Digital Redesign Approach Research Articles

Design, implementation and performance evaluation of different digital control techniques for current controlled DC-DC Buck converter

The paper presents modelling, control architecture, analysis and design of digital compensators for single feedback-loop voltage mode control as well as two feedback-loop average current mode control and peak current mode control of current controlled DC-DC Buck converter operating in continuous conduction mode with output current as control variable. The compensators are derived using digital redesign approach, simulated on MATLAB, implemented as control algorithms on Texas Instruments' 32-bit TMS320F28069M microcontroller platform, and experimentally validated by testing with a laboratory prototype of current controlled Buck converter. Simulation and experimental results are discussed, compared and evaluated for converter output current performance in tracking reference current signal as well as in regulation against input voltage and load disturbances. Salient features of each control technique are identified and described to determine its suitability in applications of DC-DC converters requiring controlled output current.

Realization of DC–DC Buck Converter Based on Hybrid ${H_2}$ Model Following Control

The buck converter is frequently introduced in the industry to maintain the stability of the voltage output when having the interference suddenly. In order to promote the robustness of the buck converter, a novel hybrid <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H₂</i> model following control (HHMFC) is developed based on digital redesign sliding mode control in this article. First, we design <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H₂</i> model following SMC in the continue-time domain. Then, by using the digital redesign approach, the continuous SMC is redesigned to a corresponding discrete-time SMC and the proposed HHMFC is achieved. Finally, we apply the developed HHMFC to realize a robust buck converter. With both the simulation and experiment results, we can conclude that the proposed HHMFC can easily and successfully apply to the practical realization for the buck converter with better robustness performance.

Hybrid H-infinity synchronization for uncertain continuous chaotic systems based on digital redesign approach

In this paper, the design of hybrid H-infinity synchronization control for continuous chaotic systems based on sliding mode control (SMC) is considered. H-infinity discrete sliding mode controllers integrated with the digital redesign approach are newly designed to achieve robust chaos synchronization. By the proposed design procedure, an H-infinity discrete-time SMC can be easily obtained to guarantee the robustness of synchronization even if the system is disturbed with unmatched perturbations. Besides, since the saturation function is adopted to eliminate the unexpected chattering phenomenon, this paper also discusses the effect of saturation function in multi-input multi-output (MIMO) SMC and the upper bounds of sliding mode trajectories are obtained which is not indicated in the literature. Finally, we perform the simulation to verify the effectiveness of the proposed controller.

Digital tracking control of the boost converter: prediction-based digital redesign approach

Several continuous-time tracking controllers of the DC-to-DC boost converters had been addressed, but few literature touched the digital tracking control because that was a challenging theoretical problem which consists of nonlinear, non-minimum phase and saturated control. Given a continuous-time nonlinear boost converter with continuous tracking control, this paper proposes a new sampled-data feedback laws from the available analog counterpart via digital redesign such that the state trajectories of the sampled-data closed-loop systems close to the continuous-time one in the sense of state-matching. An existing boost converter circuit has been demonstrated to visualize the feasibility of the proposed methodology.

Hybrid robust output tracker design for sampled‐data systems using digital redesign of sliding mode control

AbstractThis paper is mainly concerned with the design of a hybrid robust output tracker for a class of systems with a direct feed‐through term and bounded matched nonlinear disturbances. First, we present a continuous‐time linear quadratic analog tracker (LQAT) based on sliding mode control (SMC), and the existence of sliding manifold is guaranteed with the proposed controller in the continuous‐time domain. After designing the continuous‐time SMC‐based tracker, a digital redesign approach using Euler's approximation method is newly proposed to directly obtain a discrete‐time SMC‐based tracker from the continuous‐time SMC‐based tracker, and the hitting condition is also satisfied such that the existence of sliding manifold is guaranteed in the hybrid controlled systems. Therefore, the output tracking performance with the proposed discrete‐time SMC‐based tracker can be also satisfied as the continuous‐time SMC‐based tracker. Illustrative examples are given to demonstrate the success of the proposed digital‐redesign‐based SMC algorithm.

Multivariable Unconstrained Pattern Search Method for Optimizing Digital PID Controllers Applied to Isolated Forward Converter

Most of the traditional PID tuning methods are heuristic in nature. The heuristic approach-based tuned PID controllers show only nominal performance. In addition, in the case of a digital redesign approach, mapping of the heuristically-designed continuous-time PID controllers into discrete-time PID controllers and in case of the direct digital design approach, mapping of the continuous-time plant (forward converter) into the discrete-time plant, results in frequency distortion (or warping). Besides this, nonlinear elements such as ADC and DAC, and delay in the digital control loop deteriorate the control performance. There is a need to tune conventionally-designed digital controllers to enhance performance. This paper proposes optimized discrete-time PID controllers for a forward DC–DC converter operating in continuous conduction mode (CCM). The considered conventional digital PID controllers designed on the basis of the digital redesign and direct digital approaches are tuned by one of the multivariable unconstrained pattern search methods named Hooke–Jeeves (H–J) search method to ensure excellent output voltage regulation performance against the changes in input voltage and load current. Numerical results show that the H–J-based optimized PID compensated forward converter system shows tremendous improvement in performance compared to its unoptimized counterpart and simulated annealing (SA)-based compensated system, thus justifying the applicability of the H–J method for enhancing the performance.

Sampled-data control of underwater gliders: digital redesign approach

This paper discusses a sampled-data control problem for a nonlinear underwater glider based on the digital redesign (DR) technique. An analog controller is pre-designed based on the fully feedback-linearised model. The condition for the DR problem is proposed in terms of linear matrix inequality, using the delta-operator discrete-time models. We show that the DRed sampled-data controller guarantees the semiglobal practical asymptotic stability of the nonlinear steady gliding motion in the sampling period. The numerical simulations demonstrate the advantage of the developed methodology in terms of the larger sampling period and the better preservation of the original analog control performance than the conventional emulation technique.

Fuzzy filter for nonlinear sampled-data systems: Intelligent digital redesign approach

This paper presents a fuzzy filter design method for nonlinear sampled-data systems using an intelligent digital redesign (IDR) technique. Based on a Takagi–Sugeno (T–S) fuzzy model, discretized closed-loop systems with pre-designed analog fuzzy and digital fuzzy filters are presented. An IDR problem is given to guarantee both state-matching condition and asymptotic stability. Sufficient conditions for solving the IDR problem are proposed and are derived in terms of linear matrix inequalities (LMIs). Finally, a simulation example is given to show the effectiveness of the proposed method.

An On-Line Tracker for a Stochastic Chaotic System Using Observer/Kalman Filter Identification Combined with Digital Redesign Method

This is the first paper to present such a digital redesign method for the (conventional) OKID system and apply this novel technique for nonlinear system identification. First, the Observer/Kalman filter Identification (OKID) method is used to obtain the lower-order state-space model for a stochastic chaos system. Then, a digital redesign approach with the high-gain property is applied to improve and replace the observer identified by OKID. Therefore, the proposed OKID combined with an observer-based digital redesign novel tracker not only suppresses the uncertainties and the nonlinear perturbations, but also improves more accurate observation parameters of OKID for complex Multi-Input Multi-Output systems. In this research, Chen’s stochastic chaotic system is used as an illustrative example to demonstrate the effectiveness and excellence of the proposed methodology.

Decentralised control for large-scale sampled-data systems: digital redesign approach

In this paper, digital redesign (DR) techniques are presented for a decentralised controller of large-scale sampled-data systems. To improve the performance of the previous DR technique, the state-matching error is defined and directly minimised by using the state-matching error cost function. Also, the discretisation error of the interconnection term is eliminated through an exact discrete-time design approach. Sufficient conditions of the proposed DR techniques are obtained in the Lyapunov sense and are converted into optimal problems with linear matrix inequalities. Finally, two numerical examples are provided to demonstrate the performance improvement of the proposed techniques.

Design and Analysis of a Digital Controller for Boost Converter with Renewable Energy Sources for Domestic DC Load

Renewable energy sources like solar PV produces DC voltage which is converted to AC before connecting to domestic grid network. The conversion process from DC to AC and back to DC at load end introduce additional losses in the system. With increasing availability of modern DC loads and growing use of renewable energy, the use of DC network for domestic load supply is on increase in order to reduce energy conversion losses. Presented in this paper is a fast transient digital controller for DC-DC boost converter with energy source from solar PV for domestic DC loads like lightings. The boost converter was model as both steady and dynamic state. Digital controllers were designed using both digital redesign approach and direct digital redesign approach. The system demonstrated fast transient response that is essential for tightly regulated output voltage from constantly varying renewable energy generations.

An improvement on the transient response of tracking for the sampled-data system based on an improved PD-type iterative learning control

An improvement on the transient response of tracking for the sampled-data system based on an improved PD-type iterative learning control (ILC) is proposed in this paper. The developed analog ILC method and the high-gain property tracker design methodology are first combined to significantly reduce learning epochs and overcome the initial condition shift problem and discontinuous reference input in the traditional ILC. Besides, the proposed ILC improves the transient response and decreases the rate of weighting matrices Q to R under the traditional linear quadratic tracker design. First, the off-line observer/Kalman filter identification (OKID) is used to determine the appropriate (low-) order system parameters and state estimator for the physical system with unknown system equation, so that the model-based PD-type ILC can be implemented for practical applications. Then, to improve the transient response and decrease the control effort, the proportional difference type (PD-type) ILC algorithm is combined with the high-gain property linear quadratic tracker (LQT) design to construct the high performance tracker for the model-based sampled-data systems. Furthermore, the discrete-time version high performance tracker design for the unknown stochastic sampled-data system via the iterative learning control method is proposed in this paper based on the Euler method and the digital redesign approach. Finally, some examples are given for illustrating the effectiveness of the proposed method.

Fault-tolerant tracker for a class of unknown interconnected large-scale sampled-data nonlinear systems with input constraint and actuator failure

Based on the model predictive control (MPC), the soft switching method, and the observer/Kalman filter identification (OKID) method, this paper presents the decentralized fault-tolerant trackers for a class of unknown interconnected large-scale multi-input multi-output sampled-data nonlinear systems with input constraint, actuator failure, and closed-loop decoupling properties. The off-line OKID method is utilized to determine decentralized appropriate (low-) order discrete-time linear models for the class of unknown interconnected large-scale sampled-data systems by using known input–output sampled data. Then, to overcome the effect of modeling error on the identified linear model of each subsystem, an improved observer with the high-gain property based on the digital redesign approach will be presented. So, decentralized multiple MPC controllers are designed beforehand by using the identified linear models. Once a fault is detected in each decentralized controller, one of the backup control configurations in each decentralized subsystem is switched to using the soft switching approach. Thus, the decentralized fault-tolerant control with the closed-loop decoupling property can be achieved through the above approach with a high-gain property decentralized observer/tracker.

Multi-rate digital redesign of cascaded and dynamic output feedback systems

In this paper, a new indirect digital redesign method is presented for multi-rate sampled-data control systems with cascaded and dynamic output feedback controllers. These analogue controllers are often pre-designed based on desirable frequency specifications, such as bandwidth, natural angular frequency, etc. To take advantage of the digital controller over the analogue controller, digital implementation of these analogue controllers are often desirable. As only measured input-output signals are available, an ideal state reconstructing algorithm is utilised to obtain the multi-rate discrete-time states of the original continuous-time system. Based on the Chebyshev quadrature method, the gains of the multi-rate cascaded and the output feedback digital controllers are determined from their continuous-time counterparts according to the different sampling rates employed in the different parts of the closed-loop system. As a result, the respective analogue controllers with the high-frequency and low-frequency characteristics can be implemented using the respective fast-rate sampling and slow-rate sampling digital controllers. Unlike the classical direct bilinear transform method, which is an open-loop direct digital redesign method, the proposed digital controllers take into account the state-matching of the original continuous-time closed-loop system and the digitally redesigned sampled-data closed-loop system. To further improve the state-matching performance, an improved digital redesign approach is also developed to construct the multi-rate cascaded and dynamic output feedback digital controllers. Illustrative examples are given to demonstrate the effectiveness of the developed methods.

Novel Observer-Based Suboptimal Digital Tracker for a Class of Time-Delay Singular Systems

This paper presents a novel suboptimal digital tracker for a class of time-delay singular systems. First, some existing techniques are utilized to obtain an equivalent regular time-delay system, which has a direct transmission term from input to output. The equivalent regular time-delay system is important as it enables the optimal control theory to be conveniently combined with the digital redesign approach. The linear quadratic performance index, specified in the continuous-time domain, can be discretized into an equivalent decoupled discrete-time performance index using the newly developed extended delay-free model. Additionally, although the extended delay-free model is large, its advantage is the elimination of all delay terms (which included a new extended state vector), simplifying the proposed approach. As a result, the proposed approach can be applied to a class of time-delay singular systems. An illustrative example demonstrates the effectiveness of the proposed design methodology.

Robust control of observer-based sampled-data systems: digital redesign approach

This study proposes the digital redesign (DR) method for an observer-based output-feedback control in the presence of parametric uncertainties. The term DR is to convert an existing analogue control into an equivalent digital one in the sense of state-matching. The DR problem can be reduced to find the digital gains minimising the norm distance between the closed-loop states of the analogue and digital control. The main feature of the proposed DR is that the state estimation error in the plant dynamics is considered for the state-matching condition. Also, by handling the parametric uncertainties in the concerned system, the robust stability is well guaranteed in the proposed DR procedure. Its constructive conditions are expressed as the linear matrix inequalities A numerical example has been demonstrated to visualise the feasibility of the proposed methodology.

A novel linear quadratic observer and tracker for the linear sampled data regular system with a direct feedthrough term: a digital redesign approach

This paper develops a novel linear quadratic observer and tracker for the linear sampled data regular system with a direct transmission term from input to output. At the beginning, we use some existing techniques to decompose the singular system into an equivalent regular system which has a direct transmission term from input to output. Then, based on this equivalent regular system, a high-gain optimal linear quadratic analogue observer and tracker is proposed, so that it can effectively induce a high-quality performance on the trajectory-tracking design and the state estimation. Besides, the prediction-based digital redesign method is utilized to obtain a relatively low-gain and implementable digital tracker and observer from the theoretically well-designed high-gain analogue observer and tracker for the linear sampled data regular system with a direct transmission term from input to output. Several illustrated examples are given to demonstrate the performance and effectiveness of the proposed method. 15

Efficient decentralized iterative learning tracker for unknown sampled-data interconnected large-scale state-delay system with closed-loop decoupling property

In this paper, an efficient decentralized iterative learning tracker is proposed to improve the dynamic performance of the unknown controllable and observable sampled-data interconnected large-scale state-delay system, which consists of N multi-input multi-output (MIMO) subsystems, with the closed-loop decoupling property. The off-line observer/Kalman filter identification (OKID) method is used to obtain the decentralized linear models for subsystems in the interconnected large-scale system. In order to get over the effect of modeling error on the identified linear model of each subsystem, an improved observer with the high-gain property based on the digital redesign approach is developed to replace the observer identified by OKID. Then, the iterative learning control (ILC) scheme is integrated with the high-gain tracker design for the decentralized models. To significantly reduce the iterative learning epochs, a digital-redesign linear quadratic digital tracker with the high-gain property is proposed as the initial control input of ILC. The high-gain property controllers can suppress uncertain errors such as modeling errors, nonlinear perturbations, and external disturbances (Guo et al., 2000) [18]. Thus, the system output can quickly and accurately track the desired reference in one short time interval after all drastically-changing points of the specified reference input with the closed-loop decoupling property.

Iterative learning-based decentralized adaptive tracker for large-scale systems: A digital redesign approach

In this paper, a digital redesign methodology of the iterative learning-based decentralized adaptive tracker is proposed to improve the dynamic performance of sampled-data linear large-scale control systems consisting of N interconnected multi-input multi-output subsystems, so that the system output will follow any trajectory which may not be presented by the analytic reference model initially. To overcome the interference of each sub-system and simplify the controller design, the proposed model reference decentralized adaptive control scheme constructs a decoupled well-designed reference model first. Then, according to the well-designed model, this paper develops a digital decentralized adaptive tracker based on the optimal analog control and prediction-based digital redesign technique for the sampled-data large-scale coupling system. In order to enhance the tracking performance of the digital tracker at specified sampling instants, we apply the iterative learning control (ILC) to train the control input via continual learning. As a result, the proposed iterative learning-based decentralized adaptive tracker not only has robust closed-loop decoupled property but also possesses good tracking performance at both transient and steady state. Besides, evolutionary programming is applied to search for a good learning gain to speed up the learning process of ILC.

Controlling linear systems with nonlinear perturbations under sampled-data output feedback: digital redesign approach

This article develops a digital redesign (DR) technique for sampled-data observer-based output-feedback control of a continuous-time linear system with nonlinear perturbation. It is assumed that the nonlinear perturbation is a locally Lipschitz function. To deal with the discrete-time modelling error in nonlinear systems, as opposed to the previous approach, the DR problem is configured as a stabilisation one for error dynamics between the closed-loop system of nominal linear model under an analogue state-feedback controller and that of the linear system with the nonlinear perturbation under a sampled-data output-feedback controller. A constructive DR condition is formulated in the format of linear matrix inequalities. The stability of the actual sampled-data control system is guaranteed within the DR procedure. The effectiveness of the proposed DR methodology is demonstrated through a numerical simulation.