What Kind Of Plant Is Better For Control?

Cybernetics is a science about the control and communication in animals and the machines.Digging up control principle and method from the social behavior of human beings is one of the most significant ways to develop the control theory and methodology.In this dissertation,a new problem of "what kind of plant is better for control" is proposed from the challenge of the engineering feasibility for the.system integrated design.A cybernetics conjecture is proposed that under the linear control strategies,the larger the degree of controllability(DOC)of a linear time-invariant plant is,the better for control the plant is.In order to verify this conjecture,a serious of investigations are implemented in both control theory and control engineering.The main contribution is as follows.1.The definition of "better plant for control" is abstracted via the observation of the relevant social activities,which means that under the same control strategy design approach,it gets better closed-loop control effect and achieves smaller gain.Furthermore,the concept called the controlity design index is proposed for the measure of "better plant for control".Based on the characteristic and engineering meaning of DOC,it is conjectured that the appropriately defined DOC can be regarded as a local controlity index.The schedule of the frame work for verifying the conjecture is presented.2.According to above schedule,some interesting control cases including the LQR redundancy control and MPPT control in wind turbine are investigated to verify the DOC conjecture.It reveals that for the cases discussed in the dissertation,the larger the DOC of the plant is,the better its closed-loop control effect is.Meanwhile,the feedback gain may be also not bigger.The detailed results include as follows.(1)The effects of distance-based DOC on the LQR performance indexes are discussed.First,from the perspective of the quadratic optimal performance index and controller gain,we discuss the effects of distance-based DOC in the redundant optimal control.For the systems with redundant inputs,a LQR controller is obtained,and the relationship between the distance to uncontrollability and the quadratic optimal performance index,and LQR controller gain are presented.These results demonstrate that the larger the distance to uncontrollability is,the smaller the quadratic optimal performance index is,and also the smaller the LQR controller gain is(i.e.,the systems is much better for control).Furthermore,the necessary and sufficient conditions are presented for two special types of linear multi-variable systems,under which,the distance to uncontrollability increases if and only if the solution of CARE decreases.Combining these results,it is demonstrated that the larger the distance to uncontrollability can lead to the better control performance.(2)The effects of energy-based DOC on the LQR performance indexes are discussed.Similarly,first,from the perspective of the quadratic optimal performance index and controller gain,we discuss the effects of energy-based DOC in the redundant infinite-time optimal control.For the systems with redundant inputs,a LQR controller is obtained,and the relationship between the distance to uncontrollability and quadratic optimal performance index,and LQR controller gain are achieved.These results demonstrate that the larger the energy-based DOC is,the smaller the quadratic optimal performance index is,and also the smaller the LQR controller gain is.Furthermore,the effects of energy-based DOC in the redundant finite-time optimal control are discussed.The necessary and sufficient conditions are presented for the systems,under which,the energy-based DOC increases if and only if the solution of CARE decreases.Combining these results,it is found that the larger the energy-based DOC can lead to the better control performance.(3)Based on the simplified aerodynamic and motion equations of wind turbines,a linear system model is derived for the maximum power point tracking(MPPT).With this model,the expressions of the controllability degree as a function of the aerodynamic/structural parameters of wind turbines are deduced.It is found that the two types of controllability degree both increase with the decrement of rotor inertia.Meanwhile,the variation of the controllability degree versus the performance of MPPT control is investigated by simulations.It is observed that when using the same MPPT control,the higher efficiency of wind energy capture can be achieved by the wind turbine with small rotor inertia and little optimum tip-speed ratio.This implies that the better control performance can be obtained by the wind turbine with the larger controllability degree.This study shows that it is feasible to consider the controllability degree as an indicator that reflects the impacts of structural parameters on the control performance.And,the controllability degree can be further applied to the design and optimization of the structural parameters with a view of control.(4)With the objective function defined as degree of controllability(DOC),a new integrated design method that is independent of specific control strategies,is developed to design and optimize structural parameters of the controlled plants.The proposed method is employed to optimize the structural parameters of a three-blade horizontal-axis wind turbine,by which the high efficiency of maximum power point tracking(MPPT)of the turbine can be more easily obtained.In order to verify the effectiveness of the proposed integrated design method,the designed turbine is tested by the commercial simulation software for wind turbines(Bladed)using the optimal torque control method and Matlab with the nonlinear static feedback control method utilized,respectively.It is observed from simulations that when using the identical MPPT control strategy,the wind turbine whose structural parameters are optimized for larger value of DOC can achieve higher MPPT performance and accordingly capture wind energy more efficiently.Furthermore,by comparison,energy-based DOC is more suitable for the design and optimization of the structural parameters of wind turbines.(5)In order to cope with the random fluctuation of wind speed for wind turbines,the concept of a kind of energy-based DOC for linear system with external disturbance is discussed.Two novel measures of energy-based DOC with consideration of the control energy for both disturbance-rejection and system stabilization are proposed.When they are applied to wind turbines,the simulation results demonstrate that the better control performance can be obtained by the wind turbine with the larger energy-based DOC.Furthermore,by comparison,since the new measures include the two parts of control energy and are independent on the initial condition,they can be suitable for the design and optimization of the structural parameters of more controlled plants.The above results imply that for the linear time-invariant plants with the linear controller,the conjecture that the system with larger DOC of a plant is,the better for control the plant is,maybe holds in a great extent.It paves a solid way for the further studies in applying the DOC to the optimization of the structural parameters of the controlled plants.