Controllability of linear systems on lie groups

A vector field on a connected Lie group is said to be linear if its flow is a one parameter group of automorphisms. A controlaffine system is linear if the drift is linear and the controlled vector fields right invariant. The controllability properties of such systems are studied, mainly in the case where the derivation of the group Lie algebra that can be associated to the linear vector field is inner. After some general considerations controllability properties on semi simple, nilpotent and compact Lie groups are stated. The paper ends by many examples.     

Controllability of control systems on complex simple lie groups and the topology of flag manifolds

Let S be a subsemigroup with nonempty interior of a connected complex simple Lie group G. It is proved that S = G if S contains a subgroup G(α) ≈ Sl (2, $ \mathbb{C} $ ) generated by the exp $ {{\mathfrak{g}}_{{\pm \alpha }}} $ , where $ {{\mathfrak{g}}_{\alpha }} $ is the root space of the root α. The proof uses the fact, proved before, that the invariant control set of S is contractible in some flag manifold if S is proper, and exploits the fact that several orbits of G(α) are 2-spheres not null homotopic. The result is applied to revisit a controllability theorem and get some improvements.     

Sub-Riemannian structures on 3D lie groups

We give a complete classification of left-invariant sub-Riemannian structures on three-dimensional Lie groups in terms of the basic differential invariants. As a consequence, we explicitly find a sub-Riemannian isometry between the nonisomorphic Lie groups SL(2) and A ⁺( mathbbR mathbb{R} ) × S ¹, where A ⁺( mathbbR mathbb{R} ) denotes the group of orientation preserving affine maps on the real line.     

On the existence of observable linear systems on Lie groups

A vector field on a Lie group is linear if its flow is a oneparameter group of automorphisms. A linear system is obtained by adding left invariant controlled vector fields. The observability of such a system, whenever the output function is a Lie group morphism, was studied by Ayala and Hacibekiroglu. Within this framework, it is shown that no observable systems exist on semisimple groups, and necessary conditions for the existence of such a system on a general Lie group are given. The case where the output morphism is replaced by the projection on a homogeneous space is briefly discussed.      

On local linearization of control systems

We consider the problem of topological linearization of smooth (C ^∞ or C ^ω) control systems, i.e., of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that the local topological linearization implies the local smooth linearization, at generic points. At arbitrary points, it implies the local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at “strongly” singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at “strongly” singular points is tantamount to solve an intriguing open question in differential topology.     

Effect of energy storage systems on automatic generation control of interconnected traditional and restructured energy systems

During major disturbances in electric power system (PS) penetrated with renewable energy sources, primary and supplementary automatic generation control (AGC) strategies usually show inefficiency in mitigating the frequency and power oscillations because of sluggish control action. The frequency and power deviations should be controlled to retain the generation‐demand balance, which reinforce the quality and stability of overall PS. The fast‐acting energy storage systems (ESSs) having very small time constants like capacitive energy storage (CES) and redox flow battery (RFB) are utilised in this study to improve these dynamic responses. To conduct the analysis, initially, a two‐area nonreheat thermal PS with extra generations from wind turbine system (WTS) and dish‐stirling solar thermal system (DSTS) is explored extensively, and then to validate the efficacy of the method, the approach is tested on two‐area nonreheat thermal system having governor deadband (GDB) nonlinearity, reheat thermal, and restructured multisource thermal gas systems. An imperialist competition algorithm (ICA) optimised fuzzy PID‐filter‐(1 + PI) controller named as FPIDF‐(1 + PI) is utilised as supplementary controller, and its performance with CES/CES‐RFB is compared with ICA‐optimised FPIDF with/without CES and existing optimal PI/PID/PIDF/FPID controller without CES. Investigation of dynamic responses for sudden variation in power demand unveils the superiority of the control approach compared with others regarding settling time, peak undershoot, and performance index. Analysing the impact of ESSs on the responses divulges that the amalgamation of CES‐RFB in PS imparts better system dynamics. The robustness analysis suggests that ICA‐optimised controller with ESSs performs excellently and robustly for ±25% variation in PS parameters, random load disturbances, and nonlinearities.     

On the existence of monodromy groups of fuchsian systems on Riemann's sphere with unipotent genrators

In this paper we consider the following problem: For what choice of the (p+1)-tuple of conjugacy classesC ₁,…,C _p+1 in GL(n,?),p≥2, do there exist irreducible (p+1)-tuples of matricesM _j ∈C _j such that the productM ₁,…,M _p+1 equals identity? We present the necessary and sufficient conditions for the existence of such tuples in the case whereM _j are unipotent.     

Hierarchical fuzzy control of low-energy building systems

A hierarchical fuzzy supervisory controller is described that is capable of optimizing the operation of a low-energy building, which uses solar energy to heat and cool its interior spaces. The highest level fuzzy rules choose the most appropriate set of lower level rules according to the weather and occupancy information; the second level fuzzy rules determine an optimal energy profile and the overall modes of operation of the heating, ventilating and air-conditioning system (HVAC); the third level fuzzy rules select the mode of operation of specific equipment, and assign schedules to the local controllers so that the optimal energy profile can be achieved in the most efficient way. Computer simulation is used to compare the hierarchical fuzzy control scheme with a supervisory control scheme based on expert rules. The performance is evaluated by comparing the energy consumption and thermal comfort.     

Realizable growth vectors of affine control systems

In this paper, the following problem is considered: for a given nondecreasing finite sequence of positive integers, determine if there exists an affine control system whose growth vector coincides with this sequence. The answer is “yes” if and only if the Taylor series of a certain function constructed via elements of the sequence has nonnegative coefficients. It turns out that this problem is closely connected with properties of “core Lie subalgebras” of affine control systems which are responsible for a homogeneous approximation. We give a representation of core Lie subalgebras as free Lie algebras and describe sets of all possible core Lie subalgebras for systems with a fixed growth vector.     

Optimal temperature control of solar heating systems

Temperature control systems based on solar and wind energy differ in two important ways from existing fossil fuel systems. One is that solar systems, at least active solar systems, all have some kind of energy storage, the other is that the source of energy in a solar and wind energy system is variable and uncontrollable. Because of these added complications and the high capital investment required for solar and wind energy systems, considerably more sophisticated techniques are required for the design of those systems. In this study, a new technique is applied to the optimal control problem of solar heating systems.     

Optimal temperature control of solar energy systems

In this paper the application of dynamic optimization techniques to the design of solar energy temperature control systems is reviewed. Emphasis is placed on the application of Pontryagin's Maximum Principle to solar control system design. Included in the review are topics in optimal control of special interest to solar systems, i.e. Pontryagin's Maximum Principle, linear-quadratic optimization, on-off/singular control, periodic optimization, stochastic and adaptive control, and sampled-data and microprocessor control.     

Automatic generation control for hydro systems

The authors present the decision of an automatic generation control (AGC) system implemented with digital computers that periodically sample tie-line real power flows, line frequency, and generator power outputs. These analog signals are measured at 2-5 intervals and combined with desired interchange to obtain the area control error (ACE). The ACE digital quantity is allocated to regulating hydro turbines and transmitted via telemetry to the remote terminal units (RTU). The RTUs convert the raise/lower megawatts (MW) into timed relay contact closures to the governor which result in wicket gate open/close movement to change the generator output power. The output power of each generator is monitored by the digital AGC, which closes a feedback loop around the governor-turbine-generator to assure that the desired power level is attained. The feedback loop design, which is essentially a sampled-data control, is described. Additional feedback loops due to the ACE and load regulation are also analyzed. A method for allocating water usage between reservoirs on a generator command-time basis is presented. The theoretical designs are verified by online measurements     

3820kW内燃机车的研制

介绍了3820kW客、货运内燃机车的设计思想、总体布置、主要技术特性、动力装置、结构特点等.3820kW机车采用了12V280ZJ型柴油机,该柴油机安装了电子喷射装置.     

New results on control of multibody systems which conserve angular momentum

A planar system of rigid bodies interconnected by one degree of freedom rotational joints is considered. This multibody system is referred to as a multilink, and the rigid bodies are referred to as links. The angular momentum of the multilink is conserved but is not necessarily zero. We show that if the number of links is at least four, then periodic joint motions can make the absolute orientation of a specified base link track exactly a specified function of time whose time derivative is periodic. This result on the use of periodic joint motions for orientation tracking extends previous work [15], [20], [22] on using periodic joint motions for rest-to-rest reorientation. It has interesting physical consequences. Specifically, in the case of non-zero angular momentum periodic joint motions can maintain the orientation of the base link constant. In the case of zero angular momentum periodic joint motions can change the orientation of the base link at a specified angular rate. We also demonstrate that if the multilink consists of at least three links, then for any value of the angular momentum joint motions can reorient the multilink arbitrarily over anarbitrary time interval. This result extends similar results in [15] for zero angular momentum and in [20] that apply for nonzero angular momentum but not for an arbitrary time interval. In terms of their control-theoretic aspects, the problems treated in the paper can be viewed as controllability problems for a class of nonlinear control system with time-dependent drift.     

基于模糊算法的压差变流量控制研究

采用模糊算法编制压差控制系统的内部算法,用模糊算法实现对空调水系统的智能控制,详细给出模糊控制系统的设计步骤,并通过对中央空调系统特性数据的监测,验证了该技术的可行性。     

高性能冷凝水回收控制系统的研究与设计

针对不同规模的冷凝水回收系统 ,研究开发了相应的高性能自动控制系统并对其作了详细介绍     

Dynamics and control of isolated wind-diesel power systems

In this paper a comparative dynamic stability study has been carried out for wind-diesel systems with multiplicity of generation. The mathematical model considered for dynamic stability evaluation is based on small signal analysis. The Lyapunov technique is used to evaluate the optimum setting of gain parameters and comparison is made with the values given in the literature. Additionally the diesel unit equipped with a supplementary proportional integral controller is also considered and its effect on the dynamic stability of the system is investigated. It is shown that the wind-diesel system with multiple wind generation has the minimum first swing of oscillations and also higher damping of subsequent swings for disturbances due to load or due to variations in input wind power. Finally, the dynamic responses of the different power systems considered with optimal gain setting are also presented.     

Optimization and control of autonomous renewable energy systems

Recently, there has been a growing interest in harnessing renewable energy resources particularly for electricity generation. One of the main concerns in the design of an electric power system that utilizes renewable energy sources, is the accurate selection of system components that can economically satisfy the load demand. This depends on the load that ought to be met, the capacity of renewable resources, the available space for wind machines and solar panels, and the capital and running costs of system components. Once size optimization is achieved, the autonomous system must be controlled in order to correcly match load requirements with instantaneous variation of input energy. In this paper, a new formulation for optimizing the design of an autonomous wind-solar-diesel-battery energy system is developed. This formultation employs linear programming techniques to minimize the average production cost of electricity while meeting the load requirements in a reliable manner. The computer program developed reads the necessary input data, formulates the optimization problem by computing the coefficients of the objective function and the constraints and provides the optimum wind, solar, diesel, and battery ratings. In order to study the effect of parameters predefined by the designer on the optimum design, several sensitivity analysis studies are performed, and the effects of the expected energy not served, the load level, the maximum available wind area, the maximum available solar area, and the diesel engines' lifetime are investigated. A controller the monitors the operation of the autonomous system is designed. The operation of this controller is based on three major policies; in the first, batteries operate before diesel engines and hence the storage system acts as a fuel saver, while in the second diesel engines are operated first so that the unmet energy is lower but the fuel cost is high. According to the third policy, the supply is made through diesel engines only. This is done for the purpose of making a performance comparison between the isolated diesel system and the hybrid renewable energy system. The proposed optimization and control techniques are tested on Lebanese data. Although three different control policies have been adopted in this work, the software is able to accommodate other policies.     

Operational optimization and real-time control of fuel-cell systems

Fuel cells is a rapidly evolving technology with applications in many industries including transportation, and both portable and stationary power generation. The viability, efficiency and robustness of fuel-cell systems depend strongly on optimization and control of their operation. This paper presents the development of an integrated optimization and control tool for Proton Exchange Membrane Fuel-Cell (PEMFC) systems. Using a detailed simulation model, a database is generated first, which contains steady-state values of the manipulated and controlled variables over the full operational range of the fuel-cell system. In a second step, the database is utilized for producing Radial Basis Function (RBF) neural network “meta-models”. In the third step, a Non-Linear Programming Problem (NLP) is formulated, that takes into account the constraints and limitations of the system and minimizes the consumption of hydrogen, for a given value of power demand. Based on the formulation and solution of the NLP problem, a look-up table is developed, containing the optimal values of the system variables for any possible value of power demand. In the last step, a Model Predictive Control (MPC) methodology is designed, for the optimal control of the system response to successive sep-point changes of power demand. The efficiency of the produced MPC system is illustrated through a number of simulations, which show that a successful dynamic closed-loop behaviour can be achieved, while at the same time the consumption of hydrogen is minimized.