This paper reports a simple method to generate a gait tragectory of a biped walking system based on a compass type biped model. The method relies on the symmetric characteristics in the dynamics of the model. The method will be introduced through a brief discussion on the dynamical property of the model.
In this paper, we give a kinematic model of a hyper-flexible manipulator which has the mechanical structure like a string. The modeling technique of a rigid-link manipulator and classical theory of curve geometry help us to derive a simple and physically meaningful model of a string-like manipulator.
In this paper, we discuss a simple controller for two link flexible arms based on a distributed parameter model. At first, using Lyapunov method, we derive a PDS feedback controller that the closed-loop system becomes Lyapunov stable. In neighorhood of a desired configuration of the arm, we prove that the PDS controller can ensure the asymptotic stability of the closed-loop system. As the controller presented in this paper is derived based on the original distributed parameter system, we can avoid the drawbacks resulting from finite dimensional approximation.
We propose a method of collision-free trajectory optimization for a 2-link flexible robot arm by using the optimal control theory. This method has following advantages: First, we can adopt some performance index concerning the driving energy, the arm vibration and so on; Second, we can restrict the state variable at the final time so that the vibration of the link stops at that time. We can get the optimal input signal as time function. This collision-free problem is the nonlinear optimal control problem with state variable inequality constraints. We apply a penalty function and get an ordinary two-point-boundary value problem. The simulation results show the optimal collision-free trajectory.
Snake like robot has a lot of attention for its various tasks such as grasping, locomotion, manipulation, and so on. Recent researches on locomotion control mainly deals with motion on 2D plane even if 3D model is used. This paper is focused on kinematic motion of 3D snake on a smooth surface. We assume that every part of the body contact with the surface and there is no side slip. Since the shape of the body depends on that of surface, we first analyze kinematic motion of 2D continuum. And then we derive the basic kinematic strategy for 3D model based on approximation of continuum.
In this paper, we develop a new framework for partial stochastic realization in a finite dimensional space where geometric operations are performed so that the positive realness of covariance functions in a finite interval is guaranteed. To this end, we present a deterministic interpretation on the partial stochastic realization. We give necessary and sufficient conditions for positive realness based on Riccati equations, and derive a solution of the partial stochastic realization problem.
Probabilistic approach to set membership identification is presented. Especially, the size and convergence properties of the membership set are investigated in the presence of not only bounded disturbance but also bounded parameter uncertainty. The bounds of the disturbance and the parameter uncertainty are assumed to be tight in a probabilistic sense. Then, the following results are obtained. (i) The size of the membership set converges to zero with probability one as the number of samples tends to infinity. This means that the membership set converges to the true but unknown parameter. (ii) For a given number of samples, the size of the membership set can be estimated with a probabilistic confidence. This result also clarifies the necessary number of samples such that the distance between the true parameter and any parameter in the membership set is less than a specified upper bound with a specified probability.
For digital control of mechanical systems, pulse encoders, linear scales, or photonic devices with A/D converters are commonly used to measure displacements. Also, D/A converters are employed to generate control forces computed by control algorithms. That is, the measured and control signals are digital, while inputs and outputs of controlled systems are analog variables. Since digital variables are of finite wordlengths, they contain quantization errors. In precision control, such errors may deteriorate control accuracies significantly. To overcome this problem, the present paper proposes to estimate the quantization errors from the quantized input and output signals in real time, and improve the output measurements by adding the estimated quantization errors. For this purpose, we first consider identification of systems based on data of finite wordlengths, where we estimate system parameters and quantization errors simultaneously by the least square method. By simulation, it is illustrated that accuracy better than the resolution of quantization can be achieved.
Local modeling is a useful approach for nonlinear system identification. Local models are constructed on several operating regimes, and the global system model is constructed by combining these local models with a suitable interpolation function. The models are then dependent on the choice of operating regimes. Here, we propose an algorithm to select suitable operating regimes automatically. It is based on Kullback’s discrimination information (KDI) and Akaike’s information criterion (AIC). Numerical simulation results illustrate the applicability of the proposed idea.
The problem of identification of dynamic systems operating under feedback control is considered. The bias eliminated least squares (BELS) method has also been developed for identification under closed-loop system. In this paper, the equivalence of BELS method and weighted instrumental variables (WIV) method under an appropriate choice of weighting matrix for WIV method is verified through theoretical analysis and simulation studies.
Input constraints exist in almost all real-world systems. The constraints may cause unexpected and undesirable phenomena such as performance degradation or instability. Although many procedure have been suggested for this problem, precise analysis of the systems with input constraints is said to be difficult. In this paper, the systems with input constraints are equivalently represented as piecewise affine systems, and we suggest a method for analyzing L2 gain and L2 incremental gain of the systems by adopting piecewise quadratic storage functions.
This paper considers an off-line reference management technique for discrete linear systems with time-varying uncertainties and with state and control constraints. There are two features of the proposed method. One is that applying a concept of a maximal output admissible set realizes the constraint fulfillment, which is the original goal of reference governors. The other is a tracking performance improvement as well as the constraint fulfillment. The effectiveness of the proposed method is illustrated by numerical example.
This paper proposes analysis and synthesis method of state space region with guaranteed L2 performance for control systems with direct-feedthrough matrix from saturating output to saturating input. We derive new condition of the L2 performance analysis from extension of Park’s stability analysis condition. When the direct-feedthrough matrix is scalar, quasi-anti-windup control system can be synthesized by using plain search based on our analysis condition. The attained control performance result is better than that by uisng the linear analysis that considers the behavior of the states in the linear (non-saturated) region only. The validity of this analysis and synthesis method is examined by numerical examples.
In this paper, we consider scheduling control of a linear system, where control inputs have saturation nonlinearity and state variables are constrained by physical restrictions. Usually, these nonlinearity and constraints are negatively avoided by making a control-gain small in control design. By introducing a scheduling control, we show that those nonlinearity and constraints can be positively avoided, that is, we can attain better control performances. The effectiveness of the proposing control is evaluated by experiments on a magnetic levitation system.
This paper considers an anti-windup compensation in control systems with saturation nonlinearity. The performance specification is based on the output deviation between an idealized system without input saturation and the anti-windup compensated system with input saturation. The proposed design procedure for anti-windup compensators is written in terms of linear matrix inequalities. A numerical design example is provided to illustrate the properties of the resulting closed-loop system.
In this paper, we discuss a limiting property of stable inversion for sampled-data systems. It was demonstrated that solution for sampled-data stable inversion can approximate the one for continuous-time stable inversion by only shrinking the sampling period for a class of linear systems. This guarantees that we can achieve exact output tracking via iterative learning control based on sampled data of output error signal.
FIR (Finite Impulse Response) filters are preparred to IIR (Imfinite Impulse Response) filters, because of their stabilities or realizations and so on. This paper supposes a new method to approximate an IIR filter by an FIR filter, which directly deal with optimal approximation with respect to the H∞ error norm. There is an elegant way called Nehari Shuffle which makes use of what is called Nehari extention theorem, but it dosen’t necessarily give an optimal approximation with respect to H∞ norm. In cotrast to it, we regard this optimal approximated problem as the minimization problem of the error between a IIR filter and a FIR filter with respect to H∞ norm, and show this problem reduces an LMI (Linear Matrix Inequality). We also introduce this problem depends on the choice of weighting functions. Finally, we show them with numerical examples.
In digital control, we have to quantize the signal. Since quantizing is a nonlinear operation, its analysis is difficult. Often we linearize the quantizer by an additive noise model. We study a stability and performance analysis of sampled-data systems with quatization which is designed by using the linearization. We show that if the linear model is stable, the states of the real system are bounded, and if the linear model has small L2 gain, the real system has small power gain. We apply the results to the design for a quantizer which is called differential pulse code modulation (DPCM)..
In this paper we investigate the best achievable H2 tracking performance for a step reference signal using sampled-data control systems. We derive an analytical closed form expression for the optimal tracking performance, which consists of the following three parts: the nonminimum phase zeros of the continuous-time plant, the non-minimum phase zeros of the discretized plant/antialiasing filter due to sampling, and the aliasing effects of sideband harmonics.
This paper presents an integrated design of a sampled and continuous robust proper compensators using the forward difference approximation. Continuous type and sampled type of robust proper compensators are designed to construct an inverse system at worst cases of the controlled object variations.
Realizing few multiobjective control of conservativeness is examined by making the solution of simultaneous LMIs (Linear Matrix Inequalities) non-common in recent years. This research shows that the solution of simultaneous LMIs about various control problems can be made non-common by harnessing the representation capability of descriptor representations. Moreover, the validity is verified by applying the proposed method to an inverted pendulum.
This paper presents a stability criterion for 2-D discrete systems. The proposed stability criterion is based on LMI (linear matrix inequality), and hence, it is computationally tractable. Furthermore, it is less conservative than the existing LMI-based conditions. In deriving the stability criteriton, finite-order Fourier series approximation of the solution for frequency-dependent LMI plays a key role. A numerical example is also studied.
This paper presents methods for computing the H∞ and H2 norms of 2-D discrete systems. Both methods are based on LMI (Linear Matrix Inequalities), and hence, they are computationally tractable. In deriving these methods, finite-order Fourier series approximation of the solution for frequency-dependent LMI plays a key role. Numerical examples are also studied.
In this paper, we consider on the freedom of the parameters of new state feedback gain synthesis methods based on non-common Lyapunov matrices and descriptor form. The condition that authors derived with descriptor form has the design variables α and β. These parameters do not appear in the equivalent former methods proposed by Ebihara et al. and Shimomura et al., independently. They seem to modify conservativeness gap between analysis and synthesis. However, we show that the freedom is marginal and is not essential and these parameters do not modify the conservativeness. Then we give an interpretation of these parameters and verify it by numerical examples.
The guaranteed cost control problem of the decentralized robust control for nonlinear large-scale systems with both norm-bounded time-varying parameter uncertainties and time delays is considered. Sufficient condition for the existence of guaranteed cost controllers is given in terms of the linear matrix inequality (LMI). It is shown that the decentralized local state feedback controllers can be obtained by solving the LMI.
This paper is devoted to a novel iterative learning control method for physical systems. It is shown that the variational systems of a class of Hamiltonian systems have self-adjoint state-space realizations, that is, the variational system and its adjoint have the same state-space realizations. This implies that the input-output mapping of the adjoint of the variational system of a given Hamiltonian system can be calculated by only using the input-output mapping of the original system. This property is applied to adjoint based iterative learning control with optimal control type cost functions. Furthermore, experiments of a robot manipulator demonstrates the effectiveness of the proposed method.
In this paper, a new self-tuning pole-assignment control scheme is proposed for stochastic systems with unknown deterministic disturbances, whose control law is derived based on minimizing a quadratic cost function. Furthermore, some user-specified polynomials are designed based on the pole-assignment scheme. This scheme has internal models corresponding to deterministic disturbances, and the internal models are adjusted in an on-line manner. The effectiveness of the newly proposed control scheme is evaluated on a simulation example.
This paper considers on an application of adaptive PI control method to SICE benchmark problem. Using an adaptive PI control method, the closed-loop controlled system is very simple structure compared with the conventional adaptive control. Besides, this control method is similar to the conventional PI control method. We also use the parallel feedforward compensator to the plant because the adaptive PI control method can only be applied to the plant which relative degree is one. Numerical simulations are shown to illustrate the effectiveness of our method.
This paper discusses the problem about tracking and disturbance rejection for some class of nonlinear system with arbitrary relative degree. In order to overcome these problems, plug-in control structure is useful. Our study in this paper reveals such plug-in controller can be designed by solving error feedback regulation problem and by using backstepping technique.
This paper describes a Generalized Minimum Variance Control (GMVC) sterategy for Time Varying Systems (TVS). GMVC is one of predict control methods, which are effective to Time Delay system. In TVS, polynomials of model are noncommutativity. Then, the cost function can not be optimized with accuracy because noncommutative noise term remains. This paper applies a pseudocommutativity to improve the noncommutativity in TVS. The proposed pseudocommutativity has a durability against the effect of time shift of time varying multiplications. The GMVC sterategy holds a simple structure.
In this paper, we discuss the estimation problem of the order of continuous linear time invariant systems from a geometric point of view. We propose the estimation technique based on the Fourier series and the curvature of curves, then demonstrate its efficacy in experiment for DC motor.
This paper proposes a method to solve Lyapunov or Hamilton-Jacobi partial inequalities for nonlinear systems. The method utilizes sum of squares, which gives a sufficient existence condition of a nonnegative function in the linear sum of squared functional systems. The condition is characterized in terms of linear matrix inequality.
This paper gives some stability conditions of discrite-time systems with a time-varying delay. The time-varying delay has a discrite conver belt model. We discuss about stability using three Lyapunov functions, that is, i) normal qudratic form, ii) quadratic form including past state, iii) quadratic form for an expanded system. The last approach is based on quadratic stability method for discrite time-varying systems.
This report considers a computation method for solving the problem of H∞ norm assignment by state feedback in linear time invariant system. We have already proposed an assignment method of H∞ norm by state feedback for multi input linear time invariant systems in which external input matrix is equal to control input matrix. and for single input linear time invariant systems in which external input matrix is not always equal to control input matrix. In this report we treat the multi input linear time invariant systems in which external input matrix is not always equal to control input matrix. H∞ norm assignment by state feedback is considered as the inverse of H∞ norm computation. If it is given state matrix, input matrix, output matrix and direct transfer matrix, then H∞ norm can be computed. Inversely, if it is given input matrix, output matrix, direct transfer matrix, and H∞ norm, then state feedback gain which gives state matrix for closed loop system having assigned H∞ norm can be computed recursively. Finally, state feedback gain which assign H∞ norm for the numerical example of the system are computed and validated.
For general mechanical systems with collocated sensors and actuators, it is known effective to use a symmetric controller. The symmetric controller guarantees robust stability of the closed loop system by virtue of its structure having positive definite or positive semi definite symmetric coefficient matrices. This paper proposes an optimal design method of the symmetric controller in the sense of H∞ norm. In the synthesis, the optimal controller is obtained by solving the linear matrix inequality reduced from the bounded real lemma. This method has advantage over other robust control technique in its structural simplicity. Finally, we apply the design method to the actual large space structure model.
This paper describes design of a flight control system for the hypersonic flight experiment vehicle (HYFLEX) and evaluation of robustness against variations of command inputs. A nonlinear simulation model is made using the data obtained from wind tunnel experiment, etc. Linear models are computed from the nonlinear model at every second of the flight, assuming that the flight is quasi-equilibrium flight. A nominal model for controller design is made from the linear models. The type-1 LQ servo controller is employed for the controller. Six sets of control gains are computed and scheduled as a function of flight time. The effectiveness and robustness are examined through computer simulation.
A preliminary study on the guidance and flight control system for a test model of the stratospheric airship is conducted, and the result is explained. The test model is intended to stay at the altitude of 4000m, within 1km distance from the indicated point. The longitudinal and lateral flight control systems are designed, and the performance is verified by simulations, which generally show good performances. The design method of the control systems are explained, and step responces and some simulation results for the position keeping are shown.
Spaceborne GPS navigation technology has been investigated very actively since it effectively enhances the autonomy of space vehicles on Low Earth Orbit (LEO). GPS attitude determination system (ADS) uses carrier phase measurements observed at multiple antennas, and it contributes especially to simplification of the GN & C sub-system. The current topics in GPS attitude determination are directed to increase reliability and accuracy of the GPS ADS as well as to reduce its computational load. In this paper, the algorithms derived from integer search technique and least squares approach are described, and the accuracy and computational load are evaluated by the analysis of the aircraft flight test data taken in November 2001.
Most automatic transmission systems are equipped with a lock-up clutch to improve efficiency. However, the use of lock-up in the low-speed range was greatly influenced by unmodeled dynamics and disturbances. In order to suppress such uncertainties, slip control of the lock-up clutch is needed. This paper first explains the modeling of the lock-up clutch as a low-order system within the range of slip control. It then describes a slip control system designed by using a robust control method, which takes into account variations in dynamic characteristics of components. Finally, the results of driving tests are presented to demonstrate the effectiveness of the slip control system.
In this paper, a computational method for a constant output feedback gain that locally minimizes a linear quadratic performance index is proposed. First, a state feedback gain which is close to a solution is searched for by minimizing a modified LQ performance index starting from any stabilizing state feedback gain. Then, the solution is obtained from the state feedback gain by using second order polynomial approximation of the solution that satisfies a necessary condition for optimality.
This paper concerns the output feedback synthesis problem of the receding horizon H∞ control. First, we consider terminal inequality conditions, which play an important role to guarantee exponential stability of the closed loop system, and proposed a extended terminal inequality condition. Next, we discuss the receding horizon H∞ control using the extended terminal inequality conditions and derive that exponential stability of the closed loop system can be guaranteed. Further, it is shown that the stabilizing receding horizon H∞ control considered in this paper guarantees the induced norm bound condition. Finally, a example illustrates an application of the proposed technique.
Many control system design problems are cast as an infinite-dimensional linear programming, where one of the main focus is how to approximate it by a finite-dimensional problem. This paper discusses a finite-dimensional approximation of the primal-dual approach. Unlike the finite-dimensional counterpart, the optimal costs for the primal and dual problems may have duality gap. This paper provides a way to approximate the dual of the continuous-time reference management problem, and show that the gap-free approximation is possible.
The PID control is used as a basic control technology in the industries today. However, there are limitations on control performances for some controlled process, such as long dead time processes and unstable processes. In order to improve the control performances of PID control systems, we proposed a new Model Driven PID control system, which is combined with the following control scheme; the PD feedback, the Internal Model Control and the set-point filter. In this paper, the Model Driven PID control system, the design method and the stability are described.
Parameters of physical systems are uncertain and are accompanied by nonlinearity. The state space equation and the characteristic polynomial of control systems should, therefore, be expressed by an interval set of parameters. This paper examines the stability margin of that type of control system, based on the existing area of characteristic roots (i.e., eigenvalues). Particularly, in this paper, a sufficient condition for the characteristic roots that exist in the sectorial area on the left half s-plane is given by using the result of our previous paper.
Chaotic behaviors are observed in stoker-type incineration plants when conventional control strategies with relay feedback are applied. In this paper, the chaotic phenomena are analyzed using the mathematical models of the plant and feeder which are obtained from the identification of plant data. After that a periodic control, which is proposed by the author and does not generate the chaotic phenomena, is compared with the conventional control.
In this paper, we propose a new modeling method of stoker-type incinerator for refuse incineration plants in order to analyze dynamic behavior of refuse combustion process and refuse movements. The refuse incinerator model is represented by a mathematical model taking into account various kinds of refuse drying, pyrolysis, gasification and combustion process, refuse moving process, gas combustion process, etc., can simulate the dynamic behavior of refuse combustion process and refuse movements at the change of running commands, e.g. refuse inputs, combustion air, and stoker movements.
In film processes, many pairs of actuators and scanned data are utilized to control film properties. Multi-loop controllers are applied to profile control because they can be tuned without the precise process models. The selection of the measurement location corresponding to an actuator is not easy because the film is stretched and its edges are cut off. It is illustrated that inadequate pairing causes deterioration of the multi-loop controller performance. A method based on wavelet analysis is proposed to detect inadequate pairing and to prevent the deterioration of the controller performance.
A modeling error has a time-variant factor like the influence of roll wear and a factor by rolling conditions like the size characteristic. If both factors are not distinguished when learning the modeling errors and adaptation of a setup control for the following rolling piece are executed, the appropriate compensation is not obtained, then accuracy gets wores. We propose the synchronous learning algorithm for both factors with learning gain scheduling to improve learning efficiency. Finally, the application simulation using hot-rolled width data shows that standard deviation for modeling error can be reduced 20% compared with the conventional method.
This paper presents a method of PI control parameter tuning based on the estimated maximum step disturbance and the allowable peak value of the controlled variable and shows its effectiveness and limitation by simulation studies. This method is very useful to tune control parameters for chemical processes where limitations on loss prevention and quality control are represented by peak values of controlled variables.