Inherent limitations of linear control, including PID, are Bode's phase-gain relationship and the waterbed-effect. Literature showed that reset control can overcome these limitations. The 'Constant in Gain, Lead in Phase' (CgLp) reset element was developed, which can be used in combination with a conventional PID approach. The benefit is that CgLp increases the broadband phase without altering the gain.

Recently, a continuous reset (CR) CgLp was proposed to eliminate the discontinuous output of the CgLp, which for example, excites resonances in mechanical structures. Unfortunately, CR CgLp is more sensitive to measurement noise than CgLp due to CR CgLp taking the derivative of its input, amplifying noise. This causes resets to occur more frequently. Literature has shown that these excessive resets can deteriorate the system performance.

The main contribution of this work is to improve the noise robustness of CR CgLp by implementing a filter on the measurement line to attenuate measurement noise. The attenuation of noise causes a reduction of excessive resets. Two filters are designed and critically compared. First, a low-pass filter succeeded by a lead element (LL). Second, an accelerometer-aided Kalman filter (aaKF). These were validated in practice on a precision-positioning stage.

Simulations have shown that the proposed designs improve performance of CR CgLp. The overshoot of CR CgLp could be reduced by 32% and IAE could be reduced by 53%. Besides this, CR CgLp with aaKF showed to outperform a PID controller with similar bandwidth and phase margin. The overshoot could be reduced by 46% and the IAE by 34%.

Test results on a physical setup have shown that the LL filter could improve the IAE of a step response by 13% compared to a CR CgLp without filter. Compared to PID control, the CR CgLp with LL filter has a superior transient response. ... Read more

Linear time-invariant controllers are undoubtedly the most popular type of regulators used in industrial applications, with the overwhelming majority of companies employing them. The reason is mainly given by their simple design methods. In particular, frequency domain predictive performance analysis and stability methods allow the use of loopshaping techniques. Nevertheless, inherent limitations affecting linear controllers pose constraints on their performance that can only be overcome through the adoption of nonlinear control schemes. Promising findings in recent literature suggest that with reset control, a nonlinear control technique, it is possible to overcome these limitations. At the same time, reset control could also potentially allow the use of straightforward design techniques, thus making it suitable for industrial applications. The main goal of this work is to bring together the different concepts scattered in literature, in order to initialize the construction of a general framework for the design and analysis of reset controllers suitable for an industrial setting. Tuning guidelines for different structures using two classes of reset controllers, the first order reset element and the proportional Clegg integrator, were presented. Two frequency domain methods, namely open-loop higher order sinusoidal input describing functions (HOSIDFs) and pseudosensitivities computed through analytically derived (approximate) closed-loop HOSIDFs, were effectively applied to predict steady-state performance. Stability was (when possible) analysed through the frequency domain Nyquist stability vector method, which could also be implemented in the design process. The frequency domain analysis methods allowed the use of loopshaping techniques similar to LTI control for the design of reset controllers. The controllers, implemented digitally on an ASM Pacific Technology wire bonding machine, show that through reset control a significant decrease in the root mean square of the settling error compared to an equivalent LTI controller could be achieved. The existing frequency domain analysis methods, its straightforward implementation and the increase in performance achieved in experiments validate the potential of reset control as a suitable alternative to LTI control for industry. Nevertheless, limitations in the explored reset control structures still exist and further work is required in order to achieve the full potential that this technique has to offer. ... Read more

The high-tech industry continuously pushes the boundaries of controller performance to achieve faster and more precise machines. Currently, linear control is the standard in the industry. These controllers suffer from the waterbed effect and Bode's phase/gain relation, which impose inherent limitations on the precision and robustness of the system. Reset control is a popular strategy to get around these limitations and improve performance. The damping in reset control systems is not only determined by the phase margin of the system but is also dependent on the exact controller element sequence. Currently, finding the optimal controller sequence is done through simulation of the step response. However, this fails to provide insight into the underlying cause of the additional damping achieved by specific controller configurations. This thesis proposes an analytical approach to analyze the damping of the transient response reset control systems. The analytical analysis provides a better understanding of sequence-dependent damping and assists in controller design. First, the analytical expressions of the step response and states of the system are derived, which are used to define the system's energy. The step response and energy equations are used to characterize the damping in a reset control system. To show the value of the proposed method, the damping in a reset control system is assessed as an illustrative example. It is found that when a lead is in front of a reset element, the reset controller can provide more damping because it reduces the oscillatory content in the step response. ... Read more

PID is a widely used linear controller in industry field. However, PID is not sufficient enough to meet the increasing requirements because of the functional restrictions, like bode’s phase gain relation and waterbed effect. Nonlinear controllers are then interested by researchers. Reset control, as one of the nonlinear controllers, has more simple structure and easier to implement thus make more and more people pay attention to it. Integrator in PID creates high gain at low frequencies which gives benefits for reference tracking ability of the system so for high-tech industrial field more integrators are needed. The problem for more integrators in the system will introduce more phase loss at bandwidth which leads instability into the system. Reset control thus can help with dealing the problem by overcoming the limitation of linear controller. In current literature, frequency domain performance of using reset control is mainly focused. The performance in time domain should be also investigated. In this presentation, the method of designing the reset control to improve transient response with multiple integrators will be shown. ... Read more

In the present world, a new development in technology every other year is anticipated. Robots and motion stages in the high-tech sector are required to work at higher speeds being stable, more precise, and power-efficient. Linear controllers have served well but are falling short to continue with the trend. Reset elements can enhance the performance of linear filters like PID by overcoming the bounds of linear control. As the name implies, reset elements reset their state/ states, thus induce nonlinearity. This nonlinearity provides reduced phase lag with similar magnitude behaviour as linear elements. With such behaviour or by adding linear filters with reset elements, both the steady-state and transient response can be improved. The tracking precision is not needed to be compromised over stability and noise rejection. The reset control has its downsides. The resetting action (nonlinearity) produce higher-order harmonics in the output. The number and instant of resets occurring are vital in determining the closed-loop sensitivities. Ideally, only two resets should occur in one period of the reference frequency. But due to higher-order harmonics, multiple resets (zero crossings) can occur, which makes analytical closed-loop estimation difficult. This thesis provides an amplitude threshold criteria on higher-order harmonics to avoid the multiple zero crossings. Controllers following such a threshold can help benefit the system from nonlinearity rather than being adversely affected by it. An example of a control scheme with reset and linear elements for a motion stage is presented that satisfies the amplitude threshold. No multiple resets in the input signal to the reset element for any reference frequency were confirmed. ... Read more