33 research outputs found

    Vibration control for an experimental off-road vehicle using magnetorheological dampers

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    The paper presents research studies in the field of semiactive vibration control of an experimental off-road vehicle which is equipped with suspension magnetorheological (MR) dampers. Accelerometers and vehicle progressive velocity sensors are installed in body and underbody parts of the vehicle and are used in control scheme. Furthermore, IMU modules and suspension deflection sensors were used for validation of measurement part of the system. Semiactive Skyhook control algorithm, including on/off and smooth suspension MR damper control, was implemented in order to validate the control system. Quality of measurements is deteriorated by multiple factors including vehicle engine and shape of tires which was examined. Experimental results indicated better vibration suppression of vehicle body part for smooth Skyhook controller compared with passive soft and hard suspension. The presented semiactive suspension control system can be applied for complex vehicle dynamics analysis and control schemes dedicated to both the ride comfort and ride safety issues

    Optimal design of a quadratic parameter varying vehicle suspension system using contrast-based Fruit Fly Optimisation

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    In the UK, in 2014 almost fifty thousand motorists made claims about vehicle damages caused by potholes. Pothole damage mitigation has become so important that a number of car manufacturers have officially designated it as one of their priorities. The objective is to improve suspension shock performance without degrading road holding and ride comfort. In this study, it is shown that significant improvement in performance is achieved if a clipped quadratic parameter varying suspension is employed. Optimal design of the proposed system is challenging because of the multiple local minima causing global optimisation algorithms to get trapped at local minima, located far from the optimum solution. To this end an enhanced Fruit Fly Optimisation Algorithm โˆ’ based on a recent study on how well a fruit flyโ€™s tiny brain finds food โˆ’ was developed. The new algorithm is first evaluated using standard and nonstandard benchmark tests and then applied to the computationally expensive suspension design problem. The proposed algorithm is simple to use, robust and well suited for the solution of highly nonlinear problems. For the suspension design problem new insight is gained, leading to optimum damping profiles as a function of excitation level and rattle space velocity

    Design of LQG Controller for Active Suspension without Considering Road Input Signals

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    Preview-based techniques for vehicle suspension control: a state-of-the-art review

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    Abstract Automotive suspension systems are key to ride comfort and handling performance enhancement. In the last decades semi-active and active suspension configurations have been the focus of intensive automotive engineering research, and have been implemented by the industry. The recent advances in road profile measurement and estimation systems make road-preview-based suspension control a viable solution for production vehicles. Despite the availability of a significant body of papers on the topic, the literature lacks a comprehensive and up-to-date survey on the variety of proposed techniques for suspension control with road preview, and the comparison of their effectiveness. To cover the gap, this literature review deals with the research conducted over the past decades on the topic of semi-active and active suspension controllers with road preview. The main formulations are reported for each control category, and the respective features are critically analysed, together with the most relevant performance indicators. The paper also discusses the effect of the road preview time on the resulting system performance, and identifies control development trends

    Hybrid model predictive control of damping multi-mode switching damper for vehicle suspensions

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    This paper investigates the design and verification of a hybrid model predictive controller of a damping multi-mode switching damper for application in vehicle suspensions. Since the damping mode switches induce different modes of operation, the vehicle suspension system including this damper poses challenging hybrid control problem. To solve this problem, a novel approach to the modelling and controller design problem is proposed based on hybrid modelling and model predictive control techniques. The vehicle suspension system with the damping multi-mode switching damper is formulated as a mixed logical dynamical model comprising continuous and discrete system inputs. Based on this model, a constrained optimal control problem is solved to manage the switching sequences of the damping mode with respect to the suspension performance requirements. Numerical simulation results demonstrate the effectiveness of the proposed control methodology finally

    Development of Control Algorithm for Tractor Semi-Active Cabin Suspension based on Sliding Mode Control

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    ํ•™์œ„๋…ผ๋ฌธ(์„์‚ฌ) -- ์„œ์šธ๋Œ€ํ•™๊ต๋Œ€ํ•™์› : ๋†์—…์ƒ๋ช…๊ณผํ•™๋Œ€ํ•™ ๋ฐ”์ด์˜ค์‹œ์Šคํ…œ๊ณตํ•™๊ณผ, 2022.2. ๋ฐ•์˜์ค€.ํŠธ๋ž™ํ„ฐ๋Š” ๋ถˆ๊ท ์ผํ•œ ์ง€๋ฉด์„ ์ฃผํ–‰ํ•˜๋ฉฐ ๋ถ€ํ•˜๋ณ€๋™์ด ํฐ ๋†์ž‘์—…์— ์ฃผ๋กœ ์‚ฌ์šฉ๋œ๋‹ค. ์ด๋กœ ์ธํ•ด ๋ฐœ์ƒํ•˜๋Š” ํŠธ๋ž™ํ„ฐ์˜ ์Šน์ฐจ์ง„๋™์€ ์ž‘์—…์ž์˜ ๊ฑด๊ฐ•์— ์œ„ํ˜‘์ด ๋˜๊ณ  ์žˆ๋‹ค. ๋•Œ๋ฌธ์— ํŠธ๋ž™ํ„ฐ ์บ๋นˆ์˜ ์Šน์ฐจ์ง„๋™์„ ์ €๊ฐํ•  ์ˆ˜ ์žˆ๋Š” ์—ฌ๋Ÿฌ ๋ฐฉ์•ˆ๋“ค์ด ์ œ์•ˆ๋˜์—ˆ์œผ๋‚˜, ์•„์ง๋„ ๊ตญ์ œ์  ๊ธฐ์ค€๋Ÿ‰์„ ๋„˜๋Š” ์Šน์ฐจ์ง„๋™์ด ๋ฐœ์ƒํ•˜๊ณ  ์žˆ๋‹ค. ์Šน์ฐจ์ง„๋™์„ ํšจ๊ณผ์ ์œผ๋กœ ์ €๊ฐํ•˜๋Š” ๋ฐฉ์•ˆ์œผ๋กœ ์บ๋นˆ ํ˜„๊ฐ€์žฅ์น˜๊ฐ€ ์ฃผ๋ชฉ์„ ๋ฐ›๊ณ  ์žˆ๋‹ค. ์บ๋นˆ ํ˜„๊ฐ€์žฅ์น˜๋กœ ์‚ฌ์šฉ๋  ์ˆ˜ ์žˆ๋Š” ์ˆ˜๋™(passive), ๋ฐ˜๋Šฅ๋™(semi-active), ๋Šฅ๋™(active) ํ˜„๊ฐ€์žฅ์น˜ ์ค‘์—์„œ ๋™๋ ฅ ์†์‹ค์ด ์ ์œผ๋ฉด์„œ๋„ ์Šน์ฐจ์ง„๋™ ์ €๊ฐ ์„ฑ๋Šฅ์ด ๋›ฐ์–ด๋‚œ ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜์— ๋Œ€ํ•œ ์—ฐ๊ตฌ๋“ค์ด ์ˆ˜ํ–‰๋˜์–ด ์™”๋‹ค. ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜๋ฅผ ์ œ์–ดํ•˜๊ธฐ ์œ„ํ•œ ์—ฐ๊ตฌ๋“ค์€ ์Šน์šฉ์ฐจ๋ฅผ ๋Œ€์ƒ์œผ๋กœ ์ฃผ๋กœ ์ง„ํ–‰๋˜์—ˆ๋‹ค. ์Šค์นด์ดํ›…(skyhook), ์ตœ์ ์ œ์–ด, ํผ์ง€ ๋กœ์ง, ์Šฌ๋ผ์ด๋”ฉ ๋ชจ๋“œ ์ œ์–ด ๋“ฑ์˜ ๋‹ค์–‘ํ•œ ์ œ์–ด ๊ธฐ๋ฒ•์„ ํ†ตํ•ด ํšจ๊ณผ์ ์œผ๋กœ ์Šน์šฉ์ฐจ์˜ ์Šน์ฐจ์ง„๋™์„ ์ €๊ฐํ•œ ์—ฐ๊ตฌ ์‚ฌ๋ก€๊ฐ€ ๋‹ค์ˆ˜ ์ˆ˜ํ–‰๋˜์—ˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ํ˜„๊ฐ€์ƒ ์งˆ๋Ÿ‰์ด ํ˜„๊ฐ€ํ•˜ ์งˆ๋Ÿ‰๋ณด๋‹ค ํฐ ์Šน์šฉ์ฐจ๋Š” ์‹œ์Šคํ…œ ๊ตฌ์กฐ์ ์œผ๋กœ ํŠธ๋ž™ํ„ฐ์™€ ๋‹ค๋ฅด๊ธฐ ๋•Œ๋ฌธ์—, ํŠธ๋ž™ํ„ฐ ๊ตฌ์กฐ๋ฅผ ๊ณ ๋ คํ•œ ์—ฐ๊ตฌ๊ฐ€ ํ•„์š”ํ•œ ์‹ค์ •์ด๋‹ค. ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜๊ฐ€ ์žฅ์ฐฉ๋œ ํŠธ๋ž™ํ„ฐ๋ฅผ ๋Œ€์ƒ์œผ๋กœ ํ•œ ์—ฐ๊ตฌ๋Š” ์ตœ์ ์ œ์–ด ๊ธฐ๋ฒ•์„ ์ด์šฉํ•œ ์—ฐ๊ตฌ์— ๋จธ๋ฌผ๋Ÿฌ ์žˆ๋‹ค. ๊ทธ๋Ÿฌ๋‚˜ ์ตœ์ ์ œ์–ด ๊ธฐ๋ฒ•์€ ํŠธ๋ž™ํ„ฐ์˜ ๋ณต์žกํ•œ ์‹œ์Šคํ…œ์„ ์ •ํ™•ํ•˜๊ฒŒ ๊ตฌํ˜„ํ•˜์ง€ ๋ชปํ•จ์œผ๋กœ ์ธํ•ด ๋ฐœ์ƒํ•  ์ˆ˜ ์žˆ๋Š” ์‹œ์Šคํ…œ ๋ชจ๋ธ์˜ ๋ถˆํ™•์‹ค์„ฑ๊ณผ ์ž‘์—… ํ™˜๊ฒฝ์ด ์™ธ๋ž€์— ๋…ธ์ถœ๋˜๊ธฐ ์‰ฌ์šด ํ™˜๊ฒฝ์ด๋ผ๋Š” ์  ๋•Œ๋ฌธ์— ์ œ์–ด ์„ฑ๋Šฅ์ด ์ €ํ•˜๋  ์ˆ˜ ์žˆ๋‹ค. ๋”ฐ๋ผ์„œ ๋ณธ ์—ฐ๊ตฌ์—์„œ๋Š” ํŠธ๋ž™ํ„ฐ ๊ตฌ์กฐ๋ฅผ ๊ณ ๋ คํ•œ 1/2(half-car) ํŠธ๋ž™ํ„ฐ ๋™์—ญํ•™ ๋ชจ๋ธ์„ ๊ฐœ๋ฐœํ•˜๊ณ  ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜์˜ ํŠน์„ฑ๊ณผ ๋น„๋ก€์ œ์–ด๋ฐธ๋ธŒ ์ „๋ฅ˜์˜ ๋™ํŠน์„ฑ์„ ๊ตฌํ˜„ํ•˜์—ฌ ๋ชจ๋ธ์˜ ์ •ํ™•๋„๋ฅผ ๋†’์˜€๋‹ค. ๊ฐœ๋ฐœ๋œ ๋™์—ญํ•™ ๋ชจ๋ธ์„ ๋Œ€์ƒ์œผ๋กœ ๊ฐ•์ธ ์ œ์–ด ๊ธฐ๋ฒ•์ธ ์Šฌ๋ผ์ด๋”ฉ ๋ชจ๋“œ ์ œ์–ด๋ฅผ ์ด์šฉํ•˜์—ฌ ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜ ์ œ์–ด ์•Œ๊ณ ๋ฆฌ์ฆ˜์„ ๊ฐœ๋ฐœํ•˜๊ณ  ์‹œ๋ฎฌ๋ ˆ์ด์…˜ ๊ฒฐ๊ณผ๋ฅผ ๋น„๊ตํ•˜์—ฌ ์ œ์–ด ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ์„ฑ๋Šฅ์„ ํ‰๊ฐ€ํ•˜์˜€๋‹ค. ์‹œ๋ฎฌ๋ ˆ์ด์…˜ ๊ฒฐ๊ณผ์— ๋”ฐ๋ฅด๋ฉด ๊ณ ๋ฌด๋งˆ์šดํŠธ๋ฅผ ์žฅ์ฐฉํ•œ ํŠธ๋ž™ํ„ฐ์—์„œ ๋ฐœ์ƒํ•˜๋Š” ์บ๋นˆ ์ˆ˜์ง ๊ฐ€์†๋„๋ณด๋‹ค ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜๋ฅผ ์žฅ์ฐฉํ•œ ํŠธ๋ž™ํ„ฐ์—์„œ ๋ฐœ์ƒํ•˜๋Š” ์บ๋นˆ ์ˆ˜์ง ๊ฐ€์†๋„๊ฐ€ ์ž…๋ ฅ ๋…ธ๋ฉด ์กฐ๊ฑด์ด ๊ณ„๋‹จ ์ž…๋ ฅ์ธ ๊ฒฝ์šฐ 55% ๊ฐ์†Œํ•˜์˜€๊ณ , ISO8608 ๋…ธ๋ฉด ๋“ฑ๊ธ‰์ธ ๊ฒฝ์šฐ 41% ๊ฐ์†Œํ•˜๋Š” ๊ฒƒ์„ ํ™•์ธํ•˜์˜€๋‹ค. ๊ฐœ๋ฐœ๋œ ์ œ์–ด ์•Œ๊ณ ๋ฆฌ์ฆ˜์˜ ์‹ค์‹œ๊ฐ„์„ฑ์„ ๊ฒ€์ฆํ•˜๊ธฐ ์œ„ํ•˜์—ฌ ์ œ์–ด๊ธฐ๋ฅผ ๋Œ€์ƒ์œผ๋กœ Hardware-in-the-Loop ์‹œ๋ฎฌ๋ ˆ์ด์…˜์„ ์ง„ํ–‰ํ•˜์˜€๊ณ  ๋…ธ๋ฉด ์กฐ๊ฑด๊ณผ ์ƒ๊ด€์—†์ด ์บ๋นˆ ์ˆ˜์ง ๊ฐ€์†๋„์—์„œ ํฐ ๋ณ€ํ™”๊ฐ€ ๋‚˜ํƒ€๋‚˜์ง€ ์•Š์•„ ์‹ค์‹œ๊ฐ„์„ฑ์„ ๋งŒ์กฑํ•˜๋Š” ๊ฒƒ์„ ํ™•์ธํ•  ์ˆ˜ ์žˆ์—ˆ๋‹ค.Tractors travel on uneven ground and are mainly used for agricultural work with large load fluctuations. The resulting ride vibration of the tractor poses a threat to the health of the worker. Therefore, several studies have been done to reduce the ride vibration of the tractor cabin, but there are still ride vibrations that exceed the international standard. Cabin suspension is drawing attention as a way to effectively reduce ride vibrations. Among passive, semi-active, and active suspensions that can be used as cabin suspension, studies have been conducted on semi-active suspension because of its low power loss and excellent ride vibration reduction performance. Studies to control semi-active suspension were mainly conducted on passenger cars. There are many research cases that effectively reduce ride vibration of passenger car through various control techniques such as skyhook, optimal control, fuzzy logic, and sliding mode control. However, since tractor is systematically different from passenger car of which sprung mass is greater than the unsprung mass, research considering the tractor structure is needed. Research on tractors equipped with semi-active suspension remains in research using optimal control techniques. However, the optimal control technique may deteriorate control performance due to the uncertainty of the system parameter that may arise from the failure to accurately measure the complex system of the tractor and the fact that the working environment which is easily exposed to disturbance. Therefore, in this study, a half-car tractor dynamic model considering a tractor structure was developed, and the accuracy of the model was improved by reflecting the dynamic characteristics of the semi-active suspension and the proportional control valve current. And a semi-active suspension control algorithm was developed and applied to the dynamic model, using sliding mode control which is one of the robust control technique. The performance of the control algorithm was evaluated by comparing the simulation results. According to the simulation results, it was confirmed that the vertical acceleration of the cabin in the tractor equipped with the semi-active suspension decreased by 55% when the input road condition was a step input and decreased by 41% when the ISO8608 road level. And Hardware-in-the-Loop simulation was conducted on controllers to verify the real-time property of the developed control algorithm.1. ์„œ ๋ก  1 2. ์—ฐ๊ตฌ ๋ชฉ์  5 3. ๋ฌธํ—Œ ์—ฐ๊ตฌ 6 3.1. ํŠธ๋ž™ํ„ฐ ๋™์—ญํ•™ ๋ชจ๋ธ 6 3.2. ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜ ์ œ์–ด ์•Œ๊ณ ๋ฆฌ์ฆ˜ 7 4. 1/2 ํŠธ๋ž™ํ„ฐ ๋™์—ญํ•™ ๋ชจ๋ธ ๊ฐœ๋ฐœ 10 4.1. ํŠธ๋ž™ํ„ฐ ์ œ์› 11 4.2. ๊ณ ๋ฌด๋งˆ์šดํŠธ ํŠธ๋ž™ํ„ฐ ๋™์—ญํ•™ ๋ชจ๋ธ ๊ฐœ๋ฐœ 12 4.3. ํ˜„๊ฐ€์žฅ์น˜ ํŠธ๋ž™ํ„ฐ ๋™์—ญํ•™ ๋ชจ๋ธ ๊ฐœ๋ฐœ 21 4.3.1. ํ˜„๊ฐ€์žฅ์น˜ 1/2 ํŠธ๋ž™ํ„ฐ ๋™์—ญํ•™ ๋ชจ๋ธ 21 4.3.2. ์ˆ˜๋™ ๋ฐ ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜ ํŠน์„ฑ 30 4.3.3. ๋น„๋ก€์ œ์–ด๋ฐธ๋ธŒ ๋ชจ๋ธ 33 4.3.4. ํ˜„๊ฐ€์žฅ์น˜ ํŠธ๋ž™ํ„ฐ ๋™์—ญํ•™ ๋ชจ๋ธ ๊ฒ€์ฆ 36 5. ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜ ์ œ์–ด ์•Œ๊ณ ๋ฆฌ์ฆ˜ ๊ฐœ๋ฐœ 42 5.1. ๋น„๋ก€์ œ์–ด๋ฐธ๋ธŒ ์ „๋ฅ˜ ์ถ”์ข… ์•Œ๊ณ ๋ฆฌ์ฆ˜ 42 5.1.1. PI ์ œ์–ด๊ธฐ ์„ค๊ณ„ 42 5.1.2. ์™ธ๋ž€๊ด€์ธก๊ธฐ ์„ค๊ณ„ 43 5.1.3. ์™ธ๋ž€๊ด€์ธก๊ธฐ ๊ฐ•์ธ์„ฑ ํ‰๊ฐ€ 46 5.2. ์Šฌ๋ผ์ด๋”ฉ ๋ชจ๋“œ ์ œ์–ด ๊ธฐ๋ฐ˜ ๋ฐ˜๋Šฅ๋™ ํ˜„๊ฐ€์žฅ์น˜ ์ œ์–ด ์•Œ๊ณ ๋ฆฌ์ฆ˜ 48 6. ํŠธ๋ž™ํ„ฐ ์ œ์–ด ๋ชจ๋ธ ๋ฐ ์‹œ๋ฎฌ๋ ˆ์ด์…˜ 54 6.1. ํŠธ๋ž™ํ„ฐ ์ œ์–ด ๋ชจ๋ธ 54 6.2. Model-in-the-Loop ์‹œ๋ฎฌ๋ ˆ์ด์…˜ 58 6.2.1. ์ฃผํŒŒ์ˆ˜ ์˜์—ญ ๋ถ„์„ 58 6.2.2. ์‹œ๊ฐ„ ์˜์—ญ ๋ถ„์„ 60 6.3. Hardware-in-the-Loop ์‹œ๋ฎฌ๋ ˆ์ด์…˜ 69 6.3.1. Hardware-in-the-Loop ์‹œ๋ฎฌ๋ ˆ์ด์…˜ ์‹œ์Šคํ…œ ๊ตฌ์ถ• 69 6.3.2. Hardware-in-the-Loop ์‹œ๋ฎฌ๋ ˆ์ด์…˜ ๊ฒฐ๊ณผ 72 7. ๊ฒฐ๋ก  77 8. ์ฐธ๊ณ  ๋ฌธํ—Œ 79 9. ๋ถ€๋ก 85์„

    Optimal Design of Magnetorheological Dampers Constrained in a Specific Volume Using Response Surface Method

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    In recent years, semi-active magnetorheological (MR) and electrorheological (ER) fluid technology based devices and systems have been developed and successfully utilized in many applications as valves, shock absorbers, dampers and clutch/brake systems. These promising devices have the adaptivity of the fully active systems to accommodate varying external excitations while maintaining the reliability and fail-safe features of the passive systems. Compared with ER based devices or systems, MR based devices have recently received special attention due to their high performance with minimal power requirements. Moreover MR fluids have significantly higher yield strength and are less sensitive to contaminants and temperature compared with the ER fluids. The geometric optimal design of MR valves/dampers is an important issue to improve the damper performance, such as damping force, valve ratio and inductive time constant. Considering this, the primary purpose of this study is to establish a general design optimization methodology to optimally design singleโ€“coil annular MR valves constrained in a specific volume in MR damper. To accomplish this, first the damping force of MR damper has been modeled using Bingham plastic model. The magnetic circuit of MR damper has been analyzed using finite element method in ANSYS environment to obtain magnetic field intensity which can be subsequently used to obtain the yield stress of the MR fluid in the active volume where the magnetic flux crosses. Then the developed finite element model of the MR valve is effectively used to construct an approximate response function relating the magnetic field intensity to the identified design parameters in the selected design space using response surface method and design of experiment methodology. Using the derived approximate relation for the magnetic field intensity in the MR damper model, the design optimization problem has been formulated using gradient based nonlinear mathematical programming technique based on the Sequential Quadratic Programming (SQP) technique and also stochastic optimization technique based on the Genetic Algorithm (GA) to find optimal geometrical parameters of the MR valve in order to maximize the damping performance under given constrained volume. Finally a PID controller has been designed to evaluate the close-loop performance of the optimally designed MR damper in a quarter-car suspension model

    Performance measures and control laws for active and semi-active suspensions

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    This thesis concentrates on two competing performance requirements of general suspension systems: "smoothness" and tracking. The focus of the thesis is on real-time feedback controls which can be applied in microprocessors with relatively limited capacity. Evolutionary algorithms (EAs) are used as a tool in the investigation of a wide range of control algorithms. Jerk (the rate of change of acceleration) is used as the basis of the suspension comfort performance measure, and a nonlinear cost function is applied to tracking, which targets the travel limits of the suspension (termed the "rattlespace"). Tracking measures currently in use generally fail to explicitly refer to the working space width. This matter is analysed, showing that driver slowdown is a complicating factor. The test rig of the physical experiment is of the semi-active type. High performing semi-active controls are generally based on active controls. Thus active controls are also investigated in this thesis. By stiffening the suspension as it moves away from equilibrium it can be made to combine softness over smooth roads with the capacity to react to large bumps when needed. Electronic control produces a much greater range of possible responses than is possible with just rubber or neoprene bump stops. Electronic, real-time control can attempt to target a smooth chassis trajectory within the possible future limits of rattlespace. Two general methods are proposed and analysed: one that adjusts the suspension stiffening according to the current road state, and another that targets edge trajectories within the possible future movements of the rattlespace. Some of these controls performed very well. With further investigation, they may be developed into extremely high performance controls, especially because of their high adaptability to varying conditions. The problem of avoiding collisions with rattlespace limits is related to the problem of avoiding overshoot of a limit distance. It becomes apparent that the residual acceleration at the point of closest approach needs to be limited, otherwise instability results. This led to the search for controls that attain rest without overshooting the final rest position. It was found that the minimum jerk needed for a general minimum-time control that does not overshoot zero displacement is always the control with just one intermediate switch of control, instead of two switches that are generally needed. This was proven to be optimal, and because of its optimality it works consistently when applied as a closed-loop, real-time optimal control. This control deals with the most difficult part of the trajectory: the final, "docking" manoeuvre. The control proved to be robust in physical experiments and it may itself have a number of applications. Some heuristics have been developed here to account for stochastic movement of the rattlespace edges in suspension controls, and these have proven quite successful in numerical experiments. Semi-active suspensions have a limit on the forces they can apply (the passivity constraint), but clipped versions are known to produce uncomfortable jerk. One method developed in this thesis produces a vast improvement in semi-active controls in the numerical experiments
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