An adaptive cascade compensator for a wide class of stable minimum or nonminimum phase plants through time moment estimation

Robust Adaptive Control

This paper concerns the stabilization of linear time-invariant (LTI) systems subject to uncertain, possibly time-varying delays. The fundamental issue under investigation, referred to as the delay margin problem, addresses the question: What is the largest range of delay such that there exists a single LTI feedback controller capable of stabilizing all the plants for delays within that range? Drawing upon analytic interpolation and rational approximation techniques, we derive fundamental bounds on the delay margin, within which the delay plant is guaranteed to be stabilizable by a certain LTI output feedback controller. Our contribution is threefold. First, for single-input single-output (SISO) systems with an arbitrary number of plant unstable poles and nonminimum phase zeros, we provide an explicit, computationally efficient bound on the delay margin, which requires computing only the largest real eigenvalue of a constant matrix. Second, for multi-input multi-output (MIMO) systems, we show that estimates on the variation ranges of multiple delays can be obtained by solving LMI problems, and further, by finding bounds on the radius of delay variations. Third, we show that these bounds and estimates can be extended to systems subject to time-varying delays. When specialized to more specific cases, e.g., to plants with one unstable pole but possibly multiple nonminimum phase zeros, our results give rise to analytical expressions exhibiting explicit dependence of the bounds and estimates on the pole and zeros, thus demonstrating how fundamentally unstable poles and nonminimum phase zeros may limit the range of delays over which a plant can be stabilized by a LTI controller.

On the zeros of three-DoF damped flexible systems

On delay radii and bounds of MIMO systems

Use of 2‐rate controllers for robust control via zero‐placement is a topic of interest in current literature. This paper proposes a 2‐degree‐of‐freedom, 2‐rate, dynamic, output feedback controller to compensate single‐input single‐output (SISO), unstable, non‐minimum phase (NMP), discrete, linear time‐invariant (LTI) plants of relative degree unity; and achieves exactly the same loop and input‐output properties as can be achieved by a linear quadratic regulator (LQR) for the equivalent lifted LTI plant using state feedback. Such LQR‐like loop and input‐output properties, it may be noted, cannot be attained by LTI or even the existing 2‐rate output feedback controllers for plants with NMP zeros. Examples presented illustrate the efficacy of the proposed controller with respect to the existing ones.

This paper presents the diagonal with Blaschke products factorization (DBFact) approach to factor out multivariable time delay and nonminimum phase zeros from multi‐input multi‐output (MIMO) systems. Based on that, a new output‐order independent minimum variance (MV) control law for MIMO systems is proposed. The DBFact method is a two‐step factorization procedure, relying on the diagonal and Blaschke factorization methods. This method has the advantage of being a direct and non‐iterative procedure. This new factorization approach allows the calculation of an MV control law considering the multivariable time delay as a limiting‐performance factor and the nonminimum phase zeros and their corresponding directions. Based on the proposed MV control law, a performance benchmark is introduced, which can be calculated by the DBFact filters and routine operating data. The DBFact methodology was applied to two control structures of the linear plant model of Linde's heat integrated air separation, in which the MV control law output‐order dependency property and the suitability of the performance benchmark were evaluated. Some results were compared with those obtained by admitting the generalized interactor matrix instead of the DBFact filters. The results show the capability of the DBFact methodology to factor the nonminimum phase terms to provide a reliable MIMO controller performance benchmark and illustrate the importance of considering the nonminimum phase zeros and their actual directionality in the MV control law.

In this two-part paper we study stabilization and optimal control of linear time-invariant systems with stochastic multiplicative uncertainties. We consider structured multiplicative perturbations, which, unlike in robust control theory, consist of static, zero-mean stochastic processes, and we assess the stability and performance of such systems using mean-square measures. While Part 2 of this paper tackles and solves optimal control problems under the mean-square criterion, Part 1 is devoted to the stabilizability problem. We develop fundamental conditions of mean-square stabilizability which ensure that an open-loop unstable system can be stabilized by output feedback in the mean-square sense. For single-input single-output systems, a general, explicit stabilizability condition is obtained. This condition, both necessary and sufficient, provides a fundamental limit imposed by the system's unstable poles, nonminimum phase zeros and time delay. For multi-input multi-output systems, we provide a complete, computationally efficient solution for minimum phase systems possibly containing time delays, in the form of a generalized eigenvalue problem readily solvable by means of linear matrix inequality optimization. Limiting cases and nonminimum phase plants are analyzed in depth for conceptual insights, revealing, among other things, how the directions of unstable poles and nonminimum phase zeros may affect mean-square stabilizability in MIMO systems. Other than their independent interest, stochastic multiplicative uncertainties have found utilities in modeling networked control systems pertaining to, e.g., packet drops, network delays, and fading. Our results herein lend solutions applicable to networked control problems addressing these issues.

Discrete Time Multivariable Adaptive Control for Non-Minimum Phase Plants with Unknown Dead Time

Robust model reference adaptive output feedback tracking for uncertain linear systems with actuator fault based on reinforced dead-zone modification

Adaptive control methods are widely used for the control of both linear and nonlinear dynamical systems. Among the adaptive control approaches, Model Reference Adaptive Control (MRAC) method has a systematic design feature in which response of a stable reference model is targeted to be followed by the dynamical system. In general, Linear Time Invariant (LTI) Reference Models are considered in the MRAC design and the adaptation rule is formulated accordingly. In this paper, the linear reference model is altered with a stable nonlinear one and the adaptation rule is re-formulated to cope with the nonlinearity. The stable nonlinear reference model is generated by using the State Dependent Riccati Equation (SDRE) approach and the adaptation rule is also updated by using the same SDRE idea. The effects of altering the linear reference model to the nonlinear counterpart are shown in the MRAC formulations. In addition to the new MRAC formulations, the proposed MRAC algorithm is applied to a 3 DoF helicopter test bed to reveal the advantages of the nonlinear reference model.

This paper proposes a model predictive controller for multivariable systems with time-delays. The design method is derived by the following way, first to consider a design for single input single output(SISO) systems and to modify the control problem for the SISO systems with no time-delays by shifting the outputs with time-delay steps and a design method with no time-delays is applied to the modified systems. Then the SISO case is extended to multi-input multi-output(MIMO) case by replacing time-delay steps in SISO case with an interactor matrix of MIMO plants.

This study explores the integration of the adaptive control approach with the Model Reference Adaptive Control (MRAC) method, with a view to examining the impact of this integration on the performance of dynamic systems. Adaptive control is highlighted as a versatile and robust methodology that enables systems to cope with uncertainties and adapt to rapidly changing conditions in their operating environments. As a branch of adaptive control, the MRAC method focuses on efficiently achieving desired performance objectives by adjusting system parameters based on a predefined reference model. The primary focus is on investigating how these methods can be applied to optimize the functionality of systems characterized by dynamic and variable nature, such as unmanned aerial vehicles. By addressing challenges related to uncertainties, disturbances, and adaptability, the integration of adaptive control with the MRAC method demonstrates significant potential in improving the robustness, responsiveness, and reliability of such systems. This research investigates the performance of adaptive techniques in enhancing the capabilities of modern control systems. The objective of the research is to assess the effectiveness of MRAC in terms of reference signal tracking. Simulation results demonstrate the ability of MRAC to maintain accurate tracking of the desired reference for key vehicle dynamics, including roll, pitch and yaw. The results demonstrate the robustness of the MRAC algorithm in attitude control, which may lead to support for sustainability issues such as energy consumption.

The demand for ubiquitous telecommunications services forces operators to have a special concern about signal quality and the coverage area they offer to their customers. This was usually checked by using suitable propagation models for Single Input Single Output (SISO) systems, which are no longer the case for new and future mobile generations, such as 5G and beyond. To guarantee good signal quality coverage, operators started to replace these models with Multiple Input Multiple Output (MIMO) ones. To achieve the best results, these models are usually calibrated with Drive Test (DT) measures; however, the DTs available for MIMO propagation models are sparse, in contrast to SISO ones. The main contribution presented in this paper is a methodology to extend the propagation models of SISO systems so they can be applied in MIMO sytems with Single-Carrier and Frequency-Domain Equalization (SC-FDE), while still using DTs acquired for SISO systems. This paper presents the impact on Bit Error Rate (BER) performance and its coverage area resulting from the application of our proposed method. We consider a MIMO SC-FDE system with an Iterative Block Decision Feedback Equalization (IB-DFE) receiver and we present the improvement expressions for the BER that we illustrate with some simulations.

Feedforward (FF) control uses a priori knowledge about a given system and its disturbances to influence the system’s behavior in a pre-defined way. However, unlike feedback (FB) control, it does not adjust the control signal (or manipulated variable) in response to how the system actually reacts. In other words, FF control is proactive while FB control is reactive. Model-inversion-based FF (MIBFF) control is a specific type of FF control where the control variable is determined by inverting a model of the system to be controlled. It is very popular for its use in output tracking control problems, where the goal is to force the system’s output to follow a desired trajectory. Output tracking is critical in several different applications, e.g., in manufacturing, robotics, automotive, aerospace, and is typically achieved using a combination of FF and FB control. As motivating examples, consider MIBFF in ultra-precise wafer scanners used in photolithography (see Sidebar S1) and in desktop 3D printing (see Sidebar S2). As these motivating examples illustrate, non-minimum phase (NMP) zeros often arise in practical engineering applications due to non-collocated sensors and actuators, fast sampling, etc. MIBFF for systems with NMP zeros is arguably the most important (and certainly the most researched) issue related to MIBFF.

The last three decades have seen rapid development in modern control theory and microprocessors. Application of newly developed control algorithms in Industrial process control has gained popularity due to microprocessor based control systems. In this chapter all categories of control algorithms which have gained popularity amongst industrial users or which are industrially implementable are covered. We have first covered control algorithms for single-input single-output (SISO) systems and then multi-input multi-output (MIMO) systems. Three term controllers, time delay compensation techniques and fuzzy logic controllers, etc., have been discussed for SISO plants. Predictive, adaptive, optimal and state feedback controllers have been covered for both SISO and MIMO plants. We have discussed auto tuning techniques for SISO PID controllers and also briefly expert control systems. Algorithms have been described in their digital implementation form. Implementation of control algorithms in industrially available distributed digital control system has been discussed. A brief report has been given for actual implementation of some algorithms in industrial plants and benefits due to this implementation have been highlighted. In particular applications of optimal control and optimal filtering in power industry in UK and power, cement and steel industry in Japan and predictive control techniques in petroleum industries in North America have been mentioned while describing the particular algorithm. Recent research results to pool resources of linear quadratic gaussian design popular in power, cement and steel industry and predictive control (model algorithmic control and internal model control) popular in petroleum industries to evolve a better approach to controller design have been highlighted.