Showing papers on "Describing function published in 1996"
Dissertation•
01 Jan 1996
TL;DR: In this article, a dynamic friction model is presented and investigated, which is suitable both for simulation purposes and control design, and a friction force observer is developed which enables model based friction compensation.
Abstract: Friction-related problems are frequently encountered in control systems. This thesis treats three aspects of such problems: modeling, analysis, and friction compensation. A new dynamic friction model is presented and investigated. The model is described by a first order nonlinear differential equation with a reasonable number of parameters, yet it captures most of the experimentally observed friction phenomena. The model is suitable both for simulation purposes and control design. Analysis of friction-generated limit cycles in control systems is the second topic of the thesis. A distinction is made between limit cycles with and without periods of sticking. Oscillations without sticking where the velocity is zero only for single time instants can be treated as oscillations in relay-feedback systems for which tools are available. These tools are in the thesis extended to oscillations with sticking where the velocity is kept at zero for a period of time by the friction. The new tools give a procedure for exact computation of shape and stability of limit cycles caused by friction. The procedure requires the solution of a nonlinear equation system and that the feasibility of the solution is checked. The method is applied to several examples and comparisons are made with describing function analysis. The thesis also treats friction compensation based on the new model. A friction force observer is developed which enables model based friction compensation. The observer can be combined with traditional linear compensators. Stability theorems are given which allows a wide range of controller designs. The compensation scheme is applied to an example where the performance is studied with respect to model errors and disturbances. The resulting control error is thoroughly investigated. It is described how a simple statistical analysis of the error can give information on the success of the friction compensation. Furthermore the error during zero velocity crossings provides information on how model parameters should be changed.
224 citations
TL;DR: An idealized Coulomb + static friction model, dimensional analysis and the study of all possible solutions of the equations of motion are used to achieve rigorous and general results for this nonlinear problem of friction and control.
114 citations
15 Sep 1996
TL;DR: In this paper, the exact analysis of limit cycles caused by friction is presented, where necessary conditions for limit cycle oscillations are given as well as conditions for local stability of the limit cycles.
Abstract: This paper presents techniques that admit an exact analysis of limit cycles caused by friction. Necessary conditions for limit cycle oscillations are given as well as conditions for local stability of the limit cycles. There are two types of limit cycles, one where motion sticks for a time interval and another where the velocity is zero only at single time instants. The results are applied to an example with a resonant servo. Comparisons with describing function analysis are also made.
69 citations
TL;DR: Henon's method locates the switching point to a high degree of accuracy in one integration step while eliminating the need for a specified tolerance.
Abstract: Results show the importance of accurately locating the switching point between linear subdomains when numerically integrating a piecewise linear system of equations Henon's method locates the switching point to a high degree of accuracy in one integration step while eliminating the need for a specified tolerance
56 citations
17 Jun 1996
TL;DR: A black box model is proposed to describe nonlinear devices in the frequency domain and allows a better description of hard nonlinearities than an approach based upon the Volterra theory.
Abstract: A black box model is proposed to describe nonlinear devices in the frequency domain. The approach is based upon the use of describing functions and allows a better description of hard nonlinearities than an approach based upon the Volterra theory. Simulations and experiments are described illustrating the mathematical theory.
30 citations
22 Apr 1996
TL;DR: The closed-loop system of a mass with nonlinear friction is found to be amenable to control without limit cycles and by decoupling the joints of the robot the authors find similar results within a good accuracy range.
Abstract: This paper investigates the control of robots with nonlinear friction and dynamic backlash in the joints. The study is based on the describing function (DF) of nonlinear systems. The controllers studied are the first order model and the second order model variable structure controllers (FOM-VSC and SOM-VSC). The authors start by studying nonlinear plants consisting of a mass subjected to Coulomb plus viscous friction or two masses subjected to dynamic backlash. The worst case for the limit cycle generation is found to be the closed-loop system having two masses with backlash. On the other hand, the closed-loop system of a mass with nonlinear friction is found to be amenable to control without limit cycles. By decoupling the joints of the robot the authors find similar results within a good accuracy range.
30 citations
TL;DR: In this paper, the problem of constrained variance design with minimizing LQG cost function via the method of covariance control incorporating the optimal estimation for nonlinear stochastic systems is addressed.
Abstract: This note addresses the problem of constrained variance design with minimizing LQG cost function via the method of covariance control incorporating the optimal estimation for nonlinear stochastic systems. The nonlinear stochastic systems are first linearized and then are examined by way of the technique of describing functions. Finally, an application of this approach to a position servomechanism is illustrated by a numerical example.
28 citations
TL;DR: In this article, the dependence of periodic orbits on the parameters of autonomous systems with piecewise linear character-istic functions has been analyzed for two and three dimensions, and a first harmonic bifurcation diagram associated with the periodic orbits of such systems is obtained for two-and three-dimensional systems.
Abstract: The describing function method (used normally as a first approximation to study the existence and the stability of periodic orbits) is used here to analyze the dependence of periodic orbits on the parameters of autonomous systems. The method can be applied to a large class of nonlinear systems but, for simplicity, attention here is paid to a class of single-input, single-output control systems with a piecewise linear character- istic function. A first approach to the bifurcation diagram associated with the periodic orbits of such systems, called a first harmonic bifurcation diagram' is obtained for two and three dimensions. This diagram in two dimensions describes all the qualitative behaviour of such systems. Although this is not the case in three dimensions, the information contained in the corresponding first harmonic bifurcation diagram is of great value. It shows much of the complexity of the periodic structure that can be found in such three-dimensional systems; in fact, part of the first harmonic b...
26 citations
TL;DR: In this article, sufficient conditions of existence and global asymptotic stability of a limit cycle induced by a relay with hysteresis feedback in a linear time-invariant stable system are derived.
25 citations
TL;DR: In this article, the authors derived closed-form formulae of advanced guidance laws for a linear, time-invariant, acceleration-constrained arbitrary-order missile and a randomly maneuvering target with noisy position measurements.
Abstract: Explicit, closed-form formulae of advanced guidance laws for a linear, time-invariant, acceleration-constrained arbitrary-order missile, and a linear, time-invariant, arbitrary-order, randomly maneuvering target with noisy position measurements are derived. Two approaches are presented. The first approach derives the optimal guidance law for a quadratic objective. The solution is the guidance law for deterministic system with limiting on the commanded acceleration applied on the estimated state. The limiting function in this case is the saturation function. The second approach derives a control law called the average input guidance law. This approach is based on the idea of applying the average of the input that would have been applied to the plant if the noises were known. The solution has similar structure. It is the guidance law for deterministic system with limiting on the commanded acceleration applied on the estimated state. The limiting function in this case is from the family of describing functions of the saturation function. The formulas of the different guidance laws are given in terms of the transfer function of the missile and acceleration constraint, the shaping filter of the maneuver of the target, responses to initial conditions, error variance matrix of the estimated state and weights in the criterion. It is demonstrated by simulations that although the optimal guidance law has improved performance in terms of the miss distance, the suboptimal average input guidance law consumes less energy.
19 citations
TL;DR: In this article, the authors investigate the control of systems with nonlinear friction and dynamic backlash and find that the worst case for the limit cycle generation is the closed-loop system having two masses with backlash.
01 Jan 1996
TL;DR: In this paper, a theory for nonlinear oscillations of a confined flame, burning in the wake of a bluff body flame holder, is developed, exploiting the fact that the main nonlinearity is in the heat release rate, which essentially "saturates".
Abstract: Self-excited oscillations of a confined flame, burning in the wake of a bluff body flame holder, are considered. These oscillations occur due to interaction between unsteady combustion and acoustic waves. According to linear theory, flow disturbances grow exponentially with time. A theory for nonlinear oscillations is developed, exploiting the fact that the main nonlinearity is in the heat release rate, which essentially 'saturates'. The amplitudes of the pressure fluctuations are sufficiently small that the acoustic waves remain linear. The time evolution of the oscillations is determined by numerical integration and inclusion of nonlinear effects is found to lead to limit cycles of finite amplitude. The predicted limit cycles are compared with results from experiments and from linear theory. The amplitudes and spectra of the limit cycle oscillations are in reasonable agreement with experiment. Linear theory is found to predict the frequency and mode shape of the nonlinear oscillations remarkably well. Moreover, we find that, for this type of nonlinearity, describing function analysis enables a good estimate of the limit cycle amplitude to be obtained from linear theory. Active control has been successfully applied to eliminate these oscillations. We demonstrate the same effect by adding a feedback control system to our nonlinear model. This theory is used to explain why any linear controller, capable of stabilising the linear flow disturbances, is also able to stabilise finite amplitude oscillations in the nonlinear limit cycles.
11 Dec 1996
TL;DR: A method by which all parameters of PID regulators are tuned independently without using much more knowledge about process dynamics is proposed, based on specified phase and amplitude margins (SPAM).
Abstract: In this paper, based on specified phase and amplitude margins (SPAM), a method for tuning of PID regulators is proposed, by which all parameters of PID regulators are tuned independently without using much more knowledge about process dynamics. Simulation results show that the SPAM method has excellent performance.
01 Jan 1996
TL;DR: A new software package developed for designing nonlinear controllers for nonlinear systems that incorporates several nonlinear controller design methods based on the sinusoidal-input describing function method.
Abstract: This paper describes a new software package developed for designing nonlinear controllers for nonlinear systems. The package has been developed in the MATLAB and SIMULINK environment. With a powerful graphical user interface, it incorporates several nonlinear controller design methods based on the sinusoidal-input describing function method. Users of this package can easily design and compare different controller algorithms so that they can implement appropriate nonlinear controllers to meet their needs.
TL;DR: In this article, a first harmonic approach was used to analyze the dependence of periodic orbits on the control parameters of planar linear systems with single saturated feedback, and it was shown that, if the open-loop system has at least one unstable eigenvalue, periodic orbits converge monotonically to an unstable equilibrium point as the control gains go to infinity.
Abstract: A first harmonic approach (describing function method) is used here to analyze the dependence of periodic orbits on the control parameters of planar linear systems with single saturated feedback. It is shown that, if the open-loop system has at least one unstable eigenvalue, periodic orbits converge monotonically to an unstable equilibrium point as the control gains go to infinity.
TL;DR: In this paper, a nonlinear control scheme for preventing the limit cycle due to the nonlinearity of the multi-step bang-bang actuator in mechanical position control systems is proposed.
TL;DR: In this article, robust control design techniques such as H∞ and μ have been extended to the nonlinear control design problems to incorporate the thruster nonlinear dynamics, which can lead to inaccuracy in ship positions and possible control loop instability.
08 Sep 1996
TL;DR: Simulation result has proved the feasibility and accuracy of the describing function technique in the analysis of fuzzy control systems.
Abstract: In this paper, the describing function of bi-dimensional multi-level relay equivalent model of two-input-single-output fuzzy controller is derived. Based on this function, we analyze the wriggling phenomenon of fuzzy control systems, and qualitatively investigate the effect of fuzzy controller scaling factors on the wriggling amplitude. Simulation result has proved the feasibility and accuracy of the describing function technique in the analysis of fuzzy control systems.
01 Oct 1996
TL;DR: This paper proposes a mathematical model termed Signal Space, which is similar to Steer's approach but better suited to implementation for harmonic balance and uses the Signal Space approach to get expressions for oscillator parameters such as oscillation frequency, stability condition, injection locking bandwidth etc.
Abstract: Harmonic balance is today the most useful approach for nonlinear microwave network analysis. Usually FFT is used to convert the nonlinear elements time waveforms into the frequency domain as part of the harmonic balance process. This approach is straight forward for a single frequency. excitation, but is quite complicated and time consuming for the multi-frequency excitation case. Steer [1] proposed the Generalized Power Series, which enables for a given nonlinearity a direct calculation of the currents spectrum given the voltages spectrum. In this paper we propose a mathematical model termed Signal Space, which is similar to Steer's approach but better suited to implementation for harmonic balance. In [2] we extracted the signal space and made an approximation between the harmonic currents subspaces to enable a treatment of high nonlinearity of elements. Under describing function criteria we use the Signal Space approach to get expressions for oscillator parameters such as oscillation frequency, stability condition, injection locking bandwidth etc. Our results are compatible with Kurakawa's expressions.
31 Mar 1996
TL;DR: Generation of altered nonlinear characteristic block using Matlab-Simulink is presented to help teaching and understanding the concept and applications of dual-input describing function.
Abstract: Generation of altered nonlinear characteristic block using Matlab-Simulink is presented. These blocks can be added to the block library and be used to replace the corresponding nonlinear element for applying dual-input describing function in simulation. This will help teaching and understanding the concept and applications of dual-input describing function. This is a way of incorporating computer aided control systems design into education, particularly in subject such as nonlinear control theory. Examples are given to show that software such as Matlab-Simulink can be very useful in teaching and studying.
15 Sep 1996
TL;DR: Experimental results show that the proposed nonlinear control scheme is effective in suppressing undesirable persistent switching, and the performance was robust to changes in the controller gain.
Abstract: A nonlinear control scheme for preventing limit cycle due to the nonlinearity of the multistep bang-bang actuator in a mechanical position control system is proposed. A linearized model, sinusoidal input describing function (SIDF), for a multistep bang-bang actuator is introduced to compensate the nonlinearities. Using the model, an H/sub /spl infin// robust controller is proposed using loop shaping techniques with normalized coprime factorization stabilization to address the robustness. The proposed controller needs a smaller deadband as a result of compensating the nonlinearity of the actuator. A single-axis servo system model is used to verify the proposed control scheme experimentally. Experimental results show that the controller is effective in suppressing undesirable persistent switching, and the performance was robust to changes in the controller gain.
31 Oct 1996
TL;DR: In this article, a nonlinear time-delay model for the cardiovascular system and its short-term control by the autonomic nervous system is presented, with few elements the system's complex behaviour is mimicked.
Abstract: A nonlinear time-delay model for the cardiovascular system and its short-term control by the autonomic nervous system is presented. With few elements the system's complex behaviour is mimicked. The limit cycle of the system is studied with the describing function method as a function of the model parameters. Simulation and preliminary analysis results are presented.
12 Aug 1996
TL;DR: In this paper, a method to analyse the synchronized microwave oscillators is first developed by use of Volterra Series expansion, and general expressions of calculating responses in harmonic loops are obtained.
Abstract: A method to analyse the synchronized microwave oscillators is first developed by use of Volterra Series expansion. The general expressions of calculating responses in harmonic loops are obtained. Some cases such as the frequency divider and doubler are discussed in details. The results show that this method is simpler and can get higher accuracy than the describing function and harmonic balance method, and that it is more efficient than the averaging method.
08 Jan 1996
TL;DR: In this paper, a new modeling for a typical hysteresis characteristic by affine dynamical systems is presented, which includes both simultaneously, simulation and control for industrial plants which contain it.
Abstract: This paper presents a new modeling for a typical hysteresis characteristic by affine dynamical systems. It is known that the traditional method of describing functions for it only includes stationary response and does not include the transient response. Since this new method includes both simultaneously, simulation and control for industrial plants which contain it may be done more accurately than before.
13 May 1996
TL;DR: The analysis of robots with dynamic phenomena at the joints such as friction, backlash and flexibility shows that the best case in terms of performance is the robot system with nonlinear friction, while the worst one is the manipulator system with backlash.
Abstract: This paper develops the analysis of robots with dynamic phenomena at the joints such as friction, backlash and flexibility. The study adopts the describing function (DF) calculation and a decoupling procedure. The DFs are evaluated by decoupling the link inertia and ignoring the centrifugal, Coriolis and gravitational effects. The controllers studied are the first order model and the second order model variable structure controllers (FOM-VSC and SOM-VSC). Results show that the best case in terms of performance is the robot system with nonlinear friction, while the worst one is the manipulator system with backlash.