Invariant Control Research Articles

Enhancing cooperative distributed model predictive control for the water distribution networks pressure optimization

In water distribution networks (WDNs), the supply pressure to users should be homogeneous and close to the lower bound so as to reduce leakages and energy consumption while meeting users’ water demand. The large-scale features and incomplete structure information of modern WDNs increase the difficulty in modeling and pressure optimization. In this paper, an enhancing cooperative distributed model predictive control (EC-DMPC) strategy is proposed to solve this problem with enhanced operating performance. Firstly, an efficient modeling method and a partitioning method based on operation data are proposed to decompose the WDNs and construct the subsystem models. These methods are based on k-Shape clustering and canonical correlation analysis with considering the mechanism of WDNs. In order to increase the flexibility of coordination while guaranteeing the global optimization performance, a neighbourhood optimization coordination strategy is adopted, where each subsystem considers the performance of itself and that of strongly affected subsystems. Moreover, a robust invariant set and a robust invariant set control law are utilized to handle the disturbance caused by the ignored weak couplings. Part of Shanghai’s WDNs is used as the study case to demonstrate the application of the proposed methods. A comparative experiment study is developed. Results have shown the efficiency of the proposed methods. By the coordination of the EC-DMPC strategy, when the water demand of users changes, the users’ pressure can be maintained homogeneous, and the average pressure decreases, which is beneficial in the reduction of leakages and energy consumption. The distributed strategy could also improve the flexibility and scalability for large-scale WDNs.

Discrete Time Pontryagin Maximum Principle Under State-Action-Frequency Constraints

We establish a Pontryagin maximum principle for discrete time optimal control problems under the following three types of constraints: a) constraints on the states pointwise in time, b) constraints on the control actions pointwise in time, and c) constraints on the frequency spectrum of the optimal control trajectories. While the first two types of constraints are already included in the existing versions of the Pontryagin maximum principle, it turns out that the third type of constraints cannot be recast in any of the standard forms of the existing results for the original control system. We provide two different proofs of our Pontryagin maximum principle in this article, and include several special cases fine-tuned to control-affine nonlinear and linear system models. In particular, for minimization of quadratic cost functions and linear time invariant control systems, we provide tight conditions under which the optimal controls under frequency constraints are either normal or abnormal.

Development and research of the invariant automatic control system of angular speed of diesel engine

The increase in the independence of motor-vehicle engines from the influence of external loading on the engine shaft due to the improvement of the dynamic parameters of the elements of the automatic control system of angular speed is investigated. Research of dynamic parameters of the diesel engine is carried out by simulation . An invariant (combined) simulation model of the automatic control system of the diesel engine was developed and investigated and an automated control system of a self-propelled earthmover with the use of modern hardware was developed. The investigation of the invariant ACS of engine angular speed, which provides the optimum regardless of external disturbances , was continued by including the compensating element in the automatic control system. The recovery time of the steady-state value of engine angular speed under load is reduced by about 7 times, and the magnitude of angular speed drop is approximately 6 times. An algorithmic block diagram of the combined invariant ACS of engine angular speed is developed taking into account the influence of the compensating device for the case when the disturbing action is exponential and which takes into account the operation of the device of limiting the maximum permissible value of disturbance

Optimal control on SU(2) Lie group with stability analysis

Many configuration spaces of mechanical and non-mechanical problems in physical world involve matrix Lie groups. These Lie groups provide a mathematically rich formulation for studying a variety of control theory problems. While control systems have been specialized to different matrix Lie groups, study of optimal control of these systems by minimizing the input cost function has been a tempting research area. Here we take a left invariant driftless control system on the Lie group SU(2) and analyse controllability and optimal control of the system. Stability of the resulting dynamics from optimal control analysis is elaborated. Then numerical integration and some related properties are discussed via two unconventional integrators.

Shared invariance control for constraint satisfaction in multi-robot systems

In systems involving multiple intelligent agents, e.g. multi-robot systems, the satisfaction of environmental, inter-agent, and task constraints is essential to ensure safe and successful task execution. This requires a constraint enforcing control scheme, which is able to allocate and distribute the required evasive control actions adequately among the agents, ideally according to the role of the agents or the importance of the executed tasks. In this work, we propose a shared invariance control scheme in combination with a suitable agent prioritization to control multiple agents safely and reliably. Based on the projection of the constraints into the input spaces of the individual agents using input–output linearization, shared invariance control determines constraint enforcing control inputs and facilitates implementation in a distributed manner. In order to allow for shared evasive actions, the control approach introduces weighting factors derived from a two-stage prioritization scheme, which allots the weights according to a variety of factors such as a fixed task priority, the number of constraints affecting each agent or a manipulability measure. The proposed control scheme is proven to guarantee constraint satisfaction. The approach is illustrated in simulations and an experimental evaluation on a dual-arm robotic platform.

Automated design of structured gain-scheduling oil pressure controllers by modern synthesis methods

This paper presents a new systematic approach for the design of a gain-scheduling-control system for the oil pressure system of internal combustion engines. Therefore, optimal linear time invariant controllers are designed at given operating points and their characteristics are interpolated by an analytical function. An optimization algorithm finds optimal parameters for a given linear controller structure with a fixed order and two degrees of freedom. To solve the optimization problem, constraints in the $$\mathcal{H}_{\infty}$$-norm are given for six different transfer functions of the closed loop. The same restrictions are applied for all operating points. For the gain-scheduling-approach, no classical superimposition of the output variables of the linear controllers is selected, as it is often the case with gain-scheduling-controllers. Instead, the poles and zeros of the gain-scheduling-controller are functionally calculated from the linear control loops depending on the scheduling variable. Therefore, the resulting gain-scheduling-controller shows the set behaviour of the linear controllers independently of the original operating points. A control loop that is independent of the nonlinearity of the controlled system is more efficient than conventional oil pressure control systems that use too high target oil pressures for robustness reasons. This results in increased efficiency of the oil pressure system, which can make a significant contribution to fuel savings.

Features of Automatic Control of Technological Parameters of Water Level in the Drum Steam Boilers

The three-pulse system of automatic control of the water level in the boiler drum received maximum distribution in the energy sector, as well as its modifications, which have the following disadvantages : the presence of static control errors at the end of the transition process in the development of internal disturbances and disturbances of superheated steam flow; large level deviations with sharp and significant changes in the load, which often leads to unloading or shutdown of the boiler or power unit. To eliminate these drawbacks, invariant systems for automatic regulation of the power supply of the drum boiler were previously developed. In work the system of automatic control of technological parameters of water level in a drum of steam boilers is considered. The description of control systems and a detailed description of the electrical power systems of the control system are given. Various methods of tuning the PI controller of a typical three-pulse automatic power control system are considered. The application of the method of structural-parametric optimization and the theory of invariance makes it possible by changing the structure of the system and optimizing the dynamic adjustment of the automatic power control system to significantly improve the quality of maintaining the water level in the boiler drum. Invariant automatic control systems eliminate static control errors under all influences and can significantly improve the quality of maintaining the level under variable conditions. The methods are proposed to significantly improve the quality of water level control in the boiler drum, eliminating the shortcomings of the typical automatic control system. The results of the work can be used in the design of power control systems of steam drum boilers. The results obtained can be used in the development of adaptive control systems for other thermal power facilities.

Adaptive Unbalance Compensation for a Three-Pole Active Magnetic Bearing System

Mass imbalance frequently exists in a rotating machine. It may induce unbalance force, causing undesirable vibrations and noise. Active magnetic bearing (AMB) has been found to be a good device to deal with such problem. This paper is concerned with the unbalance compensation for a three-pole AMB system. An adaptive compensation scheme is proposed based on the theory of immersion and invariance (I&I) control. It is to immerse a higher-order system into a lower-order target system. The lower-order target system in this paper is the three-pole AMB system with known mass imbalance and with a stabilizing integral sliding mode controller (ISMC). On the other hand, the higher-order system is the three-pole AMB system with both the ISMC levitation controller and the adaptive compensator. The adaptive compensator is designed to deal with the case that the mass imbalance may be unknown and may be changing during operation in practical applications. It estimates the information of mass imbalance online and is incorporated into the ISMC so that the unbalance force can be eliminated. Both numerical simulations and experimental results verify the effectiveness of the proposed adaptive compensator for mass imbalance.

Robust feature sets for contraction level invariant control of upper limb myoelectric prosthesis

In spite of the tremendous progress of upper limb myoelectric prosthetic control in the field of rehabilitation engineering, there still exist several real world challenges to be met, before realizing it as a good substitute for a natural arm. Incompetence of the system to accommodate variations in contraction levels of muscle movements has been identified as one of the significant challenges, as these variations have a subsequent impact on the performance of pattern recognition based myoelectric control. Non-linear techniques are more suited to characterize myoelectric signals since one of their major properties is nonlinearity. Based on this we propose two feature combinations which can lead to a reliable control scheme that is robust against contraction level variations. The performance of our proposed features when tested on nine transradial amputees for six motion classes at three different force levels outweighed other established feature extraction methods meant for contraction variation independent control. Significant improvement of around 8% in average classification performance was achieved across all subjects and force levels, subjected to training, both with all force levels and with unseen force levels. Moreover, these features achieved superior performance in classifying flexion as well as grip movements.

Optimal fractional order PIλDμ controller for stabilization of cart‐inverted pendulum system: Experimental results

AbstractThe cart‐inverted pendulum is a non‐minimum phase system having right half s‐plane pole and zero in close vicinity to each other. Linear time invariant (LTI) classical controllers cannot achieve satisfactory loop robustness for such systems. Therefore, in the present work the fractional order PIλDμ (FOPID) controller is addressed for robust stabilization of the system, since fractional order controller design allows more degrees of freedom compared to its integer order counterparts by virtue of its two parameters λ and μ. The controller parameters are tuned by three evolutionary optimization techniques. In order to select the controller parameters optimally, a novel non‐linear fitness function using integral time square error (ITSE), settling‐time, and rise time is proposed here. The control algorithm is implemented successfully in real‐time. Moreover, stability analysis of the system compensated with a fractional order controller is presented using Riemann surface. Robustness of the physical cart‐inverted pendulum system towards multiplicative gain variations and plant parameter variations is verified. In this regard, it is shown that the fractional order controller provides satisfactory robust performance in both simulation and real‐time system.

CAD-based Approach for Identification of UAVs

The paper presents an approach for the identification of the parameters of an Unmanned Aerial Vehicle (UAV), specifically a quadrotor using experiments in a CAD environment. A linearized control model is proposed to create a global model that operates in all operation range. Usually, in this type of systems a linear time invariant (LTI) controller is used, and then a lineal control model around each operating point is needed to the design of the controller. In this study, a linear control model suitable in each operating point is developed and identified. This serial of LTI control model can be combined and provides a global control model. Therefore, through this global control model can be designed a global controller suitable for all the operating range.

U-model enhanced MIMO decoupling control of thickness and plate type of cold rolling temper mill

This paper presents a new design procedure for control of thickness and plate type of cold rolling temper mill. A novel concept for control system design - U-model based design methodology with expanded multi-input and multi-output (MIMO) formulation for this application separates specifying closed loop performance-controller from process models. In contrast to classical and methodologies, this takes two parallel formations; 1) designs an invariant virtual controller with specified closed loop transfer function in a feedback control loop; 2) determines real controller output by resolving the inverse of the plant U-model. Further, this study analyses some of the associated properties for assurance and guidance for ongoing theoretical development and applications. To validate the design procedure, it takes several computational experiments to generate simulation results, which show efficiency and effectiveness of the proposed MIMO U-model based control system design.

U-model enhanced MIMO decoupling control of thickness and plate type of cold rolling temper mill

This paper presents a new design procedure for control of thickness and plate type of cold rolling temper mill. A novel concept for control system design - U-model based design methodology with expanded multi-input and multi-output (MIMO) formulation for this application separates specifying closed loop performance-controller from process models. In contrast to classical <model based design> and <model free design> methodologies, this <model independent design> takes two parallel formations; 1) designs an invariant virtual controller with specified closed loop transfer function in a feedback control loop; 2) determines real controller output by resolving the inverse of the plant U-model. Further, this study analyses some of the associated properties for assurance and guidance for ongoing theoretical development and applications. To validate the design procedure, it takes several computational experiments to generate simulation results, which show efficiency and effectiveness of the proposed MIMO U-model based control system design.

Dynamic Correction Algorithms in Multi-axis Systems Based on Predictive and Invariant Control Methods

This article considers the issue of controlling a mobile robotic technological complex based on the use of predictive and invariant control methods for compensation of external indeterminate perturbations. Authors carry out the analysis of the perturbations arising in the control system. We propose to introduce three correction contours into the control system structure ensuring parrying of all the perturbation components. A modification of the classical predictive control scheme based on the application of complementary correction algorithms is presented. The algorithms of the complementary correction are based on the statements of the fourth modified form of invariance. We consider the application of cross-correction in the automatic control system of a robot while controlling the motion along specified technological trajectories.

Sufficient conditions for dispersiveness of invariant control affine systems on the Heisenberg group

The notion of dispersiveness in control systems is characterized by the absence of recursive properties. It implies uncontrollability and Poisson instability. The present manuscript exhibits sufficient conditions for an invariant control affine system on the Heisenberg group to be dispersive. For a control affine system with pairwise commutative matrices, the condition for dispersiveness is the drift not depend linearly on the controlled matrices. For a general control affine system, with bounded control range, the condition is the drift not be an affine transformation of the controlled matrices. These results consequently yield necessary conditions for controllability.

Optimality of Norm-Optimal Iterative Learning Control Among Linear Time Invariant Iterative Learning Control Laws in Terms of Balancing Robustness and Performance

This paper presents a frequency domain analysis toward the robustness, convergence speed, and steady-state error for general linear time invariant (LTI) iterative learning control (ILC) for single-input-single-output (SISO) LTI systems and demonstrates the optimality of norm-optimal iterative learning control (NO-ILC) in terms of balancing the tradeoff between robustness, convergence speed, and steady-state error. The key part of designing LTI ILC updating laws is to choose the Q-filter and learning gain to achieve the desired robustness and performance, i.e., convergence speed and steady-state error. An analytical equation that characterizes these three terms for NO-ILC has been previously presented in the literature. For general LTI ILC updating laws, however, this relationship is still unknown. Adopting a frequency domain analysis approach, this paper characterizes this relationship for LTI ILC updating laws and, subsequently, demonstrates the optimality of NO-ILC in terms of balancing the tradeoff between robustness, convergence speed, and steady-state error.

Priority altitude PVTOL aircraft control via immersion and invariance

ABSTRACT In this work, the immersion and invariance (I&I) control technique is used in order to design a new controller that stabilises the PVTOL (planar vertical take-off and landing) aircraft system. The controller gives priority to the control of the aircraft's altitude before controlling the lateral displacement, fact from which interesting features as less thrust effort and less aggressive manoeuvres for roll moment are gained. The fundamental idea for the development of the proposed controller is based on the selection of the target dynamic system in accordance with the nature of the translational motion system to then stabilise the off-manifold dynamics by using the rotational motion system. It is proved that the proposed control scheme is globally asymptotically stable. Simulation results validate our proposal.

Viable immersion and invariance control for a class of nonlinear systems and its application to aero-engines

This paper presents a novel approach to stabilize a class of nonlinear systems with state constraints. The motivation behind this study is the need to develop a stabilizing state feedback controller that does not require the knowledge of Lyapunov function and can regulate the states to the equilibrium while meeting the constraints. By using an integration of two relatively new tools: immersion and invariance (I&I) theory and viability theory, a sufficient condition for stability and stabilizability of a general nonlinear affine system with state constraints is derived; Then, the related results are exploited to stabilize a class of nonlinear system in feedback form and with state constraints represented by inequalities and the viable I&I stabilizing state feedback controller is obtained constructively. Further, an application to a nonlinear aero-engine model with the temperature constraint is given to illustrate the applicability and the effectiveness of the proposed method. Finally, a comparative simulation is presented, highlighting the advantages of the viable I&I controller.

On Avoiding the Effect of Non-Minimum Phase Zeros Over the Signal-to-Noise Ratio Limitation

Fundamental limitations in networked control systems have been researched for the last years with many stability results, from channel transmission minimal rate based on information theory, to minimal signal-to-noise (SNR). For the latter, it has been confirmed early on that the usual culprits increase the minimal SNR for stability, such as unstable plant poles, non-minimum phase (NMP) zeros, time delay, together with new ones such as communication channel bandwidth and colored transmission noise. In this letter we specifically propose two approaches to completely avoid the effect of NMP zeros on the minimal SNR for stability in discrete-time. The first approach stems from the observation that the controller that achieves the minimal SNR for a minimum phase plant in discretetime, has all its zeros located outside the unit circle (NMP zeros). Such observation allow then to characterize this set of NMP zeros as candidate NMP zeros of alternative plant models with the same unstable poles, which in turn will not increase the minimal SNR for stability above the expression imposed only by the plant unstable poles. Our second approach extends the set of possible NMP zeros that do not increase the SNR limitation to any location, by proposing the synthesis of a two-degree of freedom linear time invariant controller solution that achieves the minimal SNR for stability imposed only by the plant unstable poles.

Current development on using Rotary Inverted Pendulum as a benchmark for testing linear and nonlinear control algorithms

Abstract Rotary Inverted Pendulum (RIP) is an under-actuated mechanical system which is inherently nonlinear and unstable. For decades, it has been widely used as an experimental setup to explain and test different kinds of control algorithms. The main control objectives of RIP are: Swing-up control, stabilization control, switching control and trajectory tracking control. All these control objectives are described in this study. State-of-the art works proposed for each control objective have also been reviewed. These comprise the linear, nonlinear time invariant, self-learning and adaptive nonlinear controllers. Moreover, different kinds of nonlinear dynamic models of the RIP together with the developed linear models in the literature have been analyzed. This is because most of the proposed controllers applied on RIP are found to be model dependent since they are mainly based on integral and/or invariant motion. Other types of RIP are also reported along with their advantages. Future research opportunities and challenges of the previous approaches in this area of research are presented. We believe that expert researchers can use this paper as starting point for further advancement while graduate scholars can use it as an initial point.