Emre Sariyildiz

Stability and Robustness of Disturbance-Observer-Based Motion Control Systems

This paper analyzes the robustness and stability of a disturbance observer (DOB) and a reaction torque observer (RTOB)-based robust motion control systems. Conventionally, a DOB is analyzed by using an ideal velocity measurement that is obtained without using a low-pass filter (LPF); however, it is impractical due to noise constraints. An LPF of velocity measurement changes the robustness of a DOB significantly and puts a new design constraint on the bandwidth of a DOB. An RTOB, which is used to estimate environmental impedance, is an application of a DOB. The stability of an RTOB-based robust force control system has not been reported yet since its oversimplified model is derived by assuming that an RTOB has a feedforward control structure. However, in reality, it has a feedback control structure; therefore, not only the performance but also the stability is affected by the design parameters of an RTOB. A new practical stability analysis method is proposed for an RTOB-based robust force control system. In addition to that, novel and practical design methods, which improve the robustness of a DOB and the stability and performance of an RTOB-based robust force control system, are proposed by using the new analysis methods. The validity of the proposals is verified by simulation and experimental results.

On the Explicit Robust Force Control via Disturbance Observer

This paper analyzes the robustness and stability of disturbance observer (DOb)-based explicit force control systems. Conventional analysis methods, which only consider ideal robustness, are impractical due to the design constraints of a DOb, e.g., bandwidth limitations. This paper shows that not only the stability but also the robustness of a DOb-based explicit force control system changes by environmental impedance variations. The robustness of a DOb-based explicit force control system is clarified by deriving new sensitivity functions. Implicit and explicit environmental impedance estimation methods are considered by analyzing the dynamics of a force sensor and a reaction force observer (RFOb), respectively. It is shown that the stability and performance of an explicit force control system can be improved by using an explicit environmental impedance estimation method, i.e., an RFOb, intrinsically. However, an RFOb is more sensitive than a force sensor to external disturbances, and the stability of the explicit force control system drastically changes by the design parameters of a DOb and an RFOb. Force-sensor- and RFOb-based explicit robust force control systems are compared in terms of stability, robustness, and performance in detail. The validity of the proposals is verified by simulation and experimental results.

A Guide to Design Disturbance Observer

The goal of this paper is to clarify the robustness and performance constraints in the design of control systems based on disturbance observer (DOB). Although the bandwidth constraints of a DOB have long been very well-known by experiences and observations, they have not been formulated and clearly reported yet. In this regard, the Bode and Poisson integral formulas are utilized in the robustness analysis so that the bandwidth constraints of a DOB are derived analytically. In this paper, it is shown that the bandwidth of a DOB has upper and lower bounds to obtain good robustness if the plant has non-minimum phase zero(s) and pole(s), respectively. Besides that the performance of a system can be improved by using a higher-order disturbance observer (HODOB); however, the robustness may deteriorate, and the bandwidth constraints become more severe. New analysis and design methods, which provide good robustness and predefined performance criteria, are proposed for the DOB based robust control systems. The validity of the proposals are verified by simulation results.

Analysis the robustness of control systems based on disturbance observer

Disturbance observer (DOB) estimates the system disturbances by using the inverse of the nominal plant model and a low pass filter (LPF). Although the LPF provides the properness in the inner-loop, it is the main design constraint of the control systems based on DOB. The bandwidth of the LPF is designed as high as possible so that the DOB can estimate the disturbances in a wider frequency range. However, its bandwidth is limited by noise and robustness of the system. The robustness limitation is directly related with the robustness analysis methods, and they significantly affect the performance of the DOB based control systems. In this paper, three different robustness analysis methods are implemented into the DOB based control systems, and the relation between the robustness of the system and bandwidth of DOB is clearly explained. The conservatism, which is the main drawback of the conventional analysis methods, on the bandwidth of DOB is removed by proposing a new real parametric uncertainty based analysis method. The proposed methods are compared in detail, and simulation results are given to show the validation.

An Adaptive Reaction Force Observer Design

In this paper, a new adaptive design method is proposed for reaction force observer (RFOB)-based robust force control systems. It is a well-known fact that an RFOB has several superiorities over a force sensor such as higher force control bandwidth, stability improvement, force-sensorless force control, and so on. However, there are insufficient analysis and design methods for an RFOB-based robust force control system; therefore, its stability and performance highly depend on designers own experiences. To overcome this issue, a new stability analysis and a novel adaptive design method are proposed for RFOB-based robust force control systems. In the proposed adaptive design method, the design parameters of the robust force control system, i.e., the bandwidths of disturbance observer (DOB) and RFOB, the nominal and identified inertias in the design of DOB and RFOB, respectively, and the force control gain, are adjusted automatically by using an adaptive control algorithm which is derived by estimating the plant parameters and environmental impedance. The proposed adaptive design method provides good stability and performance by considering the design constraints of a DOB. The validity of the proposals is verified by simulation and experimental results.

An Acceleration-Based Robust Motion Controller Design for a Novel Series Elastic Actuator

This paper proposes an acceleration-based robust controller for the motion control problem, i.e., position and force control problems, of a novel series elastic actuator (SEA). A variable stiffness SEA is designed by using soft and hard springs in series so as to relax the fundamental performance limitation of conventional SEAs. Although the proposed SEA intrinsically has several superiorities in force control, its motion control problem, especially position control problem, is harder than conventional stiff and SEAs due to its special mechanical structure. It is shown that the performance of the novel SEA is limited when conventional motion control methods are used. The performance of the steady-state response is significantly improved by using disturbance observer (DOb), i.e., improving the robustness; however, it degrades the transient response by increasing the vibration at tip point. The vibration of the novel SEA and external disturbances are suppressed by using resonance ratio control (RRC) and arm DOb, respectively. The proposed method can be used in the motion control problem of conventional SEAs as well. The intrinsically safe mechanical structure and high-performance motion control system provide several benefits in industrial applications, e.g., robots can perform dexterous and versatile industrial tasks alongside people in a factory setting. The experimental results show viability of the proposals.

A Comparative Study of Three Inverse Kinematic Methods of Serial Industrial Robot Manipulators in the Screw Theory Framework

In this paper, we compare three inverse kinematic formulation methods for the serial industrial robot manipulators. All formulation methods are based on screw theory. Screw theory is an effective way to establish a global description of rigid body and avoids singularities due to the use of the local coordinates. In these three formulation methods, the first one is based on quaternion algebra, the second one is based on dual-quaternions, and the last one that is called exponential mapping method is based on matrix algebra. Compared with the matrix algebra, quaternion algebra based solutions are more computationally efficient and they need less storage area. The method which is based on dual-quaternion gives the most compact and computationally efficient solution. Paden-Kahan sub-problems are used to derive inverse kinematic solutions. 6-DOF industrial robot manipulators forward and inverse kinematic equations are derived using these formulation methods. Simulation and experimental results are given.

Bandwidth constraints of disturbance observer in the presence of real parametric uncertainties

Abstract Control systems based on disturbance observer (DOB) require a low pass filter (LPF) to avoid the algebraic loop and improperness in the inner-loop. Bandwidth of the LPF of DOB is desired to be as high as possible to improve the performance of a system. Two main constraints, which are noise and robustness of a system, determine the bounds on the DOBs bandwidth. Although the bandwidth constraint due to noise, which causes an upper bound on the bandwidth of DOB, directly depends on the sampling rate and measurement plants and methodology, the constraint due to robustness is affected significantly by robustness analysis methods. Conventional robustness analysis methods limit the bandwidth of DOB unnecessarily due to conservatism. This paper proposes a new robust stability analysis tool for control systems based on DOB in the presence of real parametric uncertainties. The proposed method shows that there is only a lower bound on the bandwidth of DOB to obtain robust stability, and the stability margin of a system increases as the bandwidth of DOB is increased. Consequently, the robustness of a system improves as the bandwidth of DOB is increased in the presence of real parametric uncertainties.

Performance and robustness trade-off in disturbance observer design

In the conventional design of disturbance observer (DOB), a first order low pass filter (LPF) is used to prevent algebraic loop and satisfy causality in the inner-loop. Although a conventional DOB has a good robustness, its performance is limited by the dynamic characteristics of a first order LPF. A DOB that uses a higher order LPF is called as a higher order disturbance observer (HODOB) and can be used to improve performance of a system. However, improving performance may cause robustness problems. Therefore, there is a trade-off between robustness and performance of a DOB based robust control system, and it is directly related to order of the LPF of DOB. This paper analyzes robustness and performance of robust control systems based on DOB. The relation between performance and robustness is derived analytically, and a new design tool, which improves robustness and performance, is proposed for HODOB. A general second order plant model is analyzed, and simulation results are given to show the validity of the proposed method.

Solution of inverse kinematic problem for serial robot using dual quaterninons and plücker coordinates

In this paper we present a new formulation method to solve kinematic problem of serial robot manipulators. In this method our major aims are to formulize inverse kinematic problem in a compact closed form and to avoid singularity problem. This formulation is based on screw theory with dual - quaternion. Compared with other methods, screw theory methods just establish two coordinates, and its geometrical meaning is obvious. We used dual-quaternion in plücker coordinates as a screw operator for compactness. 6R-DOF industrial robot manipulators forward and inverse kinematic equations are derived using this new formulation and simulation results are given.