Cerebellar Model Articulation Controller Controller Research Articles

Semi‐fuzzy CMAC and PD hybrid controller with compressed memory and semi‐regularisation for electric load simulator

Cerebellar model articulation controller (CMAC) and proportional derivative hybrid controller is widely used for torque control in electric load simulator. However, due to some uncertain factors and especially the strong external interference of the surplus torque, the control stability could not be guaranteed. Here, a novel semi-regularised semi-fuzzy CMAC is proposed to get an efficient control effect. This study expands the weight smoothing into a semi-regularisation algorithm, and proves the stability of the hybrid control system based on the stability of the torque motor. To save storage space and reduce computation, the memory space is compressed and a semi-fuzzy mapping rule is proposed to smooth the output of CMAC with a high calculation speed. Both of simulation and experiment results demonstrate that this novel controller could keep stable and reach a good loading accuracy.

An improved cerebellar model articulation controller based on the compound algorithms of credit assignment and optimized smoothness for a three-axis inertially stabilized platform

An improved cerebellar model articulation controller (CMAC) based on the compound algorithms of credit assignment (CA) and optimized smoothness (OS) is proposed to improve the control performances of a three-axis inertially stabilized platform (ISP). On the basis of both advantages of CA and OS algorithms, the improved CMAC neural network controller can deal with the disadvantages of conventional CMAC in learning interference and output fluctuation. As a result, the main dynamic performances of the ISP control system are systematically promoted. To verify the method, the simulations and experiments are carried out respectively, in which the LuGre friction model is introduced to represent the main disturbances. The results show that the CA&OS-CMAC controller can efficiently restrain the nonlinear disturbances and obviously improve the ISP's pointing precision and output smoothness. Compared with the conventional CMAC controller, the root-mean-square (RMS) errors of tracking the angular position under the static base swinging and dynamic base leveling conditions are reduced by 17.17% and 30.55%, respectively.

Simulation Research of Switching Power Supply Based on CMAC and PID Compound Control

As a high-performance switching power supply, DC power supply is widely used in the micro grid involving new energy generation. In this paper, for the strongly nonlinear BUCK circuit (switching power supply), the cerebellar model articulation controller (CMAC) and PID compound control algorithm is proposed to achieve nonlinear system control. By using MATLAB/Simulink simulation study, results show that the system has better steady-state and dynamic performance.

A CMAC-PD compound torque controller with fast learning capacity and improved output smoothness for electric load simulator

The compound architecture of CMAC (Cerebellar Model Articulation Controller) and PD (Proportional-Derivative) can effectively reduce the loading error and restrain the surplus torque of electric load simulators. But due to its generalization ability, the CMAC controller has an unsmooth output, which leads to the motor vibration even the divergence of control system. The unsmooth problem of CMAC is analyzed in this paper and a novel scalar cost function of CMAC is proposed, which consists of an error item and a weight smoothing item to guarantee fast learning capacity and improved output smoothness of CMAC. With the novel scalar cost function, a compound torque controller of PD and smooth CMAC is derived by using the gradient descent algorithm. Both the simulation and experimental results demonstrate that the novel CMAC-PD compound controller can effectively improve the output smoothness of the electric load simulator, eliminate the surplus torque and assure the stability of system as well.

Hierarchical fuzzy CMAC control for nonlinear systems

In this study, a novel indirect adaptive controller is introduced for a class of unknown nonlinear systems. The proposed method provides a simple control architecture that merges from the cerebellar model articulation controller (CMAC) network and hierarchical fuzzy logic; therefore, the complicated CMAC structure can be simplified. The overall adaptive scheme guarantees the uniform stability of the closed-loop system. A simulation is presented to demonstrate the performance of the proposed methodology.

Direct Adaptive Output Feedback CMAC Control with Unknown Control Gain for a Class of Nonlinear Systems

A direct adaptive output feedback CMAC (cerebellar model articulation controller) control based on only output measurements is proposed with unknown control gain function for a class of affine nonlinear systems. Therefore, it is needed to design a state observer to estimate unmeasured states of the systems. By using strictly positive-real Lyapunov theory, the stability of the closed-loop system can be guaranteed. Finally, simulation results for an inverted pendulum system show that the effect of the approximation error on the tracking error can be attenuated efficiently.

Design of a Hybrid Adaptive CMAC Tracking Control for a Class of Uncertain Chaotic Systems with only Output Measurement

This paper presents an observer-based hybrid adaptive cerebellar model articulation controller (CMAC) with a supervisory controller for uncertain chaotic systems, in which the hybrid adaptive control composed of a direct adaptive CMAC and an indirect adaptive CMAC control is performed as the sliding mode control (SMC). The total states of the chaotic system are not assumed to be available for measurement. A state observer is used to estimate unmeasured states of the systems. The supervised control is appended to assure that the hybrid adaptive CMAC controller achieve a stable closed-loop system through Lyapunov stability theory. Finally, simulation results show that the effect of the approximation error on the tracking error can be attenuated efficiently.

Application of CMAC-PID Controller Based FPGA in the Wastewater Treatment

PID controllers are widely used in the Wastewater treatment plants. However the existence of the control disturbance and measurement error may greatly reduce the controller's stabilization, and even lead the control to failure. In order to improve the performance capacity, a new compound control method based on the cerebellar model articulation controller (CMAC) is proposed. We adapt the traditional PID controller to realize the feedback control and CMAC controller to realize the feed forward control. For real-time control, Altera Nios II FPGA (Field Programmable Gate Array) is employed to construct a hardware-in-the-loop system through writing C and VHDL codes on this FPGA.The control results revealed the compound CMAC-PID controller had excellent control performance such as systemic stability, disturbance resistance, fast response rate and small overshoot. It can be concluded that the compound controller is robust, self adaptive and effective.

ADRC and CMAC combined optimization and control for a class of discrete-time uncertain chaotic systems

Immune dynamic particle swarm optimization (IDPSO) strategy integrated with active disturbance rejection control (ADRC) and cerebellar model articulation controller (CMAC) combined control is designed for uncertain nonlinear discrete-time chaotic systems. The ADRC-CMAC is comprised of a cerebellar model articulation controller (CMAC) and an ADRC controller. The ADRC controller is designed to guarantee the stability of the system and restrict the disturbance. The CMAC is used to guarantee the control precision and response speed. Immune binary-state particle swarm algorithm is used to tune online the parameters of the ADRC-CMAC. Simulation results of uncertain nonlinear discrete-time systems demonstrate that performance with favorable response speed and restrained disturbance can be achieved by using the proposed control system.

Self-Structured Organizing Single-Input CMAC Control for Robot Manipulator

This paper represents a self-structured organizing single-input control system based on differentiable cerebellar model articulation controller (CMAC) for an n-link robot manipulator to achieve the high-precision position tracking. In the proposed scheme, the single-input CMAC controller is solely used to control the plant, so the input space dimension of CMAC can be simplified and no conventional controller is needed. The structure of single-input CMAC will also be self-organized; that is, the layers of single-input CMAC will grow or prune systematically and their receptive functions can be automatically adjusted. The online tuning laws of single-input CMAC parameters are derived in gradient-descent learning method and the discrete-type Lyapunov function is applied to determine the learning rates of proposed control system so that the stability of the system can be guaranteed. The simulation results of robot manipulator are provided to verify the effectiveness of the proposed control methodology.

Self-Structured Organizing Single-Input CMAC Control for De-icing Robot Manipulator

This paper presents a self-structured organizing single-input control system based on differentiable cerebellar model articulation controller (CMAC) for an n-link robot manipulator to achieve the high-precision position tracking. In the proposed scheme, the single-input CMAC controller is solely used to control the plant, so the input space dimension of CMAC can be simplified and no conventional controller is needed. The structure of single-input CMAC will also be self-organized; that is, the layers of single-input CMAC will grow or prune systematically and their receptive functions can be automatically adjusted. The online tuning laws of single-input CMAC parameters are derived in gradient-descent learning method and the discrete-type Lyapunov function is applied to determine the learning rates of the proposed control system so that the stability of the system can be guaranteed. The simulation results of three-link De-icing robot manipulator are provided to verify the effectiveness of the proposed control methodology.

Standalone CMAC Control System With Online Learning Ability

A cerebellar model articulation controller (CMAC) control system, which contains only one single-input controller implemented by a differentiable CMAC, is proposed in this paper. In the proposed scheme, the CMAC controller is solely used to control the plant, and no conventional controller is needed. Without a preliminary offline learning, the single-input CMAC controller can provide the control effort to the plant at each online learning step. To train the differentiable CMAC online, the gradient descent algorithm is employed to derive the learning rules. The sensitivity of the plant, with respect to the input, is approximated by a simple formula so that the learning rules can be applied to unknown plants. Moreover, based on a discrete-type Lyapunov function, conditions on the learning rates guaranteeing the convergence of the output error are derived in this paper. Finally, simulations on controlling three different plants are given to demonstrate the effectiveness of the proposed controller.

Self-Organizing CMAC Control for a Class of MIMO Uncertain Nonlinear Systems

This paper presents a self-organizing control system based on cerebellar model articulation controller (CMAC) for a class of multiple-input-multiple-output (MIMO) uncertain nonlinear systems. The proposed control system merges a CMAC and sliding-mode control (SMC), so the input space dimension of CMAC can be simplified. The structure of CMAC will be self-organized; that is, the layers of CMAC will grow or prune systematically and their receptive functions can be automatically adjusted. The control system consists of a self-organizing CMAC (SOCM) and a robust controller. SOCM containing a CMAC uncertainty observer is used as the principal controller and the robust controller is designed to dispel the effect of approximation error. The gradient-descent method is used to online tune the parameters of CMAC and the Lyapunov function is applied to guarantee the stability of the system. A simulation study of inverted double pendulums system and an experimental result of linear ultrasonic motor motion control show that favorable tracking performance can be achieved by using the proposed control system.

Adaptive CMAC neural control of chaotic systems with a PI-type learning algorithm

The cerebellar model articulation controller (CMAC) has the advantages such as fast learning property, good generalization capability and information storing ability. Based on these advantages, this paper proposes an adaptive CMAC neural control (ACNC) system with a PI-type learning algorithm and applies it to control the chaotic systems. The ACNC system is composed of an adaptive CMAC and a compensation controller. Adaptive CMAC is used to mimic an ideal controller and the compensation controller is designed to dispel the approximation error between adaptive CMAC and ideal controller. Based on the Lyapunov stability theorems, the designed ACNC feedback control system is guaranteed to be uniformly ultimately bounded. Finally, the ACNC system is applied to control two chaotic systems, a Genesio chaotic system and a Duffing–Holmes chaotic system. Simulation results verify that the proposed ACNC system with a PI-type learning algorithm can achieve better control performance than other control methods.

Design of a hybrid adaptive CMAC with supervisory controller for a class of nonlinear system

This paper attempts to propose a hybrid adaptive cerebellar model articulation controller (CMAC) sliding mode control (SMC; called HAC-SMC) with a supervisory controller for a class of nonlinear system, in which the HAC composed of a direct adaptive CMAC and an indirect adaptive CMAC control is performed as the SMC. There are two methods to design the switching control law of SMC. One is the sign switching controller. The other is the CMAC switching controller. Besides, a supervisory controller is appended to the HAC-SMC to guarantee the states staying in the boundary layer. The adaptive laws of the control system are derived in the sense of Lyapunov theorem so that the asymptotic stability of the system could be guaranteed. Simulation results show that the proposed control system has satisfactory performance on the inverted pendulum system and the Chua's chaotic circuit.

Single-input CMAC control system

This paper attempts to propose a single-input cerebellar model articulation controller (CMAC) control system, which contains only one controller implemented by the CMAC. The single-input CMAC control system adopts two learning stages. An off-line learning stage is to enable the output behavior of the CMAC to approximate the control surface of a fuzzy PD-type controller. An on-line learning stage follows to improve the system stability by the modified learning rule. The linear interpolation scheme is also applied to the recall process at the on-line learning stage to ensure better accuracy of the CMAC output. Simulation results show that the single-input CMAC controller is superior to the fuzzy PD-type controller.

Adaptive fuzzy CMAC control for a class of nonlinear systems with smooth compensation

Adaptive fuzzy cerebellar model articulation controller (CMAC) schemes are proposed to solve the tracking problem for a class of nonlinear systems. The proposed method provides a simple control architecture that merges CMAC and fuzzy logic, so that the complicated structure and the input space dimension in CMAC can be simplified. Adaptive laws are developed to tune all of the control gains online, thereby accommodating the uncertainty of nonlinear systems without any learning phase. In particular, smooth compensation is adopted to overcome the chattering problem associated with conventional switching compensation. By Lyapunov stability analysis, it is guaranteed that all of the closed-loop signals are bounded and the tracking errors converge exponentially to a residual set whose size can be adjusted by changing the design parameters. Simulation results for its applications to three examples are presented to demonstrate the performance of the proposed methodology.

Mixed H2/H∞ PID tracking control design for uncertain spacecraft systems using a cerebellar model articulation controller

A mixed H2/H∞ tracking control design method for uncertain spacecraft systems with guaranteed control performance is examined. A mixed H2/H∞ controller incorporating a cerebellar model articulation controller (CMAC) learning method and sliding-mode control action is developed in uncertain spacecraft systems under plant uncertainties and external disturbances. The CMAC control system is used to adaptively estimate the non-linear uncertainties, yielding a controller that can tolerate a wider range of uncertainties. The sliding-mode control action is included to eliminate the effect of approximation error via CMAC control system approximation. The sufficient condition is developed for mixed H2/H∞ performance in terms of linear matrix inequality formulations. The proposed method is simple and the PID parameters can be obtained systematically. Simulation results indicate that the mixed H2/H∞ performance can be achieved using the proposed methods.

Missile Guidance Law Design Using Adaptive Cerebellar Model Articulation Controller

An adaptive cerebellar model articulation controller (CMAC) is proposed for command to line-of-sight (CLOS) missile guidance law design. In this design, the three-dimensional (3-D) CLOS guidance problem is formulated as a tracking problem of a time-varying nonlinear system. The adaptive CMAC control system is comprised of a CMAC and a compensation controller. The CMAC control is used to imitate a feedback linearization control law and the compensation controller is utilized to compensate the difference between the feedback linearization control law and the CMAC control. The online adaptive law is derived based on the Lyapunov stability theorem to learn the weights of receptive-field basis functions in CMAC control. In addition, in order to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. Then the adaptive CMAC control system is designed to achieve satisfactory tracking performance. Simulation results for different engagement scenarios illustrate the validity of the proposed adaptive CMAC-based guidance law.

Hydraulic actuator control with open-centre electrohydraulic valve using a cerebellar model articulation controller neural network algorithm

Real-time learning control of a hydraulic actuator is studied using a cerebellar model articulation controller (CMAC) neural network architecture. Experiments are conducted on a one-degree-of-freedom hydraulic cylinder. The main applications considered are the earth-moving equipment applications. The electrohydraulic valve used to control the flow in the hydraulic circuit is an open-centre non-pressure-compensated type of valve, the type used in most earth-moving vehicles. Large hysteresis and dead band are observed in the hydraulic system which result in a large delay and poor dynamic tracking performance. A comparison of the experimental results on the control of the hydraulic actuator for the CMAC controller and a conventional proportional-integral controller with a model-based feedforward valve transform is made.