Non-minimum Phase Dynamics Research Articles

Enhancing disturbance rejection in boost converter for CPL: A controller design approach with partial pole placement and approximate model matching

In DC microgrids, the cascade operation of the DC-DC converters leads to a constant power load fed by the boost converter, resulting in unstable behavior in addition to the non-minimum phase dynamics. An enhanced load disturbance rejection control scheme based on partial pole placement and an approximate model matching technique is proposed. This approach is inspired by the well-known direct synthesis method to achieve optimal load disturbance rejection performance. The effectiveness of the proposed control scheme has been validated through hardware implementation, demonstrating its capability in setpoint tracking and load disturbance rejection under variations in load power and input voltage. The robust stability of the suggested scheme has been investigated through the Kharitonov theorem and Monte-Carlo simulation, considering different performance matrices. The suitability of the presented scheme has been established by analyzing the comparative performance of recently reported works. The proposed controller reduces peak overshoot and settling time by ∼50%, handles system uncertainties up to 75%, and outperforms FOPID controllers tuned with particle swarm optimization, queen bee genetic algorithm, and chaos game optimization methods.

Control-relevant neural networks for feedforward control with preview: Applied to an industrial flatbed printer

The performance of feedforward control depends strongly on its ability to compensate for reproducible disturbances. The aim of this paper is to develop a systematic framework for artificial neural networks (ANN) for feedforward control. The method involves three aspects: a new criterion that emphasizes the closed-loop control objective, inclusion of preview to deal with delays and non-minimum phase dynamics, and enabling the use of an iterative learning algorithm to generate training data in view of addressing generalization errors. The approach is illustrated through simulations and experiments on an industrial flatbed printer.

Auto-tuning of reference models in direct data-driven control

Designing controllers directly from data often requires choosing a reference closed-loop model, whose behavior should be reproduced as tightly as possible by the actual closed-loop system via the selected controller structure (e.g., PID). Within a linear setting, we present a derivative-based approach to jointly select the reference model and controller parameters directly from data. The proposed strategy allows one to maximize closed-loop performance while enforcing user-defined constraints, and it is designed to handle non-minimum phase dynamics. The effectiveness of the proposed approach is shown through three numerical case studies.

Design of Robust PID Controller Using PSO-Based Automated QFT for Nonminimum Phase Boost Converter

This brief reports a novel method of synthesizing a robust PID controller for regulating boost DC-DC converter that exhibits non-minimum phase (NMP) dynamics and complex-conjugate poles in its linear model. The NMP dynamics restrict the achievable closed-loop bandwidth and make tuning of PID parameters a difficult task. To solve this problem, the proposed design method uses the Quantitative Feedback Theory (QFT) in conjunction with particle swarm optimization (PSO) to carry out automatic loop-shaping. Due to the global optimization capability of PSO, the proposed multi-objective function approach with PID simplifies the loop-shaping to compensate the converter having complex-conjugate zeros. An attractive feature of this design method is that it accounts for the worst-case scenario due to parametric variations in the converter model. The real-time simulation results and the experiments reveal the efficacy of the proposed method.

Integrated Autopilot Guidance Based on Zero-Effort-Miss Formulation for Tail-Controlled Missiles

This paper presents a control structure integrating guidance and control loops for tail-controlled missile systems. Motivated by the fact that common tail-controlled missiles involve non-minimum phase dynamics, the proposed controller is designed to prevent the internal dynamics from diverging, as well as achieving homing against the intended target. To minimize the miss distance at the end of homing, we derive a formulation of a zero-effort-miss using engagement kinematics that contain the rotating dynamics of the missile, which is different from existing approaches. Subsequently, to nullify the zero-effort-miss, a nonlinear controller is designed based on the Lyapunov stability theory. Since the derived controller has a similar structure to the conventional three-loop topology that has been utilized for various tail-controlled flight systems, it is expected that the proposed method can be applied to the actual system from a practical point of view. Numerical simulation results also show that the proposed method achieves target interception while possessing stable internal dynamics.

An Optimal Primary Frequency Control Based on Adaptive Dynamic Programming for Islanded Modernized Microgrids

In many pilot research and development (R&D) microgrid projects, engine-based generators are employed in their power systems, either generating electrical energy or being mixed with the heat and power technology. One of the critical tasks of such engine-based generation units is the frequency regulation in the islanded mode of modernized microgrid (MMG) operation; MMGs are microgrids equipped with advanced controls to address more emerging scenarios in smart grids. For having a stable and reliable MMG, we need to synthesize an optimal, robust, primary frequency controller for the islanded mode of MMG of the future. This task is challenging because of unknown mechanical parameters, occurrence of uncertain disturbances, uncertainty of loads, operating point variations, and the appearance of engine delays, and hence nonminimum phase dynamics. This article presents an innovative primary frequency control for the engine generators regulating the frequency of an islanded MMG in the context of smart grids. The proposed approach is based on an adaptive optimal output-feedback control algorithm using adaptive dynamic programming (ADP). The convergence of algorithms, along with the stability analysis of the closed-loop system, is also shown in this article. Finally, as experimental validation, hardware-in-the-loop (HIL) test results are provided in order to examine the effectiveness of the proposed methodology practically. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by the problem of primary frequency controls in modernized microgrids (MMGs) using engine generators, which are still one of the prime sources of regulating frequency in pilot research and development (R&D) microgrid projects. Although MMGs will be integral parts of the smart grid of the future, their primary controls in the islanded mode are not advanced enough and not considering existing theoretical challenges scientifically. Existing approaches to regulate frequency using industrially accepted methods are highly model-based and not optimal. Besides, they are not considering the nonminimum phase dynamics. These dynamics are mainly associated with the engine delays—an inherent issue of mechanical parts—for islanded microgrids. This article suggests a new adaptive optimal output-feedback control approach based on the adaptive dynamic programming (ADP) to the abovementioned problem under consideration. By using the proposed methodology, MMGs can deal with the issues mentioned earlier, which are challenging. The proposed approach is optimally rejecting uncertain disturbances (considering the load uncertainty and operating point variations) and reducing the impacts of nonminimum phase dynamics caused by the engine delay. Based on our currently available hardware-in-the-loop (HIL) device’s capability of modeling power systems’ components in real time, our HIL-based experiments demonstrate that this approach is feasible.

Prediction of baking quality using machine learning based intelligent models

A domestic cookie baking process was modeled using nonlinear forward and inverse models to predict surface temperature, moisture content and browning index that describe the baking quality of the end product. The baking processes were carried out at different oven temperatures (160, 180, 200 °C) and the changes in surface temperature, moisture content and browning index were determined to construct the identification models namely nonlinear polynomial models (PLN) and nonlinear artificial-neural network (ANN) model. The parameters of the artificial models were optimized using least-squares estimation and Levenberg-Marquardt optimization, respectively. The predicted baking characteristics in both forward and inverse phases were in good agreement with the measured ones even for the browning index which was difficult to model because of the its nonminimum-phase dynamics. The application results indicated that the developed intelligient models were very accurate, having low root mean-squared errors, the ANN model approximated the desired values better than the PLN models for all the state variables. Thus, the designed ANN models are applicable for the automatized industrial and domestic oven designs of the future.

Kernel-based identification of non-causal systems with application to inverse model control

Models of inverse systems are commonly encountered in control, e.g., feedforward. The aim of this paper is to address several aspects in identification of inverse models, including model order selection and dealing with unstable inverse systems that originate from inverting non-minimum phase dynamics. A kernel-based regularization framework is developed for identification of non-causal systems. It is shown that ‘unstable’ models can be viewed as bounded, but non-causal, operators. As the main contribution, a range of the required kernels for non-causal systems is developed, including non-causal stable spline kernels. Benefits of the approach are confirmed in an example, including non-causal feedforward control for non-minimum phase systems.

Semi-Adaptive Closed-Loop Control for Infusion of Medications With Transport Delay in Clinical Effects

Abstract This paper presents a semi-adaptive closed-loop control approach to autonomous infusion of medications exhibiting significant transport delay in clinical effects. The basic idea of the approach is to enable stable adaptive control of medication infusion by (1) incorporating transport delay explicitly into control design by way of a Padé approximation while (2) facilitating linear parameterization of control design model by desensitization of nonlinearly parameterized cooperativity constant associated with pharmacodynamics (PD). A novel dynamic dose–response model for control design is presented, in which the cooperativity constant exerts zero influence on the model output in the steady-state. Then, an adaptive pole placement control (APPC) technique was employed to fulfill adaptive control design in the presence of nonminimum phase dynamics associated with the Padé approximation of transport delay. The controller was evaluated in silico using a case study of regulating a cardiovascular variable with a sedative under a wide range of transport delay and pharmacological profiles. The results suggest that adaptation of transport delay and pharmacological characteristics may be beneficial in achieving consistent and robust regulation of medication-elicited clinical effects.

H2 Vs H∞ control of TRMS via output error optimization augmenting sensor and control singularities

Abstract This paper addresses the robust control problem of Twin Rotor Multi input multi output System (TRMS) via H2 and H∞ control techniques. An output error optimization technique is proposed to develop H2 and H∞ controllers for the well posed plant. Computer simulation results are presented for closed loop TRMS in hovering positions which show marked improvements over previous works. The simulated plant exhibits stable responses in hovering position at the desired pitch and yaw angles. Corrections are incorporated in model formulation to compensate control and sensor singularities. The output error optimization technique proposed in the present paper can be essentially adopted in controlling of 2 by 2 plants exhibiting non-minimum phase dynamics.

Active disturbance rejection control of DC–DC boost converter: a review with modifications for improved performance

This study provides a comprehensive review of existing active disturbance rejection control (ADRC) techniques for the control of non-minimum phase (NMP) DC–DC boost converter (DBC). A boost converter presents a challenging control task due to its non-linear and NMP dynamics while operating in continuous conduction mode. ADRC schemes, specifically those that claim improved performance for NMP systems, have been experimentally evaluated for voltage control of DBC. Additionally, a new way of incorporating known system dynamics into the control structure is proposed through a modified scheme. An averaged non-linear model of DBC is used in the simulation to analyse the effectiveness of control schemes and the results are experimentally validated on hardware. It is shown that the proposed method outperforms the reported model-assisted ADRC techniques while utilising only the system pole information.

Asymptotic tracking for linear and nonlinear systems: a two-point boundary value formulation

In this paper, the output tracking problem for linear and nonlinear systems in normal form is revisited in the case of non-minimum phase dynamics and in the absence of any model for the exosystem generating the periodic reference signal. The asymptotic output tracking is obtained by replacing the classical stability condition for the zero dynamics driven by the reference signal with the existence of a solution to a two-point boundary value problem. The latter solution allows to generate the ideal steady-state evolution of the zero dynamics. This strategy allows to retain two interesting features of standard tracking and regulation approaches, namely, i) the use of a simple linear feedback structure and without the need of solving any partial differential equation (as in tracking) and ii) avoiding minimum phase requirements (as in output regulation). Since the same kind of two-point boundary value problem usually arises in the application of the Pontryagin Minimum Principle in optimal control, a natural question to ask is whether there is an underlying connection; hence, in the linear case, further insights are achieved by comparison with an alternative solution based on optimal control problem formulated for an auxiliary affine system.

An Inversion-Based Learning Approach for Improving Impromptu Trajectory Tracking of Robots With Non-Minimum Phase Dynamics

This paper presents a learning-based approach for impromptu trajectory tracking for non-minimum phase systems, i.e., systems with unstable inverse dynamics. Inversion-based feedforward approaches are commonly used for improving tracking performance; however, these approaches are not directly applicable to non-minimum phase systems due to their inherent instability. In order to resolve the instability issue, existing methods have assumed that the system model is known and used pre-actuation or inverse approximation techniques. In this work, we propose an approach for learning a stable, approximate inverse of a non-minimum phase baseline system directly from its input-output data. Through theoretical discussions, simulations, and experiments on two different platforms, we show the stability of our proposed approach and its effectiveness for high-accuracy, impromptu tracking. Our approach also shows that including more information in the training, as is commonly assumed to be useful, does not lead to better performance but may trigger instability and impact the effectiveness of the overall approach.

Design of A Novel Feed-Forward Control Strategy for A Non-Minimum Phase System

This paper proposes a new feed-forward control strategy for a plant with non-minimum phase dynamics. A Feed-Forward controller is very essential for controlling plants with time-varying reference signals. However, designing this type of controller is a non-trivial problem in case the plant dynamics is non-minimum-phase. This is because, this controller design involves the concept of inversion of the plant model and inverse of a non-minimum-phase plant model is unstable or non-causal. For this problem, usually an approximate inversion of a plant model is applied. An approach with corrected-approximate-inverse (CAI) method is available for feed forward controller design. After analyzing the results and discussion of this CAI technique, it is seen that although it seems to be working perfectly for small duration of time but its performance is unsatisfactory in case of large span of time. Therefore, in this paper, a new feed-forward control strategy has been designed to erase the above said problem. This method has adopted a simple version of an internal plant-model structure in its time domain. The fixed-structure feed forward controller that is constructed using this method is usually a linear amalgamation of a reference trajectory and its time-derivatives with suitable weighting factors. This control strategy has been verified with appropriate simulation results applied to a studied plant and results are compared with that of the CAI technique.

Trajectory and Vibration Control of a Single-Link Flexible-Joint Manipulator Using a Distributed Higher-Order Differential Feedback Controller

The trajectory tracking in the flexible-joint manipulator (FJM) system becomes complicated since the flexibility of the joint of the FJM superimposes vibrations and nonminimum phase characteristics. In this paper, a distributed higher-order differential feedback controller (DHODFC) using the link and joint position measurement was developed to reduce joint vibration in step input response and to improve tracking behavior in reference trajectory tracking control. In contrast to the classical higher-order differential (HOD), the dynamics of the joint and link are considered separately in DHODFC. In order to validate the performance of the DHODFC, step input, trajectory tracking, and disturbance rejection experiments are conducted. In order to illustrate the differences between classical HOD and DHODFC, the performance of these controllers is compared based on tracking errors and energy of control signal in the tracking experiments and fundamental dynamic characteristics in the step response experiments. DHODFC produces better tracking errors with almost same control effort in the reference tracking experiments and a faster settling time, less or no overshoot, and higher robustness in the step input experiments. Dynamic behavior of DHODFC is examined in continuous and discontinues inputs. The experimental results showed that the DHODFC is successful in the elimination of the nonminimum phase dynamics, reducing overshoots in the tracking of such discontinuous input trajectories as step and square waveforms and the rapid damping of joint vibrations.

An Integrated Model-Data-Based Zero-Phase Error Tracking Feedforward Control Strategy With Application to an Ultraprecision Wafer Stage

In precision motion control, well-designed feedforward control can effectively compensate the reference-induced tracking error. To achieve excellent tracking performance such as nanometer accuracy regardless of reference variations, an integrated model-data-based zero-phase error tracking feedforward control (ZPETFC) strategy is synthesized for precision motion systems with complex and nonminimum phase (NMP) dynamics. The feedforward controller comprises a conventional ZPETFC controller and a gain compensation filter structured with symmetric finite impulse response (FIR) filter. Especially, the conventional ZPETFC is predesigned based on the plant model, and consequently, the feedforward controller is parameterized by the gain compensation filter coefficients, which results in excellent capacity for approximating the inverse behavior of the complex and NMP dynamics. In order to compensate the modeling error in the conventional ZPETFC design and improve the tracking performance, a data-based instrumental-variable method with impulse response experiment is developed to obtain the optimal parameter vector under the existence of noise and disturbances. Furthermore, the ridge estimate method using singular value decomposition is employed to guarantee a fast convergent iteration in the case of ill-conditioned Hessian matrix. The proposed ZPETFC strategy enables a convex optimization procedure with the inherent stability in the iterative tuning process, and is finally implemented on a developed ultraprecision wafer stage. Comparative experimental results demonstrate that the strategy is insensitive to reference variations in comparison with iterative learning control, and outperforms preexisting model-based ZPETFC and data-based FIR feedforward control.

Output consensus control of multi-agent systems with nonlinear non-minimum phase dynamics

ABSTRACTThis paper considers the output consensus problem in non-minimum phase nonlinear multi-agent systems. The main contribution of the paper is to guarantee achieving consensus in the presence of unstable zero dynamics. To achieve this goal, a consensus protocol consisting of two terms is proposed. The first term is a linear function of the states of each agent employed in order to overcome the non-minimum phase dynamics, and the second term is a function of the output of neighbouring agents which provides coupling among agents and guarantees output consensus in the network. The asymptotic stability of output consensus errors and the boundedness of the states of agents are also studied. A numerical example is presented to show the effectiveness of the proposed approach.

Fixed-Structure Feedforward Control Law for Minimum- and Nonminimum-Phase LTI SISO Systems

Fundamental limitation of the model-inverse feedforward control results from instability or noncausality of the inverse of nonminimum-phase dynamics which cannot be applied in practice. To overcome this limitation, the approximate-inverse methods have been proposed in the literature. Structures of feedforward controllers proposed so far highly depend on a plant model structure. Therefore, in general, their implementation may be inconvenient or troublesome in industrial applications. In this context, a simple fixed-structure feedforward control law is proposed in this paper in the form of a weighted linear combination of a reference trajectory and its time derivatives. Design rules for selection of the weights are derived and provided in an explicit (analytical) form. The proposed control law can be applied to both nonminimum- and minimum-phase linear time invariant single-input-single-output systems. The new method has been compared with classical feedforward controllers known from the literature, revealing its advantages and limitations. The results of numerical examples and experimental validation tests obtained for an electronic plant have been reported.

Robust PID Auto-tuning for the Quadruple Tank System

In multi-modular process architectures with independent but interacting subsystems, identification may not be the first choice at hand for closed loop control. A robust relay-based PID autotuning strategy is presented and validated on a quadruple tank system with non-minimum phase dynamics. The controller ensures a specified closed loop robustness, which is of great benefit to the overall performance. The experimental results suggest that the proposed method fulfils the robustness requirement and performs well in various operating conditions of the testbench.

Nonminimum Phase Compensation in VSC-HVDC Systems for Fast Direct Voltage Control

Newly developed VSC-HVDC systems are reaching power levels of up to 1000 MW. At this power level, the nonminimum phase behavior of the VSC-HVDC systems’ dc plant becomes a threat to the stability of the direct voltage for fast dc control-loop dynamics. This paper presents a novel compensation scheme, called RHP-zero shifting+damping, designed to deal with the nonminimum phase dynamics of the dc plant by adding additional compensation loops to the current controller of the VSC-HVDC system. The compensation scheme can work along with linear controllers and allows the closed-loop bandwidth of the direct voltage controller to be increased without affecting the direct voltage stability of high-power VSC-HVDC systems. As a result, the direct voltage variations are significantly reduced during power changes in the ac or dc network. The performance of the compensation scheme is evaluated through simulations and corroborated in a 1-kW experimental test bed.