling and control of advanced adiabatic compressed air energy storage under power tracking mode considering off-design generating conditions

Advanced adiabatic compressed air energy storage (AA-CAES) is a scalable storage technology with a long lifespan, fast response and low environmental impact, and is suitable for grid-level applications. In power systems with high-penetration renewable generation, AA-CAES is expected to play an active role in flexible regulation. This paper proposes a state-space set-point control model of AA-CAES for the application in the power tracking mode considering off-design characteristics. The part-load features of the multi-stage turbine and heat exchanger are captured by simplified models, and then tailored for improving computational efficiency in the applications with a timescale of 1 min. The set-point control (power tracking) of AA-CAES entails the coordination of turbine inlet pressure, air mass flow rate and heat transfer fluid (HTF) mass flow rate, while ensuring the secure pressure at the throttle valve linking the air storage tank and the expansion train. The set-point control problem is cast to a differential-algebraic equation (DAE) constrained optimization problem, and is reformulated as a nonlinear program via the simultaneous collocation method. Case studies validate the accuracy and applicability of the proposed AA-CAES model for power tracking under off-design generating conditions.

State-Space Control for LCL Filters: Converter Versus Grid Current Measurement

This article deals with discrete-time state-space current control of three-phase converters equipped with an LCL filter. Either the converter or grid current is measured, and the unknown states are estimated using a reduced-order observer. The stability and dynamic performance of the control designs based on these two current measurement options are compared by means of analysis and experiments at different sampling frequencies and under varying grid conditions, ranging from strong to very weak. Equal reference-tracking performance under nominal conditions is used as a basis for comparison between these two options. If a strong grid is assumed in the control tuning, the controller based on the grid current measurement (GCM) is found to be more robust against varying grid conditions in a wide range of sampling frequencies than the controller based on the converter current measurement (CCM). The CCM leads to better dynamic performance as compared to the GCM if the resonance frequency of the system falls below the critical resonance frequency.

Discrete model of hybrid stepper motor by optimal state space control

The article provides an overview of modern control methods of a stepper motor. Continuous and discrete models of a hybrid stepper motor in the state space have been developed. At each step of the control algorithm, the required torque is set in the state matrix and the values of the optimal voltage in the dq frame used in field oriented control are calculated.

Look Ahead Based Control Strategy for Hydro-Static Drive Wind Turbine Using Dynamic Programming

This research paper presents a look-ahead optimal control strategy for a Hydro-static Drive Wind Turbine when look ahead wind speed information is available. The proposed predictive controller is a direct numerical optimizer based on the well established principles of Hamilton-Jacobi-Bellman (Dynamic Programming). Hydro-static transmission based, non-linear model of wind turbine is used in this optimization work. The optimal behavior of the turbine used the non-linearity of aerodynamic maps and hydro-static drive train by a convex combination of state space controller with measurable generator speed and hydraulic motor displacement as scheduling parameters. A comparative analysis between a optimal controller based on Maximum Power Point Tracking (MPPT) algorithm as published in literature and the proposed look ahead based predictive controller is presented. The simulation results show that proposed look ahead strategy offered optimal operation of the wind turbine by closely tracking the optimal tip-speed ratio to maximize capacity factor while also maintaining the hydraulic motor speed close to the desired value to ensure that the frequency of electrical output is constant. It is observed from the simulation results that the proposed predictive controller provided around 3.5% better performance in terms of improving total system losses and harvesting energy as compared to the MPPT algorithm.

State-Space Control Systems: The MATLAB®/Simulink® Approach

Abstract These days, nearly all the engineering problem are solved with the aid of suitable computer packages. This book shows how MATLAB/Simulink could be used to solve state-space control problem...

Predictive Controller Design for a Cement Ball Mill Grinding Process under Larger Heterogeneities in Clinker Using State-Space Models

Chemical process industries are running under severe constraints, and it is essential to maintain the end-product quality under disturbances. Maintaining the product quality in the cement grinding process in the presence of clinker heterogeneity is a challenging task. The model predictive controller (MPC) poses a viable solution to handle the variability. This paper addresses the design of predictive controller for the cement grinding process using the state-space model and the implementation of this industrially prevalent predictive controller in a real-time cement plant simulator. The real-time simulator provides a realistic environment for testing the controllers. Both the designed state-space predictive controller (SSMPC) in this work and the generalised predictive controller (GPC) are tested in an industrially recognized real-time simulator ECS/CEMulator available at FLSmidthPvt. Ltd., Chennai, by introducing a grindability factor from 33 to 27 (the lower the grindability factor, the harder the clinker) to the clinkers. Both the predictive controllers can maintain product quality for the hardest clinkers, whereas the existing controller maintains the product quality only up to the grindability factor of 30.

Modelling, Parametrization and Observer Design of a 20 MW Reference Wind Turbine for Control Purposes

In the present contribution, the model development of a wind turbine with focus on an advanced control system design is reported. The aim is to produce a model that captures essential dynamics over the simplest cases but maintaining an acceptable level of complexity. The problem of parameter reduction from high-resolution models, as used in the simulation of reference turbines, to models with low number of parameters, as normally used for control purposes, is also studied. The obtained parametric model is validated by developing an observer, which can be used for state-space control as well as effective wind speed estimation. As numerical example, a 20 MW reference wind turbine is used. Very large wind turbines are very flexible and nonlinear, therefore very simple rigid models do not lead to satisfactory results. The proposed observer is adjusted during operation in order to overcome this problem.

Application of State Feedback Controller to Ensure Robust D-Stable Operation of Virtual Synchronous Generators

This article presents a comprehensive small signal model for a virtual synchronous generator (VSG) integrated into a microgrid. In the developed state-space, active and reactive power control loops of the VSG as well as resistances, and reactances of the lines are considered. Based on this model, the robust D-stable region in terms of different values of inertia constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(M)$</tex-math></inline-formula> , and damping coefficient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(D)$</tex-math></inline-formula> values of the VSG is obtained. To enhance both transient performance as well as guarantee the robust D-stable operation of VSG, an optimization problem is also proposed. Moreover, a new control method is suggested to damp frequency oscillations of the microgrid. The proposed controller is a state feedback which uses the pole placement method and can be used in both of the grid-connected, and isolating modes of operation. In this controller, poles can be placed in the desired locations in order for the microgrid to achieve the desired transient response. In order to access all state variables, a state observer is used to avoid measurement of state variables. Accordingly, one of the features of the proposed method is its ability to move poles without requiring additional sensors. The performance of the proposed method is evaluated in MATLAB/SIMULINK, which shows enhanced dynamic behavior of the microgrid.

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.

Robust control design for an industrial wind turbine with HIL simulations

This paper describes the design and implementation of a H∞-based robust controller for a commercial 2MW variable-speed variable-pitch wind turbine. The single controller is able to deliver specification performance for the entire full load region. Various aspects of modeling and design procedures including reduced order model validation, torsional mode damping of drivetrain and uncertainty estimation are explained in detail. To make the design more reliable and industrially attractive, simple routines for the derivation of required weighting functions are introduced. To investigate the benefits of the suggested design, its closed-loop performance is compared with the wind turbine’s baseline controller and an alternative state–space controller proposed in the literature. This is first evaluated using a FAST-based simulator under IEC-61400 compatible scenarios. It is then verified by a real-life hardware in the loop simulator using an industrial PLC.

Equivalence of the Integrator-Based and Disturbance-Observer-Based State-Space Current Controllers for Grid Converters

This article deals with discrete-time state-space current controllers for three-phase grid converters equipped with an LCL filter. The integral action in the controller can be implemented either using an integrator or a disturbance observer. The results show that the disturbance-observer-based and integrator-based controllers become mathematically equal if the feedforward gains are selected to be equal, the feedforward zero is placed to cancel the pole originating from the integral action, and the closed-loop poles are placed identically. The equivalent performance in both designs is verified by means of analyses and experiments. The equivalence is also shown for double-frequency current controllers.

Improved Control for Industrial Systems Over Model Uncertainty: A Receding Horizon Expanded State Space Control Approach

In this paper, an improved linear quadratic tracking control strategy using a new receding horizon expanded state space (ESS) model is proposed. Unlike traditional state space model, the new ESS model first facilitates the combination of the system state variables and tracking errors, then a subsequent new receding horizon improved linear quadratic tracking control (RHLQTC) is designed with more degrees of freedoms for the adjustment of control parameters, which yields improved control performance compared with traditional RHLQTC. Finally, simulations on a typical reverse process are done in comparison with traditional RHLQTC in terms of both servo and regulatory performance, where results show that the proposed controller provides improved performance under both situations.

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.

Adaptive control designs for control-based continuation in a class of uncertain discrete-time dynamical systems

This article proposes a methodology for integrating adaptive control with the control-based continuation paradigm for a class of uncertain, linear, discrete-time systems. The proposed adaptive control strategies aim to stabilize the closed-loop dynamics with convergence toward a known reference input, such that the dynamics approach the open-loop fixed point if the reference input is chosen to make the steady-state control input equal 0. This enables the tracking of a parameterized branch of open-loop fixed points using methods of numerical continuation without specific knowledge about the system. We implement two different adaptive control strategies: model-reference adaptive control and pole-placement adaptive control. Both implementations achieve the desired objectives for the closed-loop dynamics and support parameter continuation. These properties, as well as the boundedness of system states and control inputs, are guaranteed provided that certain stability conditions are satisfied. Besides, the tuning effort is significantly reduced in the adaptive control schemes compared with traditional proportional–derivative controllers and linear state-space feedback controllers.