Chapter 8 establishes the relationship between the input and output power spectral densities of a linear system. Limitations on results are carefully detailed and the case of oscillator noise is considered. The theory is extended to multiple input-multiple output systems.

Linear System Theory

Solar power generation by PV (photovoltaic) technology: A review

Three decades have passed since milestone publications by several industrialists spawned a flurry of research and industrial / commercial activities on model predictive control (MPC). This article reviews major developments and achievements during the three decades and attempts to put a perspective on them. The first decade is characterized by the fast-growing industrial adoption of the technology, primarily in the refining and petrochemical sectors, which sparked much interest and also confusion among the academicians. The second decade saw a number of significant advances in understanding the MPC from a control theoretician’s viewpoint, which included state-space interpretations / formulations and stability proofs. These theoretical triumphs contributed to the makings of the second generation of commercial software, which was significantly enhanced in generality and rigor. The third decade’s main focus has been on the development of “fast MPC,” a term chosen to collectively describe the various efforts to bring orders-of-magnitude improvement in the efficiency of the on-line computation so that the technology can be applied to systems requiring very fast sampling rates. Throughout the three decades of the development, theory and practice supported each other quite effectively, a primary reason for the fast and steady rise of the technology.

Model predictive control: Review of the three decades of development

Standard model predictive control (MPC) yields an asymptotically stable steady-state solution using the following procedure. Given a dynamic model, a steady state of interest is selected, a stage cost is defined that measures deviation from this selected steady state, the controller cost function is a summation of this stage cost over a time horizon, and the optimal cost is shown to be a Lyapunov function for the closed-loop system. In this technical note, the stage cost is an arbitrary economic objective, which may not depend on a steady state, and the optimal cost is not a Lyapunov function for the closed-loop system. For a class of nonlinear systems and economic stage costs, this technical note constructs a suitable Lyapunov function, and the optimal steady-state solution of the economic stage cost is an asymptotically stable solution of the closed-loop system under economic MPC. Both finite and infinite horizons are treated. The class of nonlinear systems is defined by satisfaction of a strong duality property of the steady-state problem. This class includes linear systems with convex stage costs, generalizing previous stability results and providing a Lyapunov function for economic MPC or MPC with an unreachable setpoint and a linear model. A nonlinear chemical reactor example is provided illustrating these points.

A Lyapunov Function for Economic Optimizing Model Predictive Control

The purpose of this review is examination of the present scenario of electricity production and investigation of whether an electricity powered world is possible, indicating which primary energy forms should be preferably utilized. Currently, most of the primary energy used by mankind, including that employed to generate electricity, comes from fossil fuels, which need to be phased out because they bring about severe damage to climate, environment, and human health and, additionally, their stock will be largely depleted during the present century. All the energy technologies poised to replace those based on fossil fuels, namely nuclear and renewables (wind, hydro, concentrated solar power, photovoltaics, biomass, geothermal, tidal, wave) essentially produce electricity, and this suggests that we will progressively shift to an electricity-based economy over the course of the 21st century. The economic, technical, ethical and social issues entangled with nuclear technologies and the unexpectedly fast expansion of renewable energies (particularly wind and solar) point to an increasingly important role of the latter in electricity generation. The present one way utility-to-customer energy system, designed over one century ago, will need substantial reshaping to enable the build up of a smart grid capable of dealing with variable renewable supply and fluctuating end-user demand by exchange of information between customer and utility. To accomplish this result, effort in research and development of storage devices and facilities on the small (e.g., batteries, capacitors) and large (e.g., pumped hydro, compressed air storage, electrolytic hydrogen) scale is needed. In the medium and long term, the expansion of electricity production will also likely lead to progressive replacement of internal combustion engines with electric motors in the automotive sector, accompanied by a shift from individual to mass transportation systems. We have still a long way out of the fossil fuel era, but this challenge can be won only if carbon-free electricity largely replaces the direct combustion of irreplaceable and climate-altering fossil fuel resources.

Towards an electricity-powered world

This paper presents simulation and experimental results regarding a new class of wind energy generators, denoted as KiteGen, which employ power kites to capture high altitude wind power. A realistic kite model, which includes the kite aerodynamic characteristics and the effects of line weight and drag forces, is used to describe the system dynamics. Nonlinear model predictive control techniques, together with an efficient implementation based on set membership function approximation theory, are employed to maximize the energy obtained by KiteGen, while satisfying input and state constraints. Two different kinds of KiteGen are investigated through numerical simulations, the yo-yo configuration and the carousel configuration, respectively. For each configuration, a generator with the same kite and nominal wind characteristics is considered. A novel control strategy for the carousel configuration, with respect to previous works, is also introduced. The simulation results show that the power generation potentials of the yo-yo and carousel configurations are very similar. Thus, the choice between these two configurations for further development of a medium-to-large scale generator will be made on the basis of technical implementation problems and of other indexes like construction costs and generated power density with respect to land occupation. Experimental data, collected using the small-scale KiteGen prototype built at Politecnico di Torino, are compared to simulation results. The good matching between simulation and real measured data increases the confidence with the presented simulation results, which show that energy generation with controlled power kites can represent a quantum leap in wind power technology, promising to obtain renewable energy from a source largely available almost everywhere, with production costs lower than those of fossil sources.

High Altitude Wind Energy Generation Using Controlled Power Kites

The problem considered in this paper is the design and analysis of a control strategy, for semi-active suspensions in road vehicles, based on model-predictive control (MPC) techniques. The optimal control law we compute using predictive techniques, aims to optimize the suspension performances by minimizing a quadratic cost function, while ensuring that the magnitude of the forces generated by the control law satisfies the physical constraints of passive damping. The online computation difficulties related to the predictive-control law are overcome by means of a "fast" implementation of the MPC algorithm. A performance comparison with well-established semi-active control strategies, such as Sky-Hook control and clipped control is presented. The achievable performance improvements of the proposed design procedure over Sky-Hook and clipped control laws are shown by means of simulation results obtained using a nonlinear half car model which proved to give an accurate description of the overall vertical dynamics of a vehicle equipped with continuous damping suspension systems

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Semi-Active Suspension Control Using &#8220;Fast&#8221; Model-Predictive Techniques

The problem of vehicle yaw control is addressed in this paper using an active differential and yaw rate feedback. A reference generator, designed to improve vehicle handling, provides the desired yaw rate value to be achieved by the closed loop controller. The latter is designed using the second-order sliding mode (SOSM) methodology to guarantee robust stability in front of disturbances and model uncertainties, which are typical of the automotive context. A feedforward control contribution is also employed to enhance the transient system response. The control derivative is constructed as a discontinuous signal, attaining an SOSM on a suitably selected sliding manifold. Thus, the actual control input results in being continuous, as it is needed in the considered context. Simulations performed using a realistic nonlinear model of the considered vehicle show the effectiveness of the proposed approach.

Massimo Canale

Papers

High Altitude Wind Energy Generation Using Controlled Power Kites

Semi-Active Suspension Control Using “Fast” Model-Predictive Techniques

Vehicle Yaw Control via Second-Order Sliding-Mode Technique

Robust vehicle yaw control using an active differential and IMC techniques

KiteGen : A revolution in wind energy generation

Massimo Canale

Papers

High Altitude Wind Energy Generation Using Controlled Power Kites

Semi-Active Suspension Control Using &#8220;Fast&#8221; Model-Predictive Techniques

Vehicle Yaw Control via Second-Order Sliding-Mode Technique

Robust vehicle yaw control using an active differential and IMC techniques

KiteGen : A revolution in wind energy generation

Semi-Active Suspension Control Using “Fast” Model-Predictive Techniques